Embed Size (px)
Citation preview
TRANSPORT AND ROAD RESEARCH LABORATORY
Department of the Environment
SUPPLEMENTARY REPORT 108 UC
BUS ROUTE COSTING FOR PLANNING PURPOSES
by
Arthur Andersen & Co
Any views expressed in this Report are not necessarily those of the Transport and Road Research ~boratory or of any other division, of the Department of the Environment.
Prepared by Arthur Andersen & Co under contract to the Transport and Road Research Laboratory
Special Research Branch Transport Operations Department
Transport and Road Research Laboratory Crowthorne, Berkshire
1974
1. INTRODUCTION AND SUMMARY
Page
i.i Introduction 1.2 S1~mmary 1.3 Guide to reading the report
1 3 8
2. THE COST STRUCTURE
2.1 2.2 Form of the cost structure 2.3 Relation to other route costing work 2.4 Application to route costing 2.5 Management accounts for cost control
Requirements to be served by the cost structure
3. COMPONENTS OF THE COST STRUCTURE
Introduction Direct costs Variable overheads Fixed overheads Engineering costs - cleaning, maintenance and repairs
.3.1 3.2 3.3 3.4 3.5 servicing,
l l 14 18 18 19
20 20 23 28
33
4. THE CREW COST ELEMENT OF A BUS ROUTE COST
.
4.1 The need for the crew cost element to be related to time of day
4.2 Approach to estimating the crew cost element 4.3 The relationship between crew hours paid
for and bus hours operated 4.4 The direct cost of the crew hours required
to operate the total combination of bus hours required on a route
4.5 The direct cost of the crew hours associated with changes in the hours of bus service on a route in peak and offpeak periods
4.6 Interpretation of total and marginal direct crew costs
4.7 The direct cost of crew hours associated with blocks of service
4.8 Analysis of crew costs in MPTE 4.9 Consistency with other research 4.10 Conditions forapplication in MPTE 4.11 Application in other companies
DETERMINING ROUTE NET COSTS.
4o ho
h2
44
~h
hh
h5 48 51 55 55
/
5.1 General principles 5.2 Application to routes 5.3 Revenue estimation -methods application to MPTE 5.4 Cost determination - avoidable costs
57 6o 61 64
. PILOT APPLICATION IN MERSEYSIDE PASSENGER TRANSPORT EXECUTIVE
6.1 6.2 6.3
Objectives. Coverage of the pilot study Feasibility in the pilot study, and implications for general application
66 66
67
Ownership of the Transport Research Laboratory was transferred from the Department of Transport to a subsidiary of the Transport Research Foundation on 1 st April 1996.
This report has been reproduced by permission of the Controller of HMSO. Extracts from the text may be reproduced, except for commercial purposes, provided the source is acknowledged.
.
6.4 Results prepared for MPTE 6.5 Conclusions from the pilot study
EXAMPLES OF APPLICATION IN PARTICULAR PLANNING CONTEXTS
•8.
7.1 7.2
7.3
7.4
7.5
7.6 7.7
SOME
S~,mmary Effect of street closure and free travel off~eak on route i00
Estimating the net cost of providing service at some times of the week
Estimating the cost consequences of conversion to 0MO Cost consequences of alterationsto service frequency ~
Increasing fares during peak periods • Providing increased service in offpeak periods
FURTHER DE"qELOPMENTS OF BUS ROUTE COST INFORMATION
8.1 8.2 8.3
8.4
APPENDIX
APPENDIX
APPENDIX
Introduction Changes to evening service Stopping services short of the terminus (revenue effects)
Taking action in response to short-term trends
l: Participants in the study
2: Crew Costs: models andregression analyses
3: Definition of terms
ADDENDUM: Further analysis and application ofthe method
1. Introduction to Addendum 1.1 Purposes of tNis additional work • 1.2 Reasons for addendum format ' 1.3 Structure of the addendum
2. Addendum snmmary 2.1 Applicability of cost structure to other PTE's 2.2 Peak and offpeak crew costs: Selnea and
Greater Glasgow PTE 2.3 Weekday offpeak costs MPTE 2.4 Simplified method of analysis
. Peak 3.1 3.2 3.3
and offpeak crew costs Comparison between the three PTE's Method of analysis Conclusion
. Weekday offpeak costs in Merseyside PTE 4.i Analysis of buses' operation 4.2 Results of this analysis 4.3 Higher costs of evening duties
72 73 ̧
79
82
88
93
9 7 lOb 108
n o l l O
iii 112
113
l l b
121
28 "
128 128 128
Z29 • •
1 3 o ' 130
131 131 132
134 134 136 136
138 138 139 139
i
ADDENDUM: APPENDIX i:
ADDENDUM: APPENDIX 2 :
Some relevant features of the union agreements in Selnec and Greater Glasgow PTEs
Estimating peak and offpeak crew costs in other companies
145
149
(C) CROWN COPYRIGHT 1974
Extracts from the text may be reproduced, except for commercial purposes, provided the source is acknowledged.
CHAPTER 1
INTRODUCTION AND SUMMARY
i.i Introduction This study was commissloned by the Transport and
Road Research Laboratory (TRRL) following a survey
of bus industry research requirements in 1971, and particular interest
expressed by Merseyside Passenger Transport Executive (MPTE) in
participating in the study.
The main part of the work commenced in November 1973, and
fieldwork in MPTE was essentially completed in March 1974. Brief
discussions were held with other bus companies in April 1974 to
determine the extent to which the principlesand methods developed
might be applicable to them.
Aims of the study The study's aims have been to establish principles
and methods for classifying and structuring the
total costs of bus companies so that the costs of individual services
can be determined, and so that estimates of the cost of changes to
services can be made, on a sound economic basis which Will in Principle ,
if not in exact detail, be applicable in most bus companies. It is
envisaged that the outcome of the study will be used:
(a) for attributing costs to routes, both in Merseyside and
elsewhere, to help determine the extent to which they are
(b~
making or losing money.
for budgeting and planning purposes, by MPTE Operational,
Planning and Financiai Management.
(c) in modelling the cost structure of bus companies for
research purposes.
Particular interest centered on the question of the
differences between the costs of changes to peak services, and to
offpeak services.
It was decided that our work should be initially quite
independent of the work of the National Bus Company (NBC), and of the
Chartered Institute of Public Finance and Accountancy (CIPFA) and similar
bodies Working onRoute Costing. The intention was to provide an
independent approach to Route Costing, and to concentrate particularly
on crew costs at different times of the day and week. This is an area
on-which NBC are themselves working by methods which are different from
ours, but which share a common aim of achieving greater accuracy in
accounting for an important element of bus company costs.
Our approach comes to conclusions very similar in the main
to NBC's in ~ those areas in which our aims were the same. We have
expanded on their results in differentiating further between peak and off-
peak costs, and we have taken a slightly different view on the treatment
of some engineering costs, to relate them more closely to the peak/offpeak
differences. We are now in close touch with them and other interested
parties in taking the work forward.
2
1.2 Summary
Cost structure developed We have developed a structure of bus
company*costing which classifies each
operating cost of a bus company according to two criteria:
a) with which one of three measures of activity the cost is
most closely linked: bus hours operated; bus miles
operated; or number of buses operated at peak periods, and
b) the timescale over which changes to operations would result
in changes to costs: within a week or two; within a few
months; or only over a longer period and not as a direct
consequence of changes to individual services.
Following the classification of costs according to these
criteria, standard dnit costs are developed, per bus hour, bus mile,
and peak bus. For each measure Of activity (e.g. bus hour) a separate
unit cost is derived which applies over each of the three timescales.
These standard unit costs are then used to attribute total costs to
routes, and in estimating the costs of planned changes to services.
Basis for managementaccounts By defining categories of cost for
which standard unit costs can be
developed for planning and route costing purposes, the cost structure
would also provide a basis for management accounting systems which:
a) provide estimates for budgeting purposes, related
to the expected level of activity of the company and
its separate parts
* Whenever in this report we re fer to a bus " company", we mean any undertaking which runs bus services, acting as one operating unit - e.g., one NBC operating subsidiary, a PTE, or a municipal bus undertaking.
b) allow actual costs to be compared with standard costs
c) structure costs as direct, variable overhead, and
fixed overhead, and allow detailed reporting of
the reasons for variances betweenactual and
standard costs, by responsibility.
Peak/offpeak differences We have found evidence that additional bus
hours operated in peak periods cost substan-
tially more per hour than additional off peak bus hours.
iThe crew cost per additional peak bus hour is approximately
constant, and independent of the existing level or • proportion of peak
working, at least over the wide range observed in MPTE.
The crew cost per additional offpeak hour is also approximately
constant and independent of the existing peak level of service.
We cannot yet say whether crew costs incurred by additions to
offpeak service are the same at all times of day. Evening service and
midday service may have different costs. We found that in existing
MPTE schedules, evening duties appear relatively more expensive (by i0-
20%) per bus hour than other non-spreadover duties. (See addendum.)
We are told that a significant increase in evening work (or
"late turns") would be unpopular in MPTE. We are also told that some
evening work must be included in the duty mix, in order to provide a
satisfactory rotation of types of duty. Although these factors are
not at present reflected formally in penalty payments to compensate
for the unpopularity of evening work, they do illustrate the general
point that costs cannot be extrapolated for changes which go beyond
the range within which the union agreement provides an acceptable
form of payment for unpopular or inconvenient working hours.
4
We estimate that additional peak operation in MPTE would •
lead within a few months to cost increases of the order of • £4.70
per peak bus hour added, compared with an average cash fare revenue •
per peak bus hour of approximately £3.O0. Increases to offpeak
service would lead over the same time span to increases in cost
of the order of only £1.75 per offpeak bus hour, compared with the
average cash fare revenue*per offpeak bus hour of approximately
£2.75.
Reductions to service should lead to the same cost
reductions: about £4.70 per peak, and £1.75 per offpeak bus hour.
(Fixed costs are in all cases excluded from the figures given, which
are based on analysis of one week's operation in one MPTE garage.)
Part of the cost •difference between•peak and offpeak service • .
increases comes from the extra crew cost resulting from an increase
in spreadover working and penalty payments which increased scheduled •
peak working causes. The other part comes from the • need to provide • •
extra buses as peakservice levels are increased • , and the corresponding
increase in that part of engineering costs Which is associated with
each bus owned and operated, regardless of the amount of use it
receives.
The interpreter of these figures should bear in mind that cash fares in MPTE account for only about 87% of fare revenue. Other types of passengers are multi-trip and season ticket holders (accounting for the remaining 13% of fare revenue), who travel more in peak than offpeak periods, and old age pensioners, who can travel free in offpeak periods only.
5
Possible implications The figures indicate that at present, for the
one week's operation analysed at one MPTE
garage, revenue received from peak travellers is not covering the
costs of providing peak service, and that offpeak revenue is more than
covering costs. (In both cases, the costs referred to are costs
excluding fixed overheads.)
To the extent that wider considerations of public policy
make it desirable for fare revenue more closely to approximate to
the cost of providing services, this suggests two possibilities for
the bus operator to explore further:
m
n
Application to routes
stepsare required:
increasing offpeak service provided
charging higher fares during peak periods.
i•n order to apply Our methods to costing the
routes operated by a bus company, the following
(a) using Table 2.1' as a guide, classify each of the
company's costs according to their• relationship with
bus hours, bus miles, or peak buses operated, and
according to the timescale over which the costs
change following changes to service. Allow for any
cost increases anticipated in the period being planned.
(b) calculate bus hours, bus miles and peak buses for the
company as a whole, and for each route to be costed.
(c) if the mix of peak, offpeak and weekend work is similar
on all routes, and peak and offpeak crew cost differences
(d)
are not required, then calculate standard unit costs for
each timescale by dividing the cost in each classification
by the number of units of activity to which it relates-.
use the standard unit costs in conjunction with each
route's use of bus hours, bus miles and peak buses to
estimate the costs attributable to the route.
(e) if peak/offpeak cost differences are of fnterest, then a
more detailed analysis of crew costs will be necessary
The method by which we first •succeeded in doing this •
in MPTE is described in Chapter 4. The addendum
described a later development of a simpler method with
potentially wider application, which has beenpilot
tested in t hr~e PTEs. . .
Revenue analysis, the other• major aspect Of route cost and
revenue analysis, requires . the development of methods specific tO
each company's fare structure and systems of .fare collection. The
methods we applied in MPTE involved analysis of waybills for cash
fares, and a variety of special studies and surveys for other types
of revenue.
Examples of the application of these methods to some of
MPTE's services are given in this volume, showing summary information
for all routes operated from one garage, and detail information for
three routes. (Detail flor other routes was prepared for MPTE, but
is ~ot shown in this report.~
Examples are also given in Chapter 7 of the application
of route cost and revenue analysis methods to.a variety of bus
planning problems.
7
1.9 Guide to reading the report Some readers will wish to inform
themselves in full about all
aspects of our study, and will wish to read the report straight through.
For those with more particular purposes, the following guide may prove
helpful.
Obtaining an overview of the work For those (e.g., senior bus company
managers) wishing to obtain quickly
an overview of the cost structure which we have developed, and how it
can be applied to bus route cost and revenue analysis, we suggest reading
Chapters 2, 5 and 6.
Chapter 2 outlines the cost structure we have developed,
and gives general Principles for its application in other bus
companies. The problem of costing peak operations imposes particular
requirements on the costing structure. We describe our view on peak
costing, and the way in which the structure responds to the
requirements. Table 2.1 summarises the results of our application
of the structure to the costs of MPTE's operations, and indicates
therelative sizes of main cost elements and the way in which we
have treated them.
Chapter 5 describes how the structure of costs is applied
to costing individual routes.
Chapter 6 gives examples of the sorts of information our
methods can provide. We applied the methods to the routes operated
out of one of MPTE's garages for one fairly typical week in late
1973. Tables 6.1 and 6.2 show respectively a cost and revenue summary
for all these routes, and details for one of the routes.
Applying the results in other companies For those wishing to find
out more about how to apply
the results in other bus companies, we suggest that they read Chapters
3 and 7 in addition to the Overview chapters 2, 5 and 6.
Chapter 3 gives more details of our treatment of cost
elements in the costing structure, and lists the cost elements which
we included in each celi of Table 2.1 for MPTE. It also discusses ~
considerations to be borne in mind when analysing engineeringc0sts
Chapter 7 illustrates some applications of the costing
methods and results to particular planning decisions.
Peak/offpeak crew cost differences We found in MPTE substantial
differences in the effective cost
of crew time per bus hour of operation for additions or reductions to
peak, offpeak and weekend services. Those who need to consider the
extent to which these results can be applied more generally should read ~
Chapter 4, Appendix 2, and the addendum.
Chapter 4 describes the results we obtained for MPTE:
consistently higher effective crew costsper bus hour of additions to
operation in peak periods, independent of the existing level and
proportion of peak operation over a wide range, and higher Costs also
~k
9
at weekends. It also describes the conditions under which we expect
that the results can be validly applied.
Appendix 2 gives technical details of analyses we performed
to identify these cost differences, and the addendum describes a
simpler method of analysis.
Limitations of route costin~ methods Route cost and revenue analyses
of the type we have developed
are valuable for many planning decisions, but are not adequate for
some. Those who need to know about some types of decision for which
further analyses will be required should read Chapter 8.
l0
CHAPTER 2
THE COST STRUCTURE
2.1 Requirements to be served by the cost structure
cost structure needs to be:
In order to meet the aims
identified in Chapter l, the
a)
b)
c)
d)
closely related to the way in which changes in the activities involved in operating bus services lead to changes in the costs of operation in the medium term.
useful for broad planning purposes with a planning timescale of, say, three months to one or two years, and hence not dependent on particular day-to-day features of operations.
accurate, but not necessarily to a greater extent thanthe accuracy obtainable for crew costs, and consistent with the intended use for broad planning purposes.
simple, both for a bus company to develop, and to apply in practice. Simplicity is highly desirable, and to be aimed for so far as is consistent with the other needs.
In order to develop a cost structure which meets these
needs, we found it essential to consider first the cost differences
which exist between peak, offpeak (weekday), and weekend services.
Because the proportion of peak to offpeak and weekend work may vary
considerably between routes, and because peak working is significantly
more expensive than offpeak, these cost differences are important for
accurate route costing, and we could make little progress in route
costing until these issues had been addressed.
ll
Costing peak operations Two main elements make the costs of peak
and offpeak working different:
- the costs of providing buses
- the costs of providing crews
to meet any given mixture of peak and offpeak requirements.
Provision of buses There are a set of costs which we call "ownership"
costs* which arise because a bus is owned, almost
regardless of its usage. The total amount of these costs is determined
by the peak busrequirement, and will not be significantly affected by
offpeak usage. The need to own the bus arises because it has been
decided to provide a certain level of peak operation in response to
higher demand at certain times of day. Changes in the level of peak
provision of buses will lead to changes in total ownership costs, /
which are attributable therefore to peak period changes. Peak
addition of a bus incurs one extra unit of ownership cost; offpeak
addition of a bus adds nothing to the ownership cost, provided that
for the company as a whole the offpea k level of service remains below
that at the peaks.
Crew costs ~ The effective crew cost incurred to provide an extra hour's
operation during the peak period is very significantly
higher in MPTE than the effective crew cost of an extra offpeak bus
hour, mainly because extra work in the peak requires increased spread-
over working, and its associated penalty payments.
Once the decision has been taken to acquire or retain a bus for operational use, many types of cost are automatically incurred over the service lifetime of the bus. We define these as the "ownership" costs of the bus. They are those costs of owning and operating the bus which are not significantly affected by its usage. They comprise licensing, capital costs, and certain engineering costs. Because the number of buses owned and operated is a function of peak requirements~ the Company's total ownership costs (in the medium to long-termJ will vary in proportion to the number of buses operated at peak periods.
12
We have developed a simple relationship between total weekday
crew costs and the amounts of peak and offpeak working, in such a form
that we can estimate not only total crew costs, but also the cost
effect of changes to peak or to offpeak working.
Another requirement of the crew costing method, not connected
with the peak/offpeak distinction, is that account must also be taken
of any major differences in rates of pay for different types of
operation (e.g., in MPTE, different premium rates apply for single-
deck and double-deck one-man driver/operators, and the extra cost of s
conductor on two-man buses must be allowed for).
13
2.2 Form of the cost structure In the cost structure, we show the
costs which may be expected to
change over a timescale of three months to one or two years as a
result of changes made to the bus company's operations. Furthermore,
costs which change Over a shorter period than three months are
separately identified. This is done in order to assist management
with some shorter-term planning, and to help clarify the distinction
between short and medium term cost effects of changes.
To enable route costing to be done, we find it necessary
first to understand the structure of operating costs for the bus
company as a whole. The company cost structure can be used to assist
other decisions in addition to route-related decisions - for example,
to help assess the merits of increasing offpeak working, or pricing
differentially for peak services. These aspects are taken up in
Chapter 7, together with examples of decisions related to specific
route s.
The cost structure has two aspects. In one aspect of the
structure, we classify costs according to the measure of activity to
which they are most closely linked.
In the other aspect, we classify costs by the timescale over
which changes to operations may be expected to work through into
changes in the corresponding costs.
Measures of activity For costing purposes, all bus services can be
characterised by three measures of activity:
* Definitions of each of the "measures" will be found in Appendix 3.
14
- Bus hours operated - Bus miles operated
- Number of buses operated at the height of the peak period.
Within a bus company, we identify "pools" of cost which we take
to be non-overlapping, each of which then varies in size directly
with only one of these three measures. The cost of operating a
service then has three components, which add together: the bus-
hour-related component, the bus-mile-related component, and the
peak-bus-related component. Service changes which alter only one
component (e.g. adding extra layover time to bus hours) change only
the cost of that component. Service changes which affect more than
one component produce corresponding changes in the cost of each•
component affected.
In practice, we find it necessary to further divide the
bus hour component by time of day and week because different
effective crew costs per hour are observed in different periods
(in MPTE, into weekday (peak), weekday (offpeak), Saturday morning,
and other weekend hours).
i
Timescale of the cost impact of chan~es We also characterise costs according to the
timescale over which they may be expected to
change to a new level, following changes to operations, as:
- direct costs : change within a week or two
- variable overheads : change within a few months
fixed overheads costs which do not vary over a wide range of levels of operation, or which can only be changed in relatively large increments.
15
CD
0
oo:
P c~
0
~0 u~
. . . . i
0 0
o o ~ , _ ~ +~
, - 1 0 " . 1 " O U'~ o'~ " . t C~ O I ~ ¢
i
m o~ , ~
i~ ¢-t
~ ,~ ~ ~ o ,
0 ~ ~ .H ",~ 0 "~
' O ~ O r ~ ~ f ~
2, "g oo~
o o ~ ~ 4 ~ r ._)
!
! z
• • I °
. . . . . I •
0 ~ '-40 0 I ~> $
o . ~
~,~ o~ ~o
~0 ~
..~@~
,0~ ~
~ o
N m
. ~ , , ~
-g .~ ~ = . . . .
~ ~.~,'= . ~ - ~
N N g o
~ o . ~
~ ~ 0 0
I - • •
I ~D,--I
I •
I
i
i i z
o
I
|
~, .o
~1 .,- i x
o
,-4 ~
o
z
g o
u~
o
1:o
o
o o o
-o o
u'x
c,x
o ~
o
o g
o
o
o
-o
16
Cost classification matrix In Table 2.1 (to which reference should
be made in the rest of this chapter and
in Chapter 3) we have classified each of a bus company's major
operational cost elements into one of nine cells. Rows in the Table
correspond to the "measures of activity" classification• (hours/miles/
peak buses) and columns to the "timescale" classification (direct
costs/variable overhead/fixed overhead). Each cost of the bus company
is included once and only once in the table, so that all costs are
accounted for, and total company costs are represented completely.
Figures in the Table show the percentage of total costs accounted for
by each item, for the operation of one of MPTE's garages over one week
in late 1973.
Each cost element is classified into the appropriate ~ell
in the table by considering:
a)
•b)
with which measure of activity is the cost element most closely linked
over what timescale can the cost element be expected to settle to a new level.
The classification adopted in Table 2.1 represents our
best judgement at present as to the links between levels of activity
and consequent costs in general; but application of the classifi-
cation in particular companies may require some regrouping. We
would expect such regrouping to be guided by the considerations of
the previous paragraph.
17
2.3 Relation to other route costing work The categories adopted
correspond in the main
with those adopted independently by the National Bus Company;
important differences are that we distinguish crew costs by time
period (peak, offpeak etc.), and we also treat some engineering
costs differently.
2.4 Application to route costing Two major steps are required for
route costing. First, a set of
standard unit costs are derived for each of the cells shown in Table
2.1. Costs of the company are sorted into the pools of cost
corresponding to bus hours, bus miles, peak buses; and into direct
COSTS, variable overheads, and fixed overheads. For planning purposes,
known or anticipated cost increases should be allowed for, and then
standard costs per unit of activity are calculated for the company as
a whole, or for selected cost centres only. (Crew costs require a
more complicated form of calculation, described in Chapter 4.)
Second, to apply these costs to services, each service's
use of resources is calculated: bus hours operated (by time of day
and week), bus miles operated, and peak bus requirement. These
resources are then costed at the relevant standard cost per unit, and
the total gives the cost of the service. Examples are given in
Chapters 6 and 7.
Revenue is estimated separately. We have not found it
possible to develop general methods for revenue analysis, but Chapter 5
describes the methods we were able to apply in MPTE.
18
2.5 Management accounts for cost control Table 2.1 could also be
used as a basis for the
development of management accounts. These would serve two purposes
for route costing and planning, in addition to their other management
control information functions. They could be used:
a) to provide regularly the information necessary to update the standard unit costs needed for planning purposes
b) to check that actual cost changes following changes to service are being kept in line with those planned,i and as estimated by the route working system. This is particularly important for variable overheads.
Separate cost centres could be set up for sub-units of the company,
to enable cost variances to be more closely identified, The sub-
units must be such that both actual costs, and operating data, can
be collected relating to the same sub-units (e.g., garage)
19
CHAPTER 3
COMPONENTS OF THE COST STRUCTURE
3.1 Introduction In sections 3.2 to 3.4, each cost
classification cell of the costing matrix
(Table 2.1) is discussed in turn, column by column. Direct
costs are covered in section 3.2, variable overheads in .
section 3.3, and fixed overheads in section 3.4. For each cell,
we first specify the principles to be applied for classifying
costs into that cell, then list the cost elements we included
for MPTE. We go on where necessary to describe further the
cost elements in the cell, and give some examples, to help
clarify potential difficulties.
Section 3.5 describes in more detail some of the
assumptions made in placing engineering costs into the various
classifications.
3.2 Direct costs The direct costs are those costs of bus
operation which would change to a new
level within a week or two of changes being made to scheduled
operations. The direct costs related to each type of activity
are discussed in turn (refer to the first column of costs in
Table 2.1).
Bus hour related direct costs Any payments which are directly
linked with bus and crews' hours
of operation "on the road" are regarded as falling in this cell.
20
Included in this cell are:
Standard payment for a scheduled duty worked
Spreadover penalties
Other penalty payments applying to scheduled•hours worked - e.g. early start, late finish; night work; premiums for Saturday, Sunday and public • holiday working.
Payments for scheduled standby duty only
Premium payments for scheduled overtime •only • J
Any payments which are made "per man employed" rather
than as a function of hours worked,~ are not regarded as direct costs,
but as variable overheads. The premium part of payment for
unscheduled overtime is also regarded as a variable overhead,-• as •it
depends on the level of staff shortage for•the garage as a whole,
whereas scheduled overtime premium payments are specific to a duty
sheet.
A change in operations which • results in one or more crewmen • •
b e c o m i n g " s p a r e " w i l l s h i f t an e l e m e n t o f c o s t f r o m t h e " d i r e c t C o s t " • . ~ . " .
to the "variable overhead" column of Table 2.1, without immediately
c h a n g i n g t h e c o m p a n y ' s t o t a l p a y m e n t s f o r c r e w s . I t i s f o r r e a s o n s
such as this that it is important to have effective means of reporting
and controlling overhead costs, so that management steps can be taken •
to keep actual overhead unit costs close to those planned. If this
is not done, the unit costs will change, and tend to reduce the value
of the costing system.
Obtaining the total direct crew costs is fairly straight-
forward. It is based on an analysis of payroll records, and garage
logs of duties worked.
21
In order to separate the direct crew cost effects of
changes to peak, offpeak, and weekend working (which as shown
later can vary over a range of nearly 2:1), and by type of
operation (SDOM0, DDOMO, 2-man crew) a more complex form of
analysis is required. This is described in Chapter 4t and in the
addendum.
Bus mile related direct costs
as falling in this cell.
Any costs which are directly linked
to bus miles operated are regarded
Included are costs of:
- Fuel for buses
- Fuel tax rebates (credits)
- Tyres for buses
- Any other payments determined by a per-mile rate (e.g., third party insurance and hire of buses)
If information is available from special studies or
for separate cost centres, it may be possible to establish
different fuel consumption and tyre wear costs by cost centre,
or at different times of day, or by type of terrain, or by
type of vehicle.
Peak bus related direct costs
peak buses operated.
No significant direct costs arise
as a function of the number of
Costs which are higher in peak periods as a function
of the number of peak buses operated are included elsewhere as
variable overheads.
22
3.3 Variable overheads By "variable overheads" we mean those
costs of bus operation which would change
to a new level within a few months of changes being made to
scheduled operations, provided that management is aware of the
implications of the changes, and acts to ensure that those
overhead costs which can be reduced, are reduced (for service
cuts; and vice versa for service increases) in proportion to the
change in the relevant measure of the level of activity. Management
accounts systems should provide information which enable this
control to be exercised.
Bus hour related variable overheads Under this heading are included
all other payroll costs of crew
(i.e., all crew payroll costs not included as direct costs) and all ~
costs which are in the medium term linked to operating staff numbers,
which are in turn linked to bus hours.
Included are:
Crew
All NHI, graduated pension and superannuation costs
All bonuses paid as amounts per man or per week, or otherwise unrelated to dutyhours worked e.g., attendance bonus, long service bonus, OM0 savings bonus.
Payments for crew time : on holiday sick spare (but not on
scheduled standby) training any other time not on
working duty
The premium part of payment for rest day or other unscheduled overtime working
Redundancy or severance payments
Any other crew payroll costs which are not directly related to scheduled hours worked.
23
Crew supervision and training
Payroll costs of: traffic supervision : garage administration : training staff
Operating costs of training vehicles
Other
Uniforms
Staff bus
Miscellaneous
Scheduling variance
All items on this list except the last are fairly straight-
forward, both to identify, and to classify into this cell of the
table. All these items are likely to vary in the medium-term with
crew numbers employed, and hence with bus hours worked.
"Scheduling variance" is explained in more detail in
Chapter 4. Briefly, it relates to the difference between the actual
crew (direct) costs, and the "standard cost" computed for this
garage's mix of peak, offpeak, and weekend working, using the
coefficients of Table 4.1.
Bus mile related variable overheads In this cell are included all
costs which are found to be
most closely linked in the medium term with bus miles operated, but
which are not directly related to bus miles.
24
Included for MPTE are:
At garages
- Cost of materials consumed for:
. routine maintenance of buses
. cleaning buses
• servicing buses
At works
- Payroll (excluding supervision) and material costs for:
. unit changes
. unit reconditioning
• other major mechanical and electrical repairs
. accident repairs
Costs of cleaning, servicing and maintenance of vehicles
other than buses are fixed overheads, as far as route costing is
concerned, and are included under that heading.
Materials used in the annual certificate of fitness dock
(which in MPTE is performed in the main at garages) are not
significantly related to miles operated, and are not included here.
Engineering labour costs at garages were found to be much
more closely related to bus numbers than to miles operated: the
labour cost is largely for maintenance inspection, which is performed
regularly; and for cleaning and servicing, both also performed at set
intervals, rather ~ than as a function of usage. They are therefore
regarded as ownership costs, and treated as peak bus related variable
overheads (see following paragraphs).
25
Peak bus related variable overheads All the "ownership" costs of the
bus fleet are included in this
cell. Ownership costs are those costs which arise over the service
lifetime of the bus, because it is owned, but which are not
significantly affected by the usage it receives. The costs would no
longer be incurred for individual buses if they weresold, and
corresponding staff levels etc. altered in proportion.
Included for MPTE are costs of:
Bus depreciation
Bus licensing
Garage payroll costs (excluding engineering supervision and administration) of staff employed on cleaning, servicing, routine maintenance, and other maintenance and repair of buses done at garages.
Materials used at garage for annual certificate of fitness work.
Works engineering payroll (excluding supervision and administration) and material costs for:
bodywork reconditioning (except accident repairs)
annual (if done at works) and 7,13 year etc. DoE certi- fication work.
26
As an approximation for the capital element of the cost of
owning a bus, depreciation is treated as a peak-bus related variable
overhead. More detailed information, if available, could be used for
a decision on disposal or acquisition of buses, either considering a
full discounted cash flow calculation or distinguishing between
classes of bus: older buses may be fully depreciated •already. Not
enough difference in cost is observed for new buses in MPTE between
single and double deck to make the distinction financially important
for planning.
Bus licensing costs are clearly proportional to the number
of peak buses operated, after allowing for operational reserves. Any
costs of buses owned, but not licensed, should be treated as fixed
overheads. These buses are not part of the operational fleet.
In MPTE, cleaning, servicing, and routine maintenance are
performed at garages, and the policy is to carry these out St regular
intervals. For MPTE, therefore, the payroll cost •of these operations:
forms part of the "ownership" costs of the bus. (See section 3.5 •for .•
a discussion of alternative ways of treating these costs.)
The remaining ownership costs arise out of functions which
are required at regular intervals, either legally or as a function of
the passage of time.
27
3.4 Fixed overheads By fixed overheads, we mean costs which are
fixed over a period of at least a year, and
which fall into at least one of these categories:
costs which are not affected by changes to any
of the measures of level of activity (bus hours,
bus miles, or number of peak buses) over a wide
range of changes from the present situation
b) costs which can only be changed in relatively
large increments, and by considered management
decision.
External changes may affect fixed costs - changes in rent
and rates, for example - and known or prospective Changes must be
consideredin estimating future levels of fixed costs.
For management control purposes, and possibly in justifying
subsidies, it may be important to ensure that each operating unit (be
it a garage, a type of service, or a route) makes a proportionate
contribution towards paying these fixed overheads.
The means of determining a "proportionate contribution"
must in essence be somewhat arbitrary - by definition, fixed
overheads do not vary in the medium term with any of the measures of
level of activity. One criterion for making the apportionment is to
28
take a view about the likely long-term relationship between
fixed overheads and the overall "size" of the undertaking.
We favour pro-rating most fixed overheads on the
basis of bus hours, on the hypothesis that bus hours are the
principal determinant of crew numbers, and most overheads will
in the long term be approximately proportional to crew numbers.
(A study* in 1•969/70 showed no apparent scale economies in bus
transport in Britain for "management and general expenses",
and tends to support this view.)
Some fixed overheads however are more closely related
to bus numbers - garage size, and hence rates (and rent, if paid),
depreciation of garage buildings and equipment, and engineering
• supervision, both at garages and at central works. These are
therefore pro-rated on •the basis of peak bus numbers.
It is important to emphasise again that since fixed
overheads by definition do not change as a function of changes to
levels of activity (in the medium term), they should not be
included when costing changes to activity levels, unless the
changes are so large as to cause a significant increment in
"fixed" costs (e.g., opening or closing a whole garage). The use
of "fixed overhead cost per unit of activity" is confined t•0 two
purposes:
a) determining which services are contributing less
than a proportionate share towards covering fixed
overheads.
*Lee, N. and I. Steedman "Economies of Scale in Bus Transport: Britain" J. of Transport Economics and Policy. Vol. IV, no 1. January, 1970.
29
b) determining the subsidy required to cover the
direct, variable overhead and fixed overhead
costs of operation of particular services.
In connection with the last point, it should be noted that
we do not wish to prejudge the question of whether a subsidy should,
or should not, coven a contribution to fixed overhead.
In Merseyside PTE, responsibility for fixed overheads
arises at three levels, corresponding to MPTE's organisational
structure. We have distinguished these levels in Tsble 2.1, for
clarity, but not all bus companies will have this distinction.
Bus hour related fixed overheads. In this cell are included all costs
which meet the criteria for being
treated as fixed costs, and which may be expected in the long term
to vary in general with the number of operating staff employed, and
hence most closely with bus hours operated.
Included for MPTE are:
At g a r age
"#r
Meat, light and power
Miscellaneous administration costs (excluding engineering supervision and administration payrolls)
3O
At division
- Administration payroll
- .Divisional Inspectors" payroll
- Welfare and medical benefits (a divisional • •
responsibility• in MPTE) L ~
Executlve-wide A!i headquarters costs.except non-busdepreclationp
-and englneeringmanagement. (BUsdepreclatlon is
a variable overhead for route Costing purposes, and other
deprec'iation is treated as:a peak bus related fixed overheads).
Included for MFTE are:
- Executive, managerial, and administrative payrolls Incurred by H.Q.
- Heat, light and power for H.Q, fsnctlons
- General supplies, and bought-ln services
• - Publicity materials and bought in services
- All other:H.Q, costs except as noted above
- Loan interest (loans are for non-specific p u r p o s e s .) . ~ '
• - ' O p e r a t i n g c o s t s o f . a l l n o n ' b u s v e h i c l e s . . . "
Peak bus related fixed overheads In this cell areInclude d al!i ~
. . . . costs which •meet the criteria for
being treated as fixed costs, and which may be expected in the long
term to vary in•general with the number of buses owned and operated,
and hence with the•number of-buses in use at the peak.
Included for MPTE are:
At garage
- Rates (and rent if paid)
Engineering supervision and administration payrolls (including. stores clerks, storemen, etc.)
31
Executive-wide
. Non-bus depreciation
- Central works management and administration
- Chlef Technical Officer and his section.
• . . ... . .
J
32
3.5 Engineering costs - cleaning, servicing, maintenance and repairs The central difficulty
in attributing ~
engineering costs to the operation of particular services arises from
a lack of knowledge about the relationship between "usage" of buses
(however measured) and engineering cost components.
We have had to make certain assumptions in our treatment
of engineering costs in order to separate out costs which may be
expected to behave differently with changes in levels of activity,
It was not possible to obtain information within the scope of this
study which would enable the validity of all the assumptions to be
tested (although some were). The assumptions we made aredescrlbed
in this section, so that readers may Judge for themseives the ~
reasonableness of the untested assumptions~ and In order to provlde
a framework for further development of e~ngineering costing systems
for planning purposes. ~
Classification of englneering costs We have classified the types
of Costs involved aCCOrding
to the way in which the need for them is determined. We divide
engineering costs (i.e. costs Of all operations which in MPTE
are the responsibility of the engineering function - cleaning,
servicing, maintenance and repairs into two major groups:
x
33
those which arise as a function of elapsed time, given that a bus is owned (bus "ownership" costs)
those which arise as a function of the usage a bus receives.
Within the first group, (elapsed time related) the operation giving
rise to a cost may be:
legally required at regular intervals (annual, 7,13 year etc. certificate of fitness work)
required at regular intervals for operational reasons (daily servicing ~- refuelling, topping up with oil, water etc., tyre and other inspection checks)
occasioned by the passage of time (repairs to bodywork for damage due to deterioration, corrosion etc.)
Within the second group (usage related) there are costs of operations
which are:
directly related to the usage the bus has received (maintenance and repair materials; costs of "unit changes" when major units - mainly transmission and suspension components - are exchanged; the cost of reconditioning exchanged units; and accident damage repairs).
indirectly related to usage, via engineering policy decisions which might change if there were a major change in the level or mix of measures of activity (examples include cleaning, for which MPTE's policy is to clean 3 times per week plus an internal "soap wash" every two weeks; and the labour cost component of routine maintenance - buses are examined and maintenance work is done as necessary, every two weeks).
This classification is illustrated in Table 3.1.
34
TABLE 3.1
CLASSIFICATION OF ENGINEERING COSTS
Attribution of cost based on:
Incurring of cost depends on:
ELAPSED TIME:
Legally required
Operationally necessary
Passage of time
USAGE:
Subject to management•policy (performed at regular intervals
Subject to need
OWNERSHIP COSTS
peak buses
Labour and materials costs of DoE certificate of fitness (every 1,7,13 etc. years)
daily servicing
bodywork reconditioning (excluding accident repairs)
cleaning
routine maintenance (labour only)
USAGE-RELATED COSTS
bus hours bus miles
engineering materials used at garages for routine work
unit changes
unit repairs and reconditioning
accident repairs
35
Attribution of engineering costs - principles We classify all of the first
group of costs (elapsed time
dependent) as ownership costs. They are therefore attributed to
services on the basis of peak buses used.
Costs which are incurred because of usage, but which
arise in ways not subject to management policy, are attributed
on the basis of bus miles operated.
The difficulty i n principle arises with the middle group
of costs in Table 3.1 - those which may indirectly be related to
usage, but which at present arise as a function of elapsed time
because of management policy which requires cleaning, and routine
maintenance at garages, to be performed at regular intervals.
Should they be treated as ownership costs, and therefore attributed
on a peak bus basis, or should they be attributed on the basis of
bus miles operated? The alternative we have adopted is shown by
the location given in the table to each cost element: possible
alternatives are indicated by dotted lines and question marks.
We have taken the view that in MPTE at least, these costs
should be classified as ownership costs, and hence attributed on a
peak bus basis. We say this because our discussions with management
36
lead us to believe that there will continue to be reasons in MPTE for
performing maintenance inspections and cleaning operations at regular
intervals (even though the interval migh t chang@ if significant
changes in usage took place). This means that a bus, once owned, will
be subjected to regular inspection and maintenance, and as we have
argued before, the requirement for ownership arises from peak demand.
An alternative view could be adopted in other companies,
depending on their cleaning and maintenance policy, although our
discussions with three other companies have not indicated a need to
alter our view for their mode of operations.
Attribution of engineering costs - practical difficulties Cost records are not kept in
summary form in MPTE in a
manner which enables the cost elements of Table 3.1 to be directly
and separately identified. In order to estimate these costs, we made
assumptions based in part on analyses we performed, and in part on
discussions with engineering management. We now describe these
assumotions.
Routine cleaning, servicing and maintenance costs Costs of labour for routine
maintenance at garages vary most
closely with number of buses operated at peak periods; our analysis
of cost data by garage indicated a generally linear increase in cost
with the number of buses (because these activities are performed, by
policy, at regular intervals), but with a substantial fixed cost
37
component (effectively the engineering supervision and
administration costs at each garage). We used the results
of our analysis to estimate the fixed cost element (shown in
Table 2.1 as a garage level, peak bus based, fixed overhead),
and treated the remainder of the actual garage engineering
labour costs as peak bus based variable overhead.
Engineering materials used at garages are most closely
related to bus miles operated by that garage; our analyses
again showed a linear increase in cost (but this time varying
not number of buses) with a significant fixed with bus miles,
element per garage. We have estimated the amount of the fixed
element from the analyses, and assumed that it is related in the
main to the materials required at garages for the annual
certificate of fitness work performed there.
Other engineering costs We have had to estimate the costs of
each other engineering activity from
the total costs incurred at the works coupled with judgements
by senior engineering personnel about the fraction of those costs
which relate to each of the remaining cost elements shown in
Table 3.1. We supplemented these judgements where possible by
brief ad hoc analyses. This was rendered necessary by limitations
on the time available to us within the scope of the study, but
we do not believe that is has introduced any serious errors in
the resulting unit costs derived from Table 2.1.
38
The accounts do show separately the costs of engineering
management and administrative costs at the works, and we have used
those figures for Table 2.1, in the peak bus based, fixed overhead
cell.
39
CHAPTER 4
THE CREW COST ELEMENT OF A BUS ROUTE COST
4.1 The need for the crew cost element to be related to time of day Crew payroll forms an
important part of bus
company costs -- about 37% of the total in MPTE, and 52% of costs
excluding fixed overhead. Costs which are directly affected by
schedule changes (direct crew costs) constitute 27% of MPTE's total
costs and 38% of costs excluding fixed overheads (see Table 2.1.).
Direct crew costs vary significantly between schedules having the
same content of bus hours worked, depending on the proportion of
peak, offpeak and weekend work in the schedule. Different routes
can have significantly different relative amounts of work in the
different time periods of weekday peak and offpeak, and weekend.
Accurate route costing should therefore take account of
the amounts of working in each time period.
4.2 Approach to estimating the crew cost element The NBC cost
system which
allocates bus crew costs to routes on a time basis for each type of
operation by cost centres does not specifically differentiate between
'peak' and 'offpeak' NBC recognised that this was an area requiring
f~rther research to enable the initial system to be further refined in
due course. A line of approach NBC is testing is that of costing
various alternative sets of schedules using crew computer scheduling
4O
techniques. The behaviour of costs under various alternative levels
and lengths of 'peak' is analysed to test the changing crew costs at
each cost centre brought about by the changes in schedules, and from
this to see whether a relationship can be established and a cost
model developed.
We have taken an approach which is different from NBC's.
Our approach depends on statistical analysis of data relating to
existing schedules, and also avoids, in general, the need for the
scheduling of proposed changes in order to determine their effect on cost.
The approach depends on being able to know how a change in
the number of bus hours in a period of the day affects, on average,
the number of crew hours that have to be paid for.
To discover whether there is a statistical relationship
between crew hours paid for and bus hours operated which is present
after the various procedures of the schedules have been worked through,
we need data to be available which covers a wide range of mixtures of
work in different periods of the day. Furthermore, we need the different
mixtures of work to have been performed by different groups of men, all
subject to the same union agreement, but without rotation of the
mixtures of work through any of the groups of men. This last requirement
is necessary because otherwise the paid crew hours associated with a
particular profile of bus working through the day would be likely to
result from a group of men accepting the rough with the smooth.
41
In MPTE, the necessary data was found by analysing different
duty sheets. A duty sheet in MPTE defines a set of crew duties,
worked in turn by the same group of men. There were 63 weekday duty
sheets in operation at the time of our analyses. Esch duty sheet
typically contains 20 to 40 duties. A "duty" is one day's work for
one man. These gave us a wide range of mixes of work in peak and off-
peak periods, and the necessary conditions for the analysis were
fulfilled. The details of the analysis are set out later in this
chapter after the main argument has been presented, but at this stage,
suffice it to say that a relationship was found between on the one side,
crew hours paid for and on the other side, bus hours operated in the
peak period and in the offpeak period.
We now describe the relationship; the costing information
that it gives, and the practical advantages of the form of the
information.
4.3 The relationship between crew hours paid for and bus hours operated Duty sheets in operation
at one time for the whole
of the MPTE were analysed. Their activity was separated into what
took place in peak and in offpeak periods.
The peak periods were 0700 to 0930 and 1600 to 1830, Mondays
to Fridays. They represented periods during which the most buses were
on the road for MPTE as a whole. The rest of the day was taken as being
offpeak. No distinction was made between the morning, mid-day and
evening effpeaks. Weekends were treated separately for Saturday morning
(up to 1300) and other weekend hours.
~2
The range of peak/offpeak profiles was wide; duty sheets
ranged from having an approximately equal number of buses operating
in the offpeak and peak periods up to there being over ten times as
many buses operating in the peak as in the o£fpeak. Over this wide
range, we found that (to within about 5%) the total crew hours paid
for a weekday duty sheet could be represented as a weighted sum of
the bus hours operated by the duties of the duty sheet in the peak
periods and in the offpeak periods.
Thus we have, where A and B are constants estimated in the
analysis, the number of crew hours paid is approximately equal to
A x (bus hours operated in peak periods) + B x (bus hours operated
in offpeak period).
This linear relationship with the same A and the same B is
true for the activity on each weekday duty sheet. Furthermore, since
the relationship is deduced from duty sheets which cover a wide range
of peak to offpeak ratios with a variety of combinations of routes,
the relationship may be taken to hold for individual routes.
4.4 The direct cost of the crew hours required For each type of to operate the total combination of bus hours required on a route operation (DDOMO,
SDOMO, two-man crew) there is a different, but constant, cost per crew
hour paid. This is applied to the crew hours paid to operate the
combination of peak and offpeak bus hours incurred by the route; and
hence the direct crew cost of the route is calculated-. Thus the direct
crew cost of the route as a whole is obtained. This answers one question
relating to route costing - what is the direct cost of a bus route as
43
a whole in the general context of the other routes? (that is, without
attempting to pursue the details of fitting the one route with the
schedules for other routes, but making a general allowance for the
fit which works overall).
4.5 The direct cost of the crew hours From the observed associated with changes in the hours of bus service on a route in peak and relationship described offpeak periods
in section 4.3, we obtain
the costs of making marginal changes in the peak or in the offpeak service.
For the addition or subtraction of a bus hour in the peak periods,
keeping the rest of the service the same, we have that the paid crew
hours changes up or down by an amount A. For the addition or subtraction
of each bus hour in the offpeak, keeping the service in the peak unchanged,
the paid crew hours change up or down by an amount B. Hence the direct
crew costs of marginal changes to service in the peak or offpeak are
obtained.
4.6 Interpretation of total and marginal direct crew costs
with care.
This information must
clearly be interpreted
It can only be applied with confidence to changes which come
within the range of observation on which the relationship of 4.3 is
based.
a) In MPTE, the observations do not include duty sheets where service in the peak period dips below that provided in the adjacent offpeak periods, and the relationship could not therefore be applied in general to routes
operated from such duty sheets.
~4
b)
c)
d)
e)
The various changes to routes which are being evaluated must not be so large as to change significantly the timing of "peak periods" for the company as a whole: i.e., those periods during which most buses are in service.
Nor must they be so large or so unpopular as to require amendment to the union agreement in operation.
The level of detail of the information is appropriate for general planning purposes in MPTE, but could be inaccurate for small changes to routes, which might be able to take advantage of particular marginal amounts of crew time available in the existing schedules, or made possible by alterations to only a few duties. (Such small changes can, and should, be separately costed, by detailed calculation of changes to crew hours paid for the affected duties.)
Finally, if the changes being considered would substan- tially change the relative levels of offpeak service in the early morning, mid-day, and evening offpeak periods, then the present form of the relationship, which treats all those periods as the same, might not apply.
4.7 The direct cost of crew hours associated with blocks of service We are doubtful as to
whether the planning
and control of bus routes or research into the provision of bus service,
do indeed require answers to queations such as "How should the total
crew cost be split into an all-day component and a component for the
excess peaks?" or "What are the crew costs of the service offered in
the offpeak and in the peak periods?"
45
However, if needed, these can be computed from the paid
crew hours relationship.
Excess peak service Number of buses in service /
All day service
Time of day
The cost of the excess peak service can be calculated as (A x bus
hours operated in the excess peaks), because successive removal of
bus hours from the peaks reduces crew costs by A per bus hour.
The cost of all day service can be calculated by subtraction
from the total crew cost.
Equal additions of bus hours between the peaks only, or in
the evening only, will change the profile of service through the day,
and may have different effects on total crew costs, but this we have
not so far investigated.
Peak vs. offpeak costs Service through the day can also be regarded
as consisting of the two components "peak"
and "offpeak" service.
46
Peak service
~ ~ ~ Off peak service
~-- Time of day
The cost of the offpeak service assuming that the peak
service stays constant can be calculated as (B x bus hours operated
in offpeak periods), because successive additions of offpeak bus
hours from zero increases crew cost by B per bus hour added.
The cost of the peak service is then (A x bus hours
operated in the peak periods), by subtraction of the offpeak cost
from the total.
An apparent anomaly should be noticed, which indeed throws
doubt on the usefulness of calculating total costs of blocks of
service. The anomaly arises if the offpeak service is increased
to the point where it operates at the same level throughout the day
as the existing peak service. Although service is at a constant level
through the day, the cost is now apparently higher at certain times:
in the former "peak" periods, costed at A per bus hour, vs. B per bus
hour at other times. However, even if service is level during the
day, provision of service in one period of the day may have a
discontinuous effect on total cost. (If the "day" were one shift long,
the crew hours paid for would be nearly equal to the bus hours. If
47
the "day" were to be one shift plus one hour long, the total cost
would jump. To which hour in the day should the jump in cost be
allocated, or should it be spread evenly?)
Taking the "extra" cost into the peak period in the special
case when the peak and offpeak levels of service happen to be equal
at least has the virtue of consistency and continuity with the normal
situation when the peak is higher.
Having now described the relationship, its uses for route
costing, and some of the caveats necessary in interpretation, we
describe now how our results were derived in MPTE.
4.8 Analysis of crew costs in MPTE We established the relationship
between total direct crew costs
and bus hours operated in each time period (weekday peak and offpeak,
Saturday morning, Saturday afternoon and Sunday) by a two step process.
The first step establishe~ the simple relationship already
described between crew hours paid, peak bus hours operated, and Offpeak
bus hours operated (for weekdays), and a similar relationship for
weekends.
The second step calculated the direct crew cost per crew
hour paid, for each type of operation (DDOMO, SDOM0, two-man crew).
The first step To accomplish the first step, we performed linear
regression analyses of MPTE's duty sheets, to relate the scheduled
crew hours paid for the duties on the duty sheet to the bus hours
48
operated in each time period by all duties on the duty sheet.
analyses were made for weekdays and for weekends.
Separate
The scheduled crew hours paid were calculated for each duty
using rules taken from the union operating agreement and payroll
calculation, and totalled for each duty sheet.
Some small pieces of duty are scheduled to be worked as
overtime. These were counted in "crew hours paid" at the appropriate
rate (i.e, 50% extra paid hours for overtime, and subject to certain
minimum payments).
No full duties are scheduled to be worked as overtime:
only standard rates (and penalties) were included for all full duties.
Rest day work is unscheduled, voluntary, and a function of
the (variable) level of staff shortage at each garage. The premium
part of payment for rest day work is treated as a variable overhead
for the garage, not in this part of the calculation.
Figures for bus hours operated were derived by calculating
the number of buses provided by the duty sheet in each quarter hour of
the day (using a time diagram of the duties worked), and totalling for
each duty sheet by time period.
The second step In the second step, we calculated the cost of each
crew hour paid.
Separate calculations were required for each type of operation,
and to reconcile scheduled crew hours paid as calculated from the duty
49
sheets with actual hours paid, as shown on the payroll. Differences
between the scheduled and actual hours paid arise because of:
- service cuts
- unscheduled overtime and rest day working
- time spent: on holiday
sick
spare (but not on scheduled standby)
training
any other time not on working duty
We reconciled these differences using duty sheets, the payroll cost
summaries for the particular week studied, and logs maintained at
the garage showing the work done by each man at the garage during
the week, and used as input to the payroll calculation.
Other payroll costs were calculated for inclusion in the
bus hour related, variable overheads cell of Table 2.1, by reference
to the payroll summary and the reconciliation calculations~
Results A summary of the results is presented in Table 4.1, which
shows our estimates of the direct crew cost of a bus hour
of operation in each time period for each type of operation.
Tables 4.2 and 4.3 show separately the results of the first
and second step in the analyses just described.
These results should be applied subject to the general
caveats described in section 4.6 and specific conditions for MPTE
described in section 4.9.
50
Accuracy of estimation scheduling variance The number of crew hours paid
was estimated by a simple
calculation, multiplying the bus hours in each time period by the
corresponding coefficient from Table 4.2. This estimate was compared
with the actual scheduled crew hours as calculated directly for each
duty sheet. The estimates were accurate to within 10% in all cases,
and within 5% in most.
Scheduling variance is the term we use to describe the
cost of this difference between actual and estimated crew hours paid.
Favourable variances result if the hours required by the duty sheet
to be paid for are less than the "standard hours"estimated from the
coefficients of Tsble 4.2, and vice-versa. The variance is shown in
Table 2.1 in the "variable overheads, bus hour related" cell.
4.9 Consistency with other research The numerical values we have
obtained reflect the partiCular
union agreement in MPTE, and the nature of MPTE's services and
scheduling practices. However, the results we have obtained do confirm
evidence from other research studies that the crew costs of additions
to peak period service can be substantially higher than the costs of
additions to weekday offpeak service.
London Transport Executive. A Crew cost Model for Buses, Operational Research Report R178, December 1971, and Egerton, Mark. "Statistical Analysis of Platform Labour Costs". Unpublished paper, Ministry of Transport, July 1969.
51
5"2
rO ~ I i-~ [=.I
I:~ CO Z 0 " ~ : ~ ~:~ 0 0
E-~ b-~ H
0 ~.~ ~=I
~ _~ 0
E-~ l~l O 0 09 r-~ o a:~ r.o
O Z
~Zl ~ H
O E-~
c~
~ c ~
0~
c~
°
I
O ~
0
H
o
I--I E~
,J
e~
e~
(:0 e~
r- I
e~ e ~
,.-I
b - b -
J
b-- -.4-
0 x
C'q
",.0 b -
0
e~
D-
O
C~
P~ c~
0
G" 100
0
0 0 x
o
b-- O0
d
0 0
r- I
0
,'cl
O~
',.0
,,D
~0
O0
~0
Rg
(L)
..~ 0
Ch 0
II II
C~ 0 ~
I ~ II If
O
",.1" II
e~ 0
r- I
0
,--I
r- I
E~
!
I"0
0 (D
cd 0
cd
0 E'~
0
C~
"cl
O)
.,~ P~
(D (D
0
O'J
CO 0 0
0
~C~
o "
b~O
-r l
0
I
e~
0
0
o
b~O
-r-I ~ . . ~
eJ
O 0
~ 0
0 , - ~ o o
0
, , +~ ,-~ cd
~) ,'cl ~ - ~
cd
0
b o b .
m"c~
m O
o
~ A 0
0
TABLE 4.2
CREW HOURS PAID PER BUS HOUR.
BY TIME OF DAY AND WEEK
Figures are derived from the schedules in operation in
w e e k 48, 1973, i n MPTE
DAY OF WEEK
Weekday (Monday to Friday)
Weekend**
CREW HOURS PAID TIME OF DAY PER BUS HOUR*
Peak 2.0
Off peak 1.1
Saturday up to 1 p.m. 1.3
Other weekend 2.O
Notes
Figures are quoted to the nearest tenth of an hour, ms they are subject to residualstatistical uncertainty of the order of 10%. In our calculations, three significant figures were used to ensure that total hours paid were reproduced accurately.
A few weekend "extra" duties are scheduled to be performed as overtime. For these duties, the weekend coefficients shown should be increased by the 50% overtime premium paid in MPTE.
53
TABLE 4.3
DIRECT COST PER CREW HOUR PAID,
BY TYPE OF OPERATION
TYPE OF OPERATION
Double deck, one-man operated
Single deck, one-man operated
Two-man crew (driver and conductor)
DIRECT C0,gT PER CREW HOUR PAID
P e n c e 69
67
117
Note that the costs shown are only those defined as direct costs in Chapter 3, and represent only a part of total crew payroll costs.
54
d i r %C:.t- czr,@w ea~ e%~q.~..f" t.rQu~t %s, ~a:n,~ o~r~o p, qs %dr clh:a.;n~g %s.,j~,t~e.j %b,e:~, [.sag~j!,~c!t, ~$o~ sth~ej j
general caveats desc'ribed in section 4.6, and the follo.:ow:i-n,:g:~tm,ojr:e~oai ¢'~Jxo
specific assumptions which must be checked before applying the results
of Table 4.1 in MPTE. We assume that: . . . . . . , , . , . [ [0 ~ 3 2_!: J.[.;d ~.3.3 £ ; :~ . :e"z .'.= ' ~ _ , . , : . ~ i E ~ . . . . . . .,~. 3 d ~ .J_L:~s. ~ t : o : . ,
~-,: ~-~.[ :r~g Ga,} ~uSc~ed, ul, ers nqonti:n~'e~ to i-us ~.j-the _,s,ame-, a.~.l~roach ,to Grew-~ ~.. ~ ~, .~ .,q s
=s~qhed, uli.ng,p ~:and ~c, ont-inue ~,~to iapplM ..~th.e~ ,=s, ame ~p, roq~edu~e,s: .. ~ ,* ;
and rules in the construction of schedules, . w : . i , ~ h / %b, e u % , ; - f , ; e . , T c , . - ,
the same efficiency in the use of crew time as at present.
(b) Any changes to wage rates and other payroll cost elements,
and the extent of unscheduled overtime working, sickness,
and holidays are allowed for, and used to adjust Tables 4.i
and 2.1 before use.
(c) The location of relief points on new routes is not such as
to cause a significant amount of wasted crew time resulting
from a particularly awkward fit of journey times into crew
duties (this effect does not seem to be important on
existing routes).
4.11 Application in other companies The basic cost structure of
Chapter 2 can be applied in
principle to all bus companies. Crew costs can be analysed by a
method either similar to that used in MPTE, or by a simpler method
under development, but this method of analysis will not apply in
companies with a union agreement which consolidates spreadover pay
into the basic rate.
In those undertakings, increases in peak working would
55<'
(usually) be accommodated by more spreadover working; up to a point,
this might not increase cost per peak bus hour. Beyond that point,
the consolidated rate would need to be increased to compensate for the
extra inconvenience.
A rough estimate of the resulting increase in total crew
costs could be made using MPTE's results, but it can only be an
approximation, as the effective rate will change in jumps in undertakings
with a consolidated agreement, following renegotiations of the
consolidated rate.
56
CHAPTER 5
DETERMINING ROUTE NET COSTS
5.1 General principles By the net cost of operating aroute
we mean the difference between the costs
which are attributable to operating the route, and the revenue which
is attributable to its operation. The value of knowing the net cost
of a route is that the effect on the financial position of the
company of operating this route can be determined, and the extent to
which it would need subsidy to break even can also be established.
Costs The costs attributable to the operation of a route are of
two sorts: its avoidable costs, and an apportionment of
fixed overheads. The avoidable costs are those which could be
avoided if the operation of the route were to cease, and corresponding
adjustments were made to crew schedules, crew numbers and traffic
supervisory staff, number of buses owned, engineering staff numbers
etc. Avoidable costs correspond generally to direct costs and
variable overheads, as defined in Chapters 2 and 3.
The apportionment of fixed overheads was discussed in
section 3.4. These costs would not be avoided if the route ceased
operating, and are not relevant when considering possible changes to
a route. They are merely useful for the two purposes given in
section 3.4: determining if a route is making a proportionate
contribution to the recovery of a company's fixed overhead in total,
57
and possibly in connection with the question of the amount of
subsidy required to break even, if a subsidy is being considered
on a route-by-route basis.
Revenues The revenue attributable to the operation of a route
can have more than one component.
The first group of components consists of the revenue
actually collected from passengers travelling on the route. Even
this seemingly straightforward part of the revenue is becoming
harder to determine, as company revenue is increasingly received from
sources other than cash fares collected at the time of boarding.
Use of a route by season ticket and multi-ride ticket holders,
concessionary travellers (old age pensioners, schoolchildren, police
on duty, etc.) can only be satisfactorily estimated by special surveys.
Even cash revenue attribution to routes, based on analysis of waybills,
is time-consuming and expensive to perform on a regular basis, and the
introduction of fareboxes and other forms of cash revenue collection
pose their own problems of route analysis of receipts. Our study
was not intended to address these problems in any depth, and we have
not done so, except insofar as was necessary to analyse revenue for
the routes we studied in detail.
A second group of components of the revenue attributable
to a route consists of the revenue which would be gained or lost on
related routes if this route were to cease operating. This group of
58
components will be important principally on routes which are being
considered for service alterations. Gains could occur on parallel
alternative routes if passengers switch to those routes instead.
Revenue could be lost if journeys which were made partly on this
route, and partly on connecting routes, could no longsr be made.
As a starting point, experienced judgment should be applied
to the route in question if changes are being considered, to see if
this component of revenue is likely to be important. If it is, then
special ad hoc studies may be required, or judgment -- applied to
such route revenue information as is available -- may provide
sufficiently accurate answers for the particular decision being made.
59
5.2 Application to routes
borne in mind when determining route net costs.
steps may be summarised as:
(a)
(b)
Section 5.1 described the general
principles and considerations to be
In practice, the
Determine the revenue attributable to the operation of the route.
Determine the costs attributable to the operation of the route.
Attributing revenue Systems of fare collection vary so much
between companies that we have not found it
possible to make general recommendations for attributing revenue to
routes. Section 5.3 describes what we did in MPTE, and illustrates
some of the practical requirements involved.
Attributing cost Section 5.4 describes the determination of
avoidable costs for a route. Section 3.4, in
Chapter 3, has already covered the attribution of fixed overhead.
6O
5.3 Revenue estimation - methods applicable to MPTE MPTE stage
carriage revenue
comes from four main sources: cash fares, multi-trip tickets (Bus
Economy Tickets, or BETs), schoolchildren's passes paid for by the
school authorities, and concessionary travel, which is paid for in
part directly by individual local authorities, and partly by the
general rate precept, which also covers any operating deficit. Minor
additional income is received from season tickets and other sources.
Cash Fares We analysed cash fare revenue for all the routes operated
from one garage for one week, by manual extraction of
information from MPTE's usual form of waybill. This process required
a substantial initial effort to determine which journeys in each crew
duty are worked on each route -- information which was available by
analysis of existing records, but not summarised in a useful form.
The preparation and maintenance of such a master file relating journeys,
bus "boards", and crew duties is an essential step in the routine
analysis of cash revenue by route and time of day and week.
We did not attempt to assess the secondary component of cash
revenue attributable to each route by virtue of its relations with
other routes.
Bus Economy Tickets These tickets are issued from many locations in
the city including agents (tobacconists, newsagents,
travel agents etc.) as well as from MPTE garages and public information
points. They are valid for journeys on any route, up to the fare
61
value printed on the ticket. Each ticket is valid for ten trips,
and is cancelled one trip at a time by a machine on the bus. The
tickets are sold at a discount of 20% off face value. For the
purposes of this project, MPTE hoped to mount a special survey of the
use of these tickets on the selected routes, counting the cancelled
clippings collected on each bus, and analysing them by value, route,
and time of day. However, the results were not available in time to
include them, and hence an approximate allocation of BET revenue
to routes has been made.
Schoolchildren's passes These do not account for a very high
proportion of revenue, so an arbitrary
allocation of this revenue was made to routes in proportion to the
bus hours operated during the times of day in wh~h the majority of
schoolchildren travel. ~ Further detail if required could be obtained
from an analysis of the school name and pupil's address information
on each pass, either at the time of issue, or when expired passes are
returned at the end of term.
Concessionary travel ~ The use of routes by old age pensioners and
other concessionary travellers was analysed by
MPTE staff from a survey mounted in early January. Each concessionary
traveller was issued at the time with a zero-value ticket, and special
records were kept of the number of tickets issued by each crew.
Another method, which has been used by London Transport, and may be
used in the future by other companies including MPTE, is to use a
home-based interview survey of a sample of concessionary pass holders.
62
It may provide more, and more reliable, information at about the
same or lower costs.
The revenue to be attributed to a Journey made by concessionary
travellers presents special difficulty, because they do not pay on the
basis of the number or length of journeys made. We have therefore
confined ourselves to estimating the number of journeys made on each
route by concessionary travellers. For many purposes, this is
sufficient information. For other purposes, an average value per
journey can be assigned, based on the total number of journeys made,
and the revenue which would have been obtained had they paid the
corresponding regular fare.
63
5 . 4 Cost +de~t~e~in~tib~ . " " . . . . "' "~ . . . . . . ' , _ a v o ~ d a b t ~ e ~ c o s t ~ e ' ~ T h e ~ a , v b i d : a ~ i e Z ~ o . ~ t s ~ . : o f ~ • ,
operating:,,.a Cro6,t:,ec~re thes~d
costs which could be avoided if operation on that route were to cease.
F o r a r o u t e w h o s e o p e r a t i o n c a n b e c o n s i d e r e d i n d e p e n d e n t l y , t h e
avoidable costs correspond directly to our definition of direct costs
p l u s v a r i a b l e o v e r h e a d s . T h e a v o i d a b l e c o s t s f o r s u c h a r o u t e a r e
thus estimated b~ calculating its use of bus hours, bus miles, and
peak buses, and applying the appropriate unit costs derived from "/~'- ' ,~ 3 . ~ . ~ "r " ~ ' ~ ' : e v ~ f "~ ~ t ~ . ~ J ; . ~ , " , . ~ . 1 ¢ . ~ - . , ~ . . ~ . ( t ~ ' : ; , ~ , ",] , .~ .~O~L , ; ~ . . ,
e a n d 4 . 1 , e x c l u d i n g a l l t h e f i x e d c o s t e l e m e n t s i n T a b l e
9 " ' U n d ' ~ r Ts p ' ,~ 'dT'a l ' ~ c ' i ~ g ~ m S ' ~ a ' f i c e ' s '~ ~ ~o t ~ h ~ ( f -a c t o r s ' , m a y fl'e @d 't~6 b e ~. ~ i
taken into account. ," ~ - ~,3 -'3 '' "~t ~ ~,I~(~ ~. j ..' ~',j
Just as, for revenue, there may be secondary effects on
other routes, so there may be related cost consequences on other routes
if one route ceases operation. Cancellation of service on one route
may require that additional substitute service be provided on other
routes, either to cope with increased traffic, or to provide an
acceptable alternative-standard of service.
"Fixed" overheads may become avoidable in some circumstances.
For example, the cessation of service on one route might allow a whole
garage to be closed. A potential example of this exists in MPTE.
Spare capacity is available at one garage. Another nearby garage is
also kept operating, but it is small, and costly to run. It cannot
now be closed because its buses cannot all be accommodated within the
spare capacity available. Should some of its services be cancelled,
~64
however, the remainiHg buses could be transferred to the nearby ~
larger garage with spare capacity, and the small garage could then
be closed and its fixed costs avoided.
65
CHAPTER 6
PILOT APPLICATION IN THE MERSEYSIDE PASSENGER
TRANSPORT EXECUTIVE
6.1 Objectives The objectives of our pilot application of route
costing in MPTE were twofold:
a)
b)
to ensure that any principles and methods we proposed passed the test of being feasible in at least one practical situation
to obtain results which would be of direct use to MPTE operating, planning and financial management.
6.2 Coverage of the pilot study We needed to study a sufficient
number of services to ensure, so
far as possible, that our methods would apply acceptably well to
services having different sizes of peak and offpeak working, different
numbers of buses at peak periods, and offering different types of
service to the public.
We also wanted to keep the amount of data analysis to the
minimum necessary to achieve the objectives.
With these considerations in mind, we selected all the
services operated out of one medium-sized MPTE garage, which provides
service on a mixture of route types, including suburb to suburb,
(routes 66, 88), suburb to city centre (routes 4,5,85,86,87), and a
"Cityride" shoppers' service (route lO0) on a short loop route in the
centre of Liverpool.
66
The garage chosen had little interaction with other garages'
services~ although it does provide some service on other garage routes,
and receives in return some service from ocher garages on its "own"
routes, mainly in peak periods. Service on each of its own routes is
provided from up to four different duty sheets.
Our reason for choosing a whole garage for analysis was
that it offers advantages in data collection and in ensuriug accuracy.
Much existing information is already summarised by garage, and can be
used either directly, or to check totals etc. arrived at by other
means.
One full week's operation was analysed for this garage.
This was the necessary minimum time to which much of•the important
• summary information available was related (e.g. payroll) and also,
we believed, the shortest period over which revenue could be meaning-•
fully analysed because of the likelihood of substantial variability in
the pattern of takings between routes and between days. Our findings
fully supported this initial belief.
6.3 Feasibility in the pilot study, and implications for ~eneral application It proved possible in the
pilot study to achieve the
cost and revenue analyses we had been aiming for.
67
The main steps were :
a)
b)
c)
d)
e)
to analyse crew duty sheets for the whole of MPTE to derive the direct crew cost coefficients described in Chapter 4.
to structure andanalyse costs into the format of Table 2.1, in order to derive unit costs of operation per bus hour, bus mile and peak bus t distinguishing direct costs, variable overheads and fixed overheads. This was done for one week's operation in the pilot garage. Some overheads were pro-rated from management accounts figures for the whole Executive.
to calculate each route's Use of bus hours and bus miles by time of day, and its peak bus requirement, for all routes operated from the pilot garage.
to calculate route costs by combining a), b), and c) for each route operated from the pilot garage.
to analyse revenue by route.
Three types of effort were involved in each step:
i)
ii)
iii)
Work such as would be required initially to design the system.
Work such as would be required initially in setting up an ongoing system - compilation of basic data and its analysis.
Work such as would be required in an ongoing system.
With the assistance of MPTE staff, it was found to be possible in the
period of the pilot to perform all these steps.
Initial work to design the system We spent sufficient time on this
aspect of the pilot work only to
ensure that it would be feasible to complete our pilot analyses with
the resources available to us. We developed manual methods of data
compilation and analysis which worked acceptably well on a pilot
68
scale, but we were not aiming to design a system which would be most
efficient in routine use.
The larger the scale of application, the more effort it is
worth putting into system design to make it as efficient, practical,
and useful as is feasible. Our pilot results give some indications
of the type of analysis which has proved possible, but more extensive
design work would be needed before launching on full-scale implemen-
tati on.
Implications for setting up systems Set up effort depends to a great
extent on the complexity of route
service structure in the bus company, on the amount of initial analysis
required to establish peak, offpeak, and weekend crew costs, and on the
ease with which existing cost records can be structured into a table
like Table 2.1.
In all cases, it will be necessary to set up a file relating
bus journeys, crew duties, and each bus's work during the day in order
to be able to calculate each route's use of bus hours, bus miles and
peak buses and to attribute cash revenue to routes, by time period.
The file will be simple if the provision of service on routes is simply
related to duties. In MPTE, as in some other undertakings, this was not
the case for a substantial proportion of crew duties, for which detailed
analysis of the work on different routes was required, journey by journey.
The file can be compiled manually in the first instance, as we compiled
it. A computer system which allows the file to be generated from
computer-stored schedules data would increase the accuracy and speed of
preparation and updating of the file.
69
Establishing crew costs by time of day requires a second
substantial set up effort. The method we oniginally used in MPTE may be
applicable in some other companies, but we have developed a simpler method
of analysis, which we believe will apply for the analysis of peak and
offpeak crew costs in most bus companies with unconsolidated union
agreements.
A third set up requirement is the preparation of an overall
cost structure like Table 2.1, which requires the classification of
expenses as direct costs, variable overheads, and fixed overheads, and
according to the type of activity to which they are most closely related
(bus hours, bus miles, or peak buses).
This Table must be built up from records for the company as a
whole for some overhead costs, but can be compiled for parts of the
company only for other costs.
Our principal difficulty in compiling Table 2.1 for the pilot
garage arose for the engineering costs, for which records were not kept
in a form suitable for easy use in developing Table 2.1. This difficulty
was discussed in section 3.5.
The system requirement is for a clearer separation in the
recording of engineering costs, into the headings shown in the cells
of Table 2.1:
m
cleaning and maintenance materials used at garages
major maintenance (excluding bodywork)
accident repairs
cleaning, servicing and garage maintenance payroll, excluding supervision and admin. payrolls
other major maintenance
engineering supervision and administration.
70
Implications for ongoing systems As a rough indication of the scale
of effort that might be required in
an ongoing system, we estimate that a section of 6-8 clerical staff
could prepare quarterly route cost and revenue reports like those
shown later in Tables 6.1 and 6.2, using manual methods such as those
we developed for the pilot, and applying them to the routes served by
MPTE's 1400 buses. We do not recommend manual methods for long-term
use except in small companies, but they could provide a useful interim
step prior to computer system development.
We would expect that a high proportion of the effort would
be devoted to revenue analysis. Cash revenue analysis needs either a
complete analysis of waybills for a whole week or more, each time the
analysis is done, or will require great care in sampling techniques
based on extensive prior research, if applied more selectively to
certain days or journeys only. We found very considerable variations
in cash revenue, both between days on the same route, and in the
pattern of revenue takings through the week on different routes. No
consistency of pattern could be established on the basis of our one-
week analysis.
It would be desirable for accuracy of analysis of other
revenue by surveys, etc., to build into the survey design a means of
analysing non-cash-fare passenger journeys by time of day and week.
71
6.4 Results prepared for MPTE The main management planning reports
which we have prepared as a result
of the pilot application in MPTE are illustrated in Tables 6.1 and
6.2 at the end of this chapter. They are respectively a summary of
route cost and revenue for the whole garage studied, and a detailed
report for each route. The unit costs and the revenues used were
those applicable to the one week of operation of the pilot garage which
we studied in most detail.
Route 86 is used for illustration of the format of the
detailed report: similar reports were prepared for each other route,
and are included in a report submitted to MPTE. Two of them are also shown in
Chapter 7.
It is envisaged tha~ these reports would be prepared several
times per year, one summary like Table 6.1 for each of MPTE's garages,
and one detailed report like Table 6.2 for each route •or special service.
Interpretation of the information shown on the reports is described in
a series of notes following the two tables.
Particular attention should be paid to columns (P) and (Q)
of the reports. Column (Q) -- fare revenue contribution to fixed
overheads per bus hour of operation -- is in our view the best single-
figure financial yardstick to apply to a service's operation, and
should be used in preference to the traditional "revenue pence per
mile" figure, wherever possible.
Note that no allowance has been made on the revenue or
contribution columns for the carriage of 0APs, which is free offpeak.
72
Some of the uses which can be made of reports of this type
and of our costing methods are illustrated later, in Chapter 7.
A number of other special reports were prepared, and are also
contained in the report to MPTE. The discussion in section 6.3 was based in
part on these other reports, particularly the comments on the
variability of cash revenue. The reports were mainly of detailed
interest to MPTE, but the following general observation can be made.
Losses at some times of the week The route detail reports show that
all routes at the garage whose
operations we analysed make losses at peak periods, not even making a
positive contribution towards fixed costs (except for one route
operating only one bus), and all routes except two made losses on
Sunday.
The losses ranged from £0.45 to £3.70 per peak bus hour,
before fixed overhead attribution, and totalled about 22% of present
peak farerevenue or 7% of weekly total revenue. For further details,
see section 7.6.
Sunday losses range from £0.07 to £1.26 per bus hour, before
fixed overhead allocation, but the overall loss on Sunday is small
because of the one busy, profitable route, 86.
6.5. Conclusions from the pilot study Judgment of the potential
usefulness of the types of
results which we have achieved in the pilot can perhaps best be made
after reading Chapter 7, which describes some potential uses of the
results. Our own belief is that they offer considerable promise for
improved bus company planning.
73
v |
|
v
e ~ v
• : , : ,
0 ¢*) n • I I
m m ~
v. :~ O | • ~.*
I u
e
0
~ : °
c:; ~:* vl
0
e : o I
- -4
|
I--I i
e
; l : ~ l v e
O m
| |
I II
. 4 "
e u
e ~
i : l a l ILl
|
: . . . . . . . . s , . N :
| I
| e . . ; n u - - - - ° , o . . . . . . .
t s
N ~ ~, ~. =o ~ ~ ~ .~ .~ ~ ~ . r . .
l r l It • , , . -
.~ : ~ --. ,
: ~ N Z e # I
u
r ~ n
- U
u
;/)it J I q T ~ m '-~* II ~ N ~ I e . m
Im I
m l ~ o
u
T S
I n
I-- u
~ g
m u
u
N m
t m m
| II a
, ~
r a
~ u
i . ~ u ~ U
(1)
0
> .
0
< 0 0
0 , 0
C~ ' . . )
o
0
0
C~
0
z
',,0
C ~
Z LTJ ;>
O CJ
0 c~
< c~ <
74
Notes to Table 6.1
(A): Routes covered
The numbered routes are public stage carriage services. "BSS" refers to a service provided under a recurring contract to carry passengers from British Rail's station to the cross-channel ferry. "Sch/Univ" are school and University special services, mainly for carrying school and University students to and from playing fields on sports days. Football services are run from various points in the city to the local teams' grounds when they are playing, and special cash fares are charged on these services.
"Non-garage" lines on the report summarise iuterworking with other garages, and provide the reconciling items to agree the totals by route to the garage's grand total. The "out" line refers to service provided, and revenue collected, by this garage working on others' routes, and the "in" line to the reverse situation. Negative amounts, or losses, in the contribution and net revenue columns are shown in parentheses; since the losses on the "in" line belong to other garages, they are shown with a minus sign preceding them, and go to reduce this garage's loss.
(B) to (F): Revenue
The set of "revenue" columns analyse route revenue. Cash fare revenue is shown in column (B), by route. It was obtained as described in Chapter 5, by analysis of waybills, and is still the dominant form of revenue.
Column (C) shows an estimate of revenue from BETs (Bus Economy Tickets), based on an approximate allocation. Travellers Ticket revenue was ignored in the pilot application (it is less than 1% of total revenue).
routes. Column (D) shows an attribution of scholars' revenue to
Column (E) shows miscellaneous fare revenue-- in th~s instance, for the BSS contract and ~chool and University services only.
Total fares are shown in the next column (F), which is a total of columns (B) to (E).
75
(Notes to Table 6.1~ continued)
(G), (H): Passengers carried
These next two columns show an estimate of the number of passengers carried ou each route, obtained for 0APs from a special zero-value ticket issue survey, and for other passengers by dividing total revenue by an assumed average fare per passenger. These two numbers provide a means of assessing the relative and absolute importance of concessionary vs. other travellers on each route.
(I) to (M): Cost
This second set of columns shows the components of the direct costs and variable overheads on each route. All figures are in £s.
Direct costs related to bus hours are shownin column (I); those related to bus miles in column (J).
Columns (K), (L) ana (M) show variable overheads related to bus hours, bus miles, andpeak buses respectively.
(N) to (Q): Contribution
These columns show revenue less direct cost and Variable' overhead, respectively for cash revenue only (columns (N), (0)) and taking all fare revenue into account (columns (P), (Q)).
Column (N) = (B) - (I) -.(J) - (K) - (L) -(M)
C o l u m n ( p ) = ( F ) - ( I ) - ( J ) - ( K ) - ( L ) ' - (M)
Columns (P) and (Q) are arguably the most important columns in this report, and in Table 6.2. Column (P) shows the net contribution (or loss) to fixed overheads which would be given up within a few months if this service ceased to operate. Column (Q) is the best single-figure financial "index of merit" of a route we have been able to devise.
(R): Fixed overhead allocation
This figure indicates the amount of contribution which should be expected from each service in proportion to its use of bus hours and peak buses in accordance with the allocation of Table 2.1.
(S), (T): Net revenue
These columns show fare revenue contribution less fixed overhead allocation, both in £, and £ per bus hour. (Column (S) = (P) - (R)).
76
1
I I
~ e
!
e
r
~ e
i
l e
~ l
0
v l
- J
I n e
|
r
O l I ~ .
U J I ~
X : . g :
~ m
n ~ o I
: >~ :~.,
n ~
( I I ~ :
: ~ . J
~ m
I-.- w .
I,,,) I I Z: ILl
I'-- •
!
I
. . . . " ~ ~ , ,~ ~ o :
{.~ I I 0,. I , ~
u~
e ~ m
• N
l : o a •
, < 0
~- % It:
I •
I - I
r c. ~ :
~ I 0 I
r I r I ; , | •
c .
I / I I-~ I { , I
~ e ,,It a e e
| •
i i ! • i |
0 ;
~ r~ i ~ ~ e ~ 0 ! 0
I I
I
r ~ I I
I !
~ , . ~ ,
r
0 I
I I
0 0 0
I I I I I
I r I
0 ~ - - I
I 0 1
I •
! I I r N
, , ; ."
.:, .-. , , ~ , , ~ = I I I ~ n
' • '2; I[ I I
o , , ." | |
• I I I
', ' I :
I I I .~I" II I I I N
I I I ~ I • I II ~ I I I I I I
• I I I I I
., . I o i I e
e ~ i e I
I , , ,
$ I I
$
I I I I
° : n
" I • | •
R
~ m
O m
I . ' ~ n e ~ n ! ,41 m
g ;
o
o
.< ©
o
e . .
o Z
©
Z 0
©
.< [.-,
z
[--.
8
??
Notes to Table 6.2
(A): Period
Shows the period of the week to which the line refers.
Weekday: 0200 Monday to 2400 Friday, Saturday 0001 to 0200.
Peak: 0700 to 0930, 1600 to 1830 0ffpeak: All other times
Weekend:
Saturday: Sunday:
0200 Saturday to 0200 Sunday. 0200 Sund~y to 0200 Monday.
(B) to (Q): Revenue r cost, contribution
As for Table 6.1
(U): Percent service cuts
This column shows the extent to which services scheduled were not run, for whatever reason, in the period being analysed. It is expressed as a Percentage of scheduled bus hours which were dropped.
(V), (W), (X): Scheduled bus hours, miles, buses
These columns show (V) the bus hours (to the nearest whole hour), and (W) thousands of bus miles (to the nearest 100 miles) scheduled for one week's operation in each time period; and (X) the average number of buses in service during each period, to the nearest whole bus.
78
CHAPTER 7
EXAMPLES OF APPLICATION IN PARTICULAR
PLANNING CONTEXTS
7.1 Summary In this Chapter we give examples of the ways in which
the cost and revenue analyses could be used in a
variety of possible planning decisions*:
a)
b)
c)
d)
e)
f)
To estimate the revenue and cost consequences of changes to the "Cityride" route following the closure of a city-centre street for pedestrianisation, and the council's decision to provide free service on the route during offpeak hours (section 7.2).
To estimate the net cost of providing service at some times of the week on one route (section 7.3).
To estimate the cost consequences of conversion of a route to 0M0 (section 7.4).
To estimate the cost consequences of altering service frequency on a route (section 7.5).
To assist in a discussion of the value of increasing fares at peak periods (section 7.6).
To assist in a discussion of the value of inmreasing service in offpeak periods (section 7.7).
Within each of these sections we first briefly describe
the planning problem, then illustrate, by a table, the route costing
information which can be used to assist the planning decision. In
several cases the table takes the form of a Costing Worksheet (see
Table 7.1), a worksheet on which the unit costs described in Chapters 2
and 4 are set out in a form suitable for calculations based on bus
hour, bus mile and peak bus data.
* The broader implications of planning decisions are not, of course, discussed in this report.
79
The effects of operational changes on hours, miles and peak
buses operated have to be calculated separately; a note following
the table indicates considerations to be borne in mind in each case,
but details of those calculations are outside the scope of this
report.
The unit costs shown on the worksheet are then applied to the
operational changes shown in column (A)of the worksheet. Columns are
provided for separate calculation of direct costs, variable overheads,
and fixed overhead allocation. As described in section 3.4, the use of
the latter is confined ~o two purposes:
a) determining whether a route is contributing to overheads in proportion to its use of bus hours and peak buses
b) in determining the amount of subsidy required to achieve the required level of contribution.
We have not illustrated these uses here; they are simple to apply
for these purposes.
80
il
v
E-+ ~-.-,
+ o
r ~ O
• I:::l
° ~
"~ o o ~
a ~
, l : u
0 ~
N
0 H
0
+
11
IJ
II
n
,,<
II
0
o~ I il il o ~ ~
o , ~ ~
• il • 0
S S ,...; ,-; ' o '
I
I I
g o o
II ~ IIII
o
II n
n n
I i u i i i i
,.,-I
Q,I
i/ iI °
0
s
8 1
7.2 Effect of street closure and free travel offpeak on route lO0 Early in 1974 the local
authority closed a busy
central shopping street to traffic to make it into a pedestrian area.
Many bus routes were affected by this closure and had to be re-routed.
The Cityride' service (route lO0) was most significantly affected,
providing as it does a service in both directions round a loop in
central Liverpool, which was considerably lengthened and diverted
round other one-way streets when Church Street was pedestrianised.
Subsequently, the local authority requested MPTE to provide
the service free to passengers, outside peak periods.
The questions at issue were: what was the cost of these
changes, what was the revenue loss, and what was the net cost?
Cost Table 7.2 shows the calculations required for costing this
change, by applying the unit cost coefficients to the changes
in operations. We estimate by this means an additional cost (direct
cost plus variable overhead) of approximately £4,400 p.a., compared
with a corresponding cost before the change of about £19,000 p.a. --
a 23% increase.
82
m .m m m
m
M r ~
~,~,,
+ O f f
° ° ° ;I P4 P.I 0 .
° ° ;I - n I i • 0 .
¢~" I ~ [ - t II
• :21:: ~ II
0 0 ~ I!
• I~s., II r ~ < 1
II @
, " "+ ~I
11 ~) O} II m m II ~ QI II @ (b
p, " " , ; , o o ,
II Ii
m: ~'I i i
m+ I |
°1 ii
~ ~ ' , = a m l
,," . ~ , - o l i c , ~ o !
ii
O 0 ~ . ~D C '~ 0 u"~_
0 ~ 0 t ' ~
00, ~,~ ~D C ~"
o ~
,~1 o , ~1 ~
o ~ ~ ~ ~ o
(%1 I I
c~ o .-, ,-; '
I !
l
! I I
I
: I ! !
i
)
n (0 Ii ~:~ fl
0
o l
o ~ o x
( 0 .
~ .
. n fl n
n
~ .gg
I n . e : n u
n u 0 n n
! n
1 " ! i! n
i i ~ I | n Ii H I|
o ~ o ~
, -0
xO
0 3 . n
(*3 .
¢Q n II
:=:: . n
o
o
ii ° • i - I
0 ,.~
0
os
I:::
P, o
,,i[3
,P.
o
III
4 ) r - I
4 ) tO
0
0
P)
I-+
o~
f-i o
o l,...l r - I 0
:>r+ I ' 4
"I"4
P~ ,.i-I
0+
+.,+ o I:I
+- u ' J v
S~
Notes to Table 7.2
1. To convert this week's figures to an annual equivalent,
a multiplier of 52 weeks per year was assumed. This possibly
understates annual costs since extra crew costs are incurred
at holiday times through higher rates on public holidays and
more overtime in the summer holiday period. More detailed
investigation could suggest a more accurate multiplier.
2. Hours, miles and peak bus data were calculated from
the revised duty sheets following the change. Earlier, but
less accurate, estimates could be made, using the proposed
bus running timetable, with an estimated allowance for time
required by crews and buses for out of service travelling
between the garage and the start of the route; and vice
versa.
3. The service is provided by single-deck OMO buses
(includiug some extra peak working) so the SDOMO crew rates
in column (B) are used.
4. Fixed overhead allocation is not relevant to this
calculation, so columns (D), (G), and (I) of the worksheet
are not used.
8~
Revenue Loss Table 7.3 shows revenue and costs on route 1OO in
week 48, 1973, before the change was made. ~/e calculate
the loss of revenue offpeak as £346 for this one week, or about
£18,000 p.a. The assumptions made in the calculations are noted
following the Table. It should be noted in particular that we do not
know at this stage-the possible inaccuracy in the £1'8,O700 estimate
which could result~ from week-to-week fluctuations In revenue. Regular
preparation of the" revenue data would permit this to be done.
Net~:cost Su$~ject to th~ caveats shown above, theinet ciost of the
.... r o u t e lO0 c h a n g e s was t h u s a b o G t £ 2 2 , 0 0 0 . T h i s fian be ; - •
compared with ~ the small net annual contribution of route IOO before
ther changes of_ about" £ 3 0 0 p.a.
\ • . .
i• ..
£
J
r
A
i
85
#
3 c(
w
o z ~
~- a~ - .
~ m
: = = . o | • = i
e I • I
= "=:
0
ocu i w •
0 0 0
0 0 0
: 5 ' ~ " i i i ..-,-~ e ~,II i i ~l.i i
_,~, le ~,i.. o I
~ I l : l I
gi i'i i Jd l e
i ~,/i o e : g : :
~ n ~.~
> - : ~
> u :=
0 ~ e
0 ! e ! 0 ! I |
I I
i i $ e i - i i
~o. le z I I e n I l l
i i i ~ i l , - m o l
u I c I I I
~ , - ~ e e • I i I
~u o . . . . . . : = ,
. ~1 o o 1o1 i ~Z I I I
i • m I I i u
,," a' z : r . i ' " ~ I I ~" , I ~1 i e I
, ~."-. . ~ I ~ i i~ . i i
u _- : I
~ I : : )
I I •
0 • g 0 •
0 0 0 0
~- o ~ ~
I I •
Z
, : ,~:
l I in
I • I
I " t • , ! : : i
• I ~"o I | i I I ii ,, : , .
• , , : .
I e u
I I u
• t •
• e i
I I m I I u
e l s
O | |
| • o 0 u
I e a I i o • | e •
= o : o ! , o . ' .
e | m e e u
l e ~ I | •
o e I ~ 1 1 i ! i u
c~
o
o
>
0
r - .
c~
o
o z
o
o
"8
E E
86
Notes to Table 7.3
1. From this Table, one can see that of the total fare
revenue of £371 for the week, only £25 was collected during
the weekday peak periods. An abolition of the offpeak fare
would therefore directly have lost revenue of approximately
£346 in this week.
2. Scaling up by a factor of 52 weeks per year, and
assuming that week 48 is representative of the year, this
would imply an annual loss of revenue at fare levels
current in December 1973 of approximately £18,000. (This
may slightly overstate the revenue loss, since revenue is
lower on public holidays and in holiday periods.)
3. Some caveats are necessary. We do not as yet have
any detailed information by route on week-to-week variability
of revenue, so that we cannot say how accurate this scaled-
up £18,000 estimate is likely to prove. Also, the "BET
and Traveller ticket" revenue is only an approximate allocation;
this allocation scales up to about £700 of the annual loss of
revenue.
4. Regular preparation of the detail cost and revenue
report would allow the variability to be assessed, and
surveys of the actual use of BETs would improve the
estimate of their use by route.
87
7.3 Estimating the net cost of providing service at some times of the week Sunday services on
all but two of
MPTE's routes at this garage lose money - fare revenue contribution
to fixed overheads ranges from a profit of £0.94 per bus hour on
Sunday to a loss of £1.26 per hour (see Table 7.4).
This section considers the question of estimating the net
cost of providing service on the route (route 87) with the
largest loss. The section illustrates the principles described in
Chapter 5.
Table 7.5 shows detailed route cost and revenue data for
route 87. A straight scaling up of the (negative) contribution from
Sunday service would indicate an annual loss of about £3,300; however,
it is at this point that the interaction between routes must be
considered. Routes 86 and 87 provide service on partially overlapping
routes, so that estimation of the net cost of route 87 service must
allow for the revenue that would be transferred to route 86 if route 87
were partially or completely withdrawn.
After taking this into account, a better estimate of the
net cost of route 87 Sunday service £3,900 is reached, as described
in the notes to Table 7.5.
88
TABLE 7. 4
SUNDAY SERVICE: FARE REVENUE CONTRIBUTION
BY ROUTE
Route
4
5
66
85
86
87
88
I00"
_ _ _ c _ o _ n _ t _ r _ ~ k u _ t _ ~ o _ ~ - _ ( _ ~ _ o s s )
Z/week £/bus hour
(52) (o.93)
(25) (0.61)
(3) (o.o7)
(35) (o.6o)
119 0.94
(63) (I .26)
6 0.43
Basic service frequency
(rains. interval)
3O
30
30
2O
15
3O
6o
* No Sunday service
Sources: Route detail reports and published timetable.
89
g, q~
g
) . .
=°,o
O C , . I . . l .~l
Q m I
: : ) l l ~ 0 :
~ : , 0 :
m ~ i i c ) 0 • =c I
~. ,,. : ~. :
: :
:
e w e i i m : i
o c u o =
u n z i l~l
I ~,. I .al I l&l I
m x:
n e m |
~o
0 o o
~ : ~ : .0 , |
• • e
d " ~ ' t
= ; : e e ; l
| e
I~ la -J I e ~ •
.Jll • • I
; ; " ° : , , . . . . . ' ~:n~ m = --', • t e > . . : : , : ,
~ : ~ " ~ ~. : ~ :
~ 1 ~ . ~ ~ : ~- ,
o e l ~ e e e IV l I e
0e ~ . ~ e l , - • : : . ~ : ~= : : ~ 1 = , n ~ 1 , 1 1 1 1
L ° , : ~ 1
e I
l i= •
i
u
u
m
l e e
: I
~ : ~ : : ~- : ¢ e
~ , : ~ _~ : :~ :
~ : : :
~ : : ~ : ~ : z • .i I
( . ~ s ! I I t
o • ~ : ~ : .~ , sa.
° o : - : : * ~ e e t
I • I • I I I
0 0 0 ~ ' -
0 0 0
2, : . . : : , , : I I I •
,, : ; = . . . .
; ; ; - : e I , , : ,',
°
o
• |
• • l ~ n
I i o ~ l I • I u
. : =
e e •
e i
e e • i I I i I I I H
I I I B
I ~ m | I •
| e I n • I I • • e I a
o o .o: :;:
e i i I
I t i ~ m
I • •
I I I T I
~ U
,..M c~
o
o
~g
.< o o t ~
e-.
o
c~
0
z
o
z
©
o
.o
;--4
o ~o
E .E
o
90
Notes to Table 7.5
1. Revenue Total Sunday fare revenue was £55 in week 48,
or about £2,900 p.a. Since much of the route
of the 87 bus is common with that of the 86 we need to
consider the interaction of the two routes. Not all of the
revenue on route 87 would be lost, as some passengers could
use ~he 86 instead. Assume that 25% of existing route 87
passengers would travel instead by route 86, to give a net
estimated revenue loss of about £2,200 p.a. (75% of £2,900).
Iu practice, traffic staff should be able to assist
in making this judgment, based on their experience. We have
taken 25% for illustration of the principle that route
interactions must be considered.
2. Cost The avoidable costs (see Chapter 5) of Sunday
service are in this case quite straightforwardly
the direct cost and variable overhe~.d components of the
route cost for Sunday, a total of £118 per week, or about
£6,100 p.a.
Since SUnday buses are rarely full, no extra capacity
is likely to be needed on route 86 (the 25% switch of route
87 Sunday passengers to route 86 0nly adds about 3% to the
number of route 86 passengers, as can be seen from the
91
(Notes to Table 7.5 continued)
existing figure of 1,O00 Sunday passengers shown for route
87, compared with the corresponding figure of 8,000 Sunday
passengers on route 86 obtained from its detail report, shoWn
earlier as Table 6.2.
3. Net saving The net saving after a few months is
estimated at £3,900 p.a., cost savings
of £6,100 being partially offset by fare revenue loss of
£2,200. Achievement of these savings would depend on
management taking action to ensure that variable overheads*
are correspondingly reduced following the service cut.
The variable overhead component is an important part (31%)
of the savings; in particular, if rest day working and
operating staff numbers were not reduced promptly, only a
part of the savings would be achieved.
mainly other staff payroll costs (NHI, graduated pension, etc.), rest day overtime premium, supervision and training, maintenance materials, major overhaul and accident repair costs -- see Table 2.1.
92
7.4 Estimating the cost consequences of conversion to OMO There are three principal
stages required in performing
this calculation. In the first, the effect of slower boarding on the
running speed of the route must be calculated. In the second, this
slowdown must be translated into a new timetable, and its changed
requirements calculated for bus hours, bus miles, and peak buses. In
the third, the costs of these changed requirements are calculated.
Table 7.6 illustrates the third stage, the calculation of
the cost saving (excluding revenue effects) for a hypothetical
conversion of one route to OMO -- hypothetical, because all MPTE
services at this garage are already OMO.
The operational changes resulting from the switch are
illustrative only. We believe they are reasonable although they are
not based on real data. The notes to the Table indicate how they
might be calculated (the first two stages of calculation discussed
above) in a practical case. Thus the conversion savings indicated of
~329 per week on direct costs plus variable overheads should not be
considered as an indicator of real cost savings.
93
qMO aJ .(:o'[8':evs(.)o t~ " ",~
] 8
v ~
~ 0 < ~
O
~ ~ O
O ~
O O ~ ~ j . ~
~ X
N
O H
v ~
9
x , <
0
] I
"21 O I
I ~ O , ~ I
v
,'-4 ,-4 v v v
I I I
,-1 , - I
• - - °
,4 6 6 ,4
r~ o c~
,-4
U3 .
N ',:
, - I v
em
i 0 i c ~
" il o
• I I 6
• I
I
I
I I
I
I . - . 1 ~
I ~ )
I I I I 4
ii ~ I1
• r t
~J
hO
¢1
°
0
ff 0
,--4
C
]
0 "< ~-I
,-4
r~
~rj v
9 4
Notes to Table 7.6
1. Slowdown of service Detailed calculation of the slowdown
likely to be experienced on OMO
conversion is outside the scope of this study. In brief, it
must consider the fare collection system and its effect on
boarding time per passenger, the "dead time" per stop, the
number of stops on the route, and the number of passengers
boarding and alighting.
Although we are not concerned with estimating it here,
it should also be noted that revenue changes can be expected
following conversion.
2. Estimating operational changes The effect of the slow-
down on bus hours, bus
miles and peak buses is very strongly influenced by the relation
between the frequency of service and the length of the basic
journey time between end points on the route.
A small increase in journey time resulting from OMO
conversion can often be accommodated by reducing the layover
time, and no extra bus hours, bus miles, or peak buses are then
required. The only cost changes are then those of the higher
rate paid to 0MO driver/operators, less the savings from
eliminating the conductor, plus the other operating cost
differences between OM0 and two-man buses, if any.
To accommodate a larger increase in journey time, or on
a service with only a small existing layover allowance,
either an alteration to the frequency of service, or an
95
(Notes to Table 7.6, continued)
additional bus and crew (or sometimes both) will be
required.
3. Assumptions used We have assumed that the peak service
requires 10% more bus hours because
of the slowdown, and ¼ of an extra bus in the peak hours. We
also assume that a part of peak service will still be provided
by two-man buses.
We have assumed a requirement for an additional 5% of
bus hours of f peak (weekdays), when passenger numbers are
smaller than during peaks and the influence on boarding
times is less, rising to 15% on Saturdays but dropping to
only 2% on Sunday.
We assume that additional mileage amounts to 200 miles
per week, from the extra ¼ peak bus.
4. Calculations Column (E) shows the net direct cost
effect of the increase in SDOM0 work,
offset by a greater reduction in two-man work -- for example,
the entry for weekday peak is calculated as:
(198 hrs. x £1.33/hour) minus (177 hrs. x £2.34/hour) = £151 saving, shown as (151).
Total savings are estimated at £329 per week on direct costs
plus variable overheads.
96
m
7.5 Cost consequences of alterations to service frequency In the case of a change to
off peak frequency which is
uniformly applied throughout the day, an approximate estimate of the
cost change resulting from the change in service frequency is obtained
by taking the existing offpeak costs from the route detail report
(e.g. Table 7.3), and multiplying by the ratio between the new
frequency and the old, both expressed in buses per hour. This is
illustrated in Table 7.7 for route 100.
A more accurate estimate can be made by comparing new and
old timetables to calculate offpeak bus hours and bus miles, •using
a standard allowance for the bus hours required in addition to "wheel
turning time" for layover and for travelling out of service between
the garage and the route. The hours and miles are then costed as
usual. Table 7.8 shows an example of this calculation (based on a
different route from the example of Table 7.7).
Peak changes Changes to peak frequency are more difficult to cost,
since the relation between peak frequency and peak
buses required is not always simple, and inaccuracies in calculating
peak bus requirements can have a considerable effect on cost estimates.
Proposals for a revised bus timetable should be worked out, to
calculate the peak bus requirement, and the bus hours and bus miles
to be operated in the peak period. These are then costed as usual.
An example is given in Table 7.9 and is described in the notes to the
Table. The example illustrates the considerable importance of the
"peak bus" cost component of the change.
97 i•
TABLE 7.7
COSTING OFFPEAK FREQUENCY CHANGES: SIMPLE APPROXIMATE METHOD
This example is hypothetical, but illustrated by reference
to the route I00 data previously shown in Table 7.3.
Cost of existing off-peak (weekday) service
- related to bus hours
- related to bus miles
Direct Variable Costs Overhead
£ 68 £44
19 23
£ 87 £67
Total £~54
Proposed new service interval lO minutes = 6 buses / hr.
Current service interval 15 minutes = 4 buses / hr.
Estimated cost of new offpeak service
= £154 x 6/4 = £231 per week
Cost increase £ 77 per week (50%)
Notes
I. This method works because the only costs of offpeak
service are those related to bus miles and bus hours,
both of which are approximately proportional to the bus
frequency.
2. The method will be least accurate for services where:
the journey length is long compared with the duty length.
98
(Table 7.7 continued)
the access time out-of-service between garage and route is significant.
service is infrequent, and the relation between journey length and service interval is awkward giving rise to disproportionate layover times either before or after the change.
99
il
v
~ 0 ~
~ * o
O ~
0
~ 0
0 ~
o O ~
O ~
0
;I 0
ii
u
I i
0
v ~ o
°1 ~ o
0
~ o
J J
o o o o
~ u
3 g
~ o ~
, j J ,...:,
I I
~ o ,'-4 0
• I
I !
I !
I
,, ,-, ~. I 0
I
I I I I
• I
I , ~ ~ 1 "t" m
I I I I !
I
!
I
o o
o o
o
o
m
i
g
g
o
cd 0
ff
0
*&
I00
Notes to Table 7.8
I. Offpeak frequency is assumed to be 20 minutes during the
day (between morning and evening peaks) and every 30 minutes
in the evening, to be changed to every 15 minutes during the
daytime, leaving evening service unchanged.
2. From these changes, bus hours and bus miles are
recalculated for the new service, to derive the figures
shown in Column (A).
3. We assume the crew costs of off peak service to be the
same at all weekday offpeak times, as we have at present
no quantitative evidence to the contrary.
4. Overall cost increases by £183 per week, compared
with existingcosts (excluding fixed overhead) of £577 per
week for offpeak service*- a cost increase of 32% for a
service frequency increase of about 24%. The simple
method of Table 7.7 applied to the daytime frequency
increase would estimate the cost increase as only about
£137, pro-rata to the frequency increase. It ignores
the interaction between journey length, service interval,
layover time and duty length, which is an awkward one in this
particular example.
5. This example is for a different route from that of Table 7.7;
the two results should not be compared directly.
*Derived from the route detail report (not shown here).
i01
ii
H u
~ )) ,,
_ Ii I I • + 0 1 ;
~ 4 . ~.
N
O
O
o
°
u
n
. . g P~l
21 u
" 21 u O
, , , 0 v v
~0 v
~ ~ o ~
v
r 4
{ x z
o o o o
u
, - I v v
. ~ ~ ~ o
i - -4 ~XZ
I
I
i , -- I I 1 "~ I I xO Ox ~--I , - I u
i [ - , , i i
m
o
I 1
o • I I
o •
• !
I I
J
I
I ! I
0, ~. ~ ~
m i
i
¢
I
~ N ~ u m w
A
cO
O
g -O
g
X
ff .r4
~o r 4
a~
*g
r ~
:102
Notes to Table 7.9
1. Frequency of DDOMO peak service is being reduced
from every 10 minutes to every 12 minutes (from 6 to 5
buses/hr).
2. Peak buses can be reduced from 13 to IO, because of
a better fit in the schedules allowing more than the
pr0-rata reduction (which would be 2 buses).
3. Overall saving is estimated at £267 per week, or 20%
of the existing cost of £1,360, for a frequency reduction
of 16.7%. The bulk of the saving comes from the
reduction in the number of peak buses required.
103
7.6 Increasing fares during peak periods All MPTE stage carriage
services from the garage
whose operations we analysed lose money* at peak periods, except for
one service (route 88) which only uses one bus. Table 7.10 shows
revenue and contribution, by route, for the peak periods.
If peak costs, excluding fixed overheads, are to be covered,
then additional revenue of about £1,200 per week would be needed at
this garage. This is equivalent to 22% of current peak fare revenue,
or 7% of the week's total fare revenue.
Notes after the Table indicate some of the factors that
would have to be borne in mind by the bus operator if this extra
revenue were to be generated by higher fares in peak periods, rather
than by other means.
One alternative to higher fares could be a subsidy to cover
losses on peak operations. The figures given here illustrate the size
of loss being made, and could form a basis for negotiation if a
subsidy is considered.
* i.e., contribution to fixed overheads is negative; direct costs plus variable overheads exceed total peak fare revenue.
104
TABLE 7 .I0
PEAK PERIODS CONTRIBUTION TO FIXED OVERHEADS
BY ROUTE
(Week 48,1973)
Route
4
5
66
85
86
87
88
I00-
Fare Revenue
Contribution (loss)
E/peak bus hour £ £
601 (227) (I ,33)
759 (186) (0.93)
552 (239) (I .46)
911 (174) (0.75)
2,032 (196) (0.45)
548 (89) (0.66)
200 30 0.73
25 (137) (3.70)
5,628 (1,218) (0.85)
A high proportion of route lO0's peak operation is out of service running between garage and route service, since route lO0 is primarily a daytime only shoppers'"Cityride" offpeak service. We believe that this accounts to a large extent for the high loss per bus hour.
Source: Route detail reports.
105
Notes to Table 7.10
Factors to be considered in connection with means of
recovering peak losses include basic choices of where additional peak
revenue should be raised - from higher peak fares, cross-subsidization
from other time periods, government subsidy or other source. Many
important issues are involved, beyond the scope of our study, but we
can comment on some relevant points mif higher peak fares are thought
to be an appropriate way of obtaining additional revenue.
.
.
.
Loss of passengers
Research results I indicate that the percentage loss of passengers following a fare increase is less than the percentage increase in fare, so that overall, total revenue is increased by higher fares. This is particularly true for peak period travel.
Indications I are that ~ passenger loss could be (very approximately) of the order of 0.2% for each 1% increase in fare - towards the lower end of the range of demand elasticities deduced from studies of travel
behavi our.
Traffic congestion
Any significant switch from buses to cars in peak periods could increase traffic congestion. However, bus fares are not generally a very significant factor in the choice of mode for the journey to work 2 and few passengers would switch to cars as a result of higher fares. Poor service is a much more common reason given by car drivers for not choosing public transport.
Lonser-term effects
Fare increases are unpopular, and increases at peak periods affect people with little choice but to pay them (that is one reason why overall revenue increases). If fare increases are not accompanied by improvements in comfort and reliability, the public's image of the bus company may be adversely affected, possibly causing undesirable long-term effects. Local authorities may also be influenced unfavourably in their attitude towards the bus company.
106
(Notes to Table 7.10, continued)
4. Method of collection
References
Effective means would need to be devised to make clear to passengers and bus crews just when the peak fare must be paid. Alternatives include charging according to: the actual time of boarding the bus; the scheduled time at which the'bus should have passed the particular stop at which the bus was boarded; • the scheduled time of arrival of the bus at major destination points (effectively peak fares on certain bus journeys); and so on.
Different fare levels between peak and off-peak have already been tried in a number of companies,3 but in some cases have been dropped because of practical difficulties.
For the reader's convenience, references are quoted from
one publication: "Proceedings of a Symposium on Public
Transport Fare Structure," held at the Transport and Road Research
Laboratory in November 1973 (Supplementary Report 37 UC). The
conclusions described are often based also on other research studies,
to which further reference is given.
I. Smith, M.G. and P.T. Mclntosh. "Fares Elasticity:
Interpretation and Estimation." See especially pp. 29,
32.
2. Kemp, M.A. "Reduced Fare and Free-fare Urban Transit
Services - Some Cases Studies." See especially pp 38, 45.
3. For example, London Country Bus services~ Alder Valley
Services, Eastern Counties Omnibus Co Ltd., Midland Red Omnibus
Co Ltd, and Western Welsh Omnibus Co Ltd.
107
7.7 Providing increased service in offpeak periods Advantages from increasing
offpeak services can be
suggested, based on the route detail reports such as Tables 6.2 and
7.3. At the garage analysed in MPTE, all offpeak services (except on
Sunday) make positive contributions to fixed overheads, and in general,
higher contributions per bus hour are achieved on the more frequent
services (see Table 7.11).
The positive contribution made by offpeak services is
achieved even without making any allowance for the benefits from
services provided free to old-age pensioners, and other concessionary
travellers.
Although it is not to be expected that more offpeak bus hours
provided will continue to attract the same additional revenue per hour
as the existing average, more offpeak service may (up to a point)
obtain more contribution in total, and in any event provides improved
levels of service to many people with limited alternative modes of
travel, at relatively low additional cost to the bus operator.
108
TABLE 7.11
0FFPEAK (WEEKDAY) CONTRIBUTION TO FIXED OVERHEADS
BY ROUTE
(Week 48, 1973)
Route
4
5
66
85
86
87
88
I00
Fare Revenue*
£
Contribution*
£/offpeak bus hr.
Basic service** interval (minutes)
558 134 0.57 24
626 159 0.61 24
580 136 0.57 30
834 262 0.88 20
3,334 1,951 2.73 ~ 8
572 126 0.54 20"
316 172 2 .07 60
282 128 I .29 15
7,102 3,068
Notes
Excludes any allowance for carrying concessionary travellers, who travel free of f peak.
Daytime, between the peaks. Early morning and evening service is sometimes less frequent.
Sources: Route detail reports and published timetable.
109
CHAPTER 8
SOME FURTHER DEVELOPMENTS OF BUS ROUTE
COST INFORMATION
8.1 Introduction There are some bus route planning and control
decisions which require cost and revenue inform-
ation with a type of detail which is different from that which has
been the subject of this report. Three such decision problems and
their implications for information needs are discussed in this
Chapter.
8.2 Changes to evening service The methods we have applied in
MPTE do not give sufficient
information to enable either the revenue or the cost consequences of
changes to evening service to be estimated with precision.
Revenue To obtain an estimate of evening revenue by route, more
detailed analyses of waybills could be made for cash revenue,
and surveys of other sorts of passengers (especially of 0AP's) could
distinguish "evening" as a time period for analysis.
Cost Our methods will give an approximate cost for evening service,
subject to an important qualification described below. By
calculating bus hours and bus miles involved in evening service, in
the usual way, and applying direct and variable overhead unit costs,
these costs can be estimated for either an existing evening service or
Ii0
a proposed change. The "offpeak" crew cost should be used.
Caution The important qualification is that we do not know at this
stage whether evening work can be regarded as having the
same effective crew cost as other offpeak work. It is true that no
special payments are made for evening work, but we are told that (a)
some must be included in the mix of work and (b) it is Unpopular.
This means that significant changes to evening work may not be possible
without renegotiation and possibly the introduction of additional
penalty payments of some sort. Under these circumstances, no confident
estimate can now be made of the new crew costs.
8.3 Stopping services short of the terminus (revenue effects) The smallest unit of service
for which we obtained revenue
figures was a single journey of one bus travelling one way along its
route.
No analysis is therefore possible on this basis of the
revenue effect of stopping the ServiCe short of its present destination,
because we have no data on the numbers of passengers carried at
different stops along the route.
Much more detailed record keeping on board the bus, or
special bus loading surveys, would be needed to provide firm data for
estimating revenue loss from stopping a service short.
lll
8.4 Taking action in response to short-term trends The cost and revenue reports which
were shown in Tables 6.1 and 6.2
are not intended to be used for monitoring short-term trends in either
revenue or cost and relating them to routes. The effort required iu
the reports' preparation, involving as it does detailed analysis in
accordance with the often complex interrelationships between duties
and routes, is significant.
To the extent that more frequent information would be of
value for management, more economical, but perhaps less route-specific,
methods of analysis should be sought.
For example, revenue could be simply monitored in MPTE by
totalling the cash revenue takings of crews who have worked during the
day on one set of duties. These correspond approximately to routes in
most instances so that significant changes in takings by duty sheet
would quickly direct attention to the need for further investigation,
and limit it to one or a few routes.
The monitoring of short-term changes in costs could serv e
two purposes related to route costing:
a)
b)
to make it possible for management to ensure that variable overheads are changed appropriatelY in response to service changes, and
to provide revised estimates of the unit costs required for planning purposes.
Additionally, the figures could beused to direct attention to
significant changes requiring management action.
112
APPENDIX 1
PARTICIPANTS IN THE STUDY
STEERING COMMITTEE
Department of the Environment
Dr. F.V. Webster
Mr. J.K. Welsby
Mr. T.M. Coburn
Dr. P.H. Bly
Mr. D.R.C. Hepburn
Transport and Road Research Laboratory
Headquarters
Transport and Road Research Laboratory
Transport and Road Research Laboratory
Transport and Road Research Laboratory
Merseyside Passenger Transport Executive
Mr. B.B.P. Kinsman Financial Manager
National Bus Company
Mr. A. Beetham Group Executive, Planning
PROJECT TEAM
Arthur Andersen & Co.
Mr. D.R. Kaye
Dr. J.W. McClenahan
Mr. D.R. Holman
Mr. R. Sturman
Partner
Project Manager
Consultant
Consultant
Merseyside Passenger Transport Executive
Mr. J. Bidewell Management Accountant (Liaison Officer)
Miss M. Ewing
M i s s M. M c N a l l y
113
APPENDIX 2
CREW COSTS: MODELS AND REGRESSION ANALYSES
I Aims of the analyses As described in Chapter 4, we were aiming
to establish coefficients A and B for
weekdays, such that we could describe the number of crew hours needed
to pay for any given duty sheet's mix of peak and offpeak bus hours
as:
Crew hours paid
= A x peak bus hours
+ B x offpeak bus hours
withacceptably small discrepancies between the crew hours paid as
calculated from this equation on the one hand, and as derived from the
scheduled payments made for the duties on the duty sheet, on the
other hand.
A similar relationship was sought for weekend work (extra
is paid for Saturday afternoon and Sunday work) of the form:
Crew hours paid (weekend)
= C x Saturday morning bus hours
+ D x other weekend bus hours.
2. Models With this aim in mind, we could choose between several
different regression models in our attempts to fit the
observed data.
1!4
For economy of notation in describing the models, we write:
PAIDHOURS
PEAK
0FFPEAK
TOTAL
= Drew hours paid
= Peak bus hours; i.e. bus hours • operated in weekday peak periods
= Offpeak bus hours; i.e. bus hours operated on weekdays, outside peak periods.
= Total weekday bus hours; i.e. peak plus offpeak bus hours.
Straightforward estimation by a regression model which uses
directly the hours paid and bus hours operated would use the model:
PAIDHOURS = AlxPEAK + Blx0FFPEAK + C1 + E1 (1)
Transformations of this model can be made, to improve the
statistical properties of the error terms, and to minimise the effects
of correlation between the PEAK and 0FFPEAK variables. These
transformations include : •
PAIDHOURS 0FFPEAK
PAiDHOURS PEAK
PAIDHOURS TOTAL
PEAK = A2x----- + B2 + E2
OFFPEAK
A3 + B ̂ OFFPEAK = 3 x P-E~--K + E 3
• PEAK + 0FFPEAK = A4XTOTA L B4x •TOTAL * E4
( 2 )
( 3 )
(4)
In addition, non-linear terms in any of the three bus hour variables
could be added.
In these equations, the A and B coefficients of each under-
lying model are distinguished by s suffix (A1, A2,..., etc.). The "E"
terms (El, E2,..., etc.) denote the residual differences between the
model assumed, and actual observations: the distribution of error
terms and errors in the coefficients will be different for each model.
1i5
For weekend work, the following model was used:
PAID HOURS = C + DxOTHER WEEKEND + E5 (5) SATURDAY A.M. SATURDAY A.M.
3. Results obtained The costs and coefficients of Tables 4.1 to 4.3
were based on results from models (2) and (5).
Separate regressions were performed for duty sheets representing
"block timetables" and those representing "extra duties". The former
consist predominantly of work on one or a few routes, each duty
msually working on only one route. The latter contain duties working
on several routes , mostly during peak periods.
The results from the two sets of duty sheets were not very
different (see Table A1), but we noted that the extra-duty sheet
coefficients wer~ somewhat higher both for peak and for offpeak work:
this distinction seemed worth preserving in the costing. We have
done this in all calculations of route cost and for Table 4.1, but
Table 4.2 showed only a weighted average approximation, for simplicity
of exposition.
Figures A1 and A2 show graphs of the fit of model (2) to the
two sets of data. When plotted, some points overlapped, so the number
of points appearing on the graphs is slightly smaller than the number
of observations.
i16
Separate analyses of each of MPTE's three operating
divisions showed no significant differences between divisions.
L
Trials of model (I) showed that the constant term ci was
not significant, and since its presence would have complicated the
c o s t i n g p r o c e d u r e s , model (1) was n o t a d o p t e d .
Model (3) was not pursued. Our understanding of the way
in which a higher proportion of peak working leads to more spreadover
duties, and hence higher payments, indicated that it was less suitable
as a model of the underlying process.
Model (4) has the drawback that the estimation of the error
of A4 is more difficult It was not used in this exercise, although
we are considering itJin connection with a simpler method of analysis
based on individual duties.
Residual analyses The distribution of residuals from model (2)
showed no marked deviation from normality,
and was uniform Over the range of variation of peak/offpeak rstlos.
There was no evidence of non-linearity in the relationship, over a
rang e of ratios of peak to offpeak bus hours from 0.4~I to over 4:I.
Residuals were mostly less than 5% of the value of crew
hours paid.
lit
~ TABLE. AI
COEFFICIENTS OF CREW HOURS PAID PER BUS HOUR
(Figures in parentheses show the standard errors of the coefficients)
Weekday Block Timetables Extra Duty Sheets
.96 2.12 A. Peak (~.ll)_ (0.09)
B. Offpeak 1.03 (0.07)
1.15 (o. 34)
Weekend All Duty Sheets
C. Saturday before 1300 I .34 (o.i~)
D. Remainder of weekend 1.96 (0.09)
118
0 .(Z
o
2 0 ¢-
3"50
3.25
3-00
2"75
2"50
2"25
2"00
1"75
1"50
1"25
0 I
0
/
y=-.
/7" 0.2 0"4 0.6 0"8
Peak bus hours /Of fpeak bus hours
P
! ' 0 1"2
Fig. A1 BLOCK TIMETABLES, CREW HOURSPAID/OFFPEAK BUS HOURS V.S. PEAK/OFFPEAK RATIO
119
co
O t -
co r~
¢0
CZ
o
¢o Q.
O ¢-
C)
20
18
16
14
12
10
8
/. 4
2
~ O N
/- y w
qP A J
0 2 4 6 8 10
Peak bus hours / Offpeak bus hours
12
Fig. A2 E X T R A D U T Y SHEETS: CREW HOURS PAID/OFFPEAK BUS HOURS V.S. P E A K / O F F P E A K RATIO
! 2 0
APPENDIX 3
DEFINITIONS OF TERMS
i. Bus hours, bus miles and peak buses "Bus hours" are those hours during
which a bus is crewed and out of the
garage. "Bus hours" include time spent driving between the garage
and the starting point of route service, and layover time.
"Bus miles" are the miles covered by the bus during its
bus hours of operation, as defined above.
Bus hours and bus miles can both be subdivided by the
time period during which they are operated.
"Peak buses" are the number of buses required for service
during the period for which the bus company's requirement for buses is
at its height. For MPTE, there is an hour in the morning peak (0745
to 0845) and an hour in the evening peak (1645 to 1745) for which this
requirement is within 1% if its absolute maximum. We define the average
peak bus requirement as the number of bus hours operated during this
period, divided by the length of the period. In this way, services
3 which require a bus for only (say) ~ hour of the 2 hour period are
charged only with 3/8 of a "peak bus": the remaining 5/8 of a "peak
bus" will be charged to some other service, which uses the bus during
the remainder of the 2 hour period.
121
The usage of bus hours, bus miles and peak buses can be
calculated for a route, duty sheet, garage, or any other subdivision
of the bus company's operation, or for its operations in total, as
is appropriate.
2. Paid hours Scheduled paid hours are the hours for which a bus
company schedules to pay its crews, assuming no
rest day working and no service cuts. The paid hours are a function
of the union agreement. In the case of a company with an unconsolidated
union agreement, the scheduled paid hours may be calculated for each
duty from the agreement and the duty sheets. Actual paid hours take
account of understaffing and service cuts, to reach the actual number
of hours paid for each category of staff.
3. Summary of MPTE Operating Agreement (as effective at ist December 1973)
Basic Rates
Crew Driver Crew Conductor SDOMO Driver/Operator DDOMO Driver/Operator
Hourly Rate (units)
1.00 0.98 approx. 1.20 1.25
Notes:
1.
2.
3.
Rates vary by approx. 1% dependent on length of service.
Basic PAYMENT is for 8 hr. day regardless of hours worked.
Basic WORK may be any period up to 8 hours 24 mins. but must average no more than 40 hours over 5 day week - any duty shorter than 7 hours 45 mins. counts as 7 hours 45 mins. for averaging.
122
Penalty Rates (as a fraction of basic rate)
Saturday Working after 1300 Sunday Working Public Hols. (excl. Good Friday
and Christmas Day) Good Friday and Christmas Day Night Duty (Cbmmence post 2200;
Finish pre 0800) (Not cumulative for O/T etc.)
Early Morning Duty (pre 0530) Delay Time (Breakdown, fog etc.) Spreadover Duties (i.e. duties
exceeding 8 hours 24 mins. in overall length):
First ½ hr. or part thereof of the excess
Each further ½ hr. or part thereof
Note - 0nly the highest penalty rate applies: are not compounded.
Overtime
All overtime worked (rounded to ½ hr. above)
Minimum Payments (Gross)
No break between duty & overtime As above but if finish time later
than 2400 Call out - pre 1159 Call out - post 1200 Rest Day - no work performed Rest Day work performed
Attendance Bonus
Paid unless late, on vacation, sick etc. (paid weekly)
Service Payment
Payment depends on length of service Minimum (over 6 months) Maximum (over 20 years) (paid half-
yearly)
they
Hourly Rate (units)
1.50 1.50
1.50 2.00
1.25
1.00
1.50
Fixed Payment
0.25 hr.
0.50 hr. 0.25 hr.
1 00 hr.
2. O0 hr s. 4.00 hrs. 3.00 hrs. 4 • O0 hr s. 8.00 hrs.
55p/week
50p/week
150p/week
123
4. Duties, duty sheets and duty rosters in MPTE A "duty" is a day's work for a bus
crew. Scheduled overtime of less
than a full day's work is a "duty piece" and may be usually attached
to a full duty to be worked with it. Any part of a duty (e.g., half
of a spreadover duty) may also be called a "duty piece".
Duties are collected together into "duty sheets". Separate
duty sheets are prepared for weekdays, for Saturdays, and for Sundays.
Duties on a "block timetable" duty sheet work generally on one route,
or a few routes. Duties on "extra" duty sheets provide additional
service to a variety of routes, mainly to cover peak work requirements.
Duty sheets for weekday, Saturday and Sunday for each route
group are linked together to form directly the "duty roster". Each
crew works on successive days a duty with a number one higher on the
duty sheet, taking the weekday, Saturday, or Sunday sheet as appropriate.
Days off are allocated so as to provide fewer crews on Saturday and
Sunday, since these duty sheets require fewer men thsn the weekday
sheets to which they are linked.
5. Bus running boards A bus running board is one day's work for
a bus. It links together journeys on routes:
some running boards provide for operation on only one route, others may
cover several routes. Running boards may be classified into one of
four types (on weekdays) :
m all day, from early morning to late evening
124
daytime only, from just before the start of the morning peak, to just after the evening peak
peak only, providing work mainly in peak periods
miscellaneous.
The last category includes a few special types of board,
such as (to give one example) those on a route where service is not
provided in the early morning or in the evening, and where each board
corresponds to one duty only.
. Apportionment of layover and dead time ("out of service working")
I. 0nly true out of service working is counted in "bus hours"
i.e. standby duties and off-duty pieces of split shifts are
omitted from bus hours (but not from "hours paid").
2. Where only one route has been worked in a duty piece, all
out of service working is allocated to that route.
3. Where out of service working is at an end of a duty piece,
that out of service working is allocated to the route worked
adjacent to the end of the duty.
4. Where out of service working occurs between two segments of
work on the same route, the out of service work is allocated to
tha~t route.
5. Where out of service working occurs between two segments of
work on different routes any apportionment is by nature arbitrary.
].25
The following rules were used in MPTE.
a) If the period of out of service working is an even number of busquarter-hours,* the period was divided by 2 and apportioned equally to the two routes.
b) If the period of out of service working is an odd number of bus quarter-hours, the period has been split so that the route where the segment of working contains the larger proportion of peak working (or if neither contains any peak working the segment which begins or ends closest to the peak periods) was charged with the odd quarter hour, and the remainder was allocated equally between the routes.
In a system which calculates to the nearest minute, the out
of service bus hours can be allocated between routes in proportion to
the bus hours worked on each route during the duty.
7. Types of fare collected
I. Cash Money collected by the conductor or driver/operator
at the time of travel.
2. B.E.T. (Bus Economy Ticket) Purchased from an agency before
travel and valid for l0 journeys although costing
the equivalent of 8 times the single fare. Cancelled by machine
on the bus.
3. Scholar's Pass Fixed sum collected from Local Education
Authority. Valid for schooldays only,
and only at specified times.
All our bus hour calculations were rounded to the nearest quarter hour.
126
4. Scholar's Permit Fixed sum collected from Local Education
Authority. Validity as for Scholar's
Pass. Allows scholars over fifteen living within three miles
of their place of study to travel at half fare.
5. OAP Passes Issued free to OAP's for unlimited travel
offpeak.
6. TraVellers' Tickets Issued by MPTE offices for fixed sums
dependent on duration of validity (one
week or one month). Valid at all times on all bus, train and
ferry services within the MPTE boundaries.
127
ADDENDUM
FURTHER ANALYSIS AND APPLICATION OF THE METHOD
i. INTRODUCTION
1.1 Purposes of this additional work The work reported in this
addendum had four
purposes:
a)
b)
c)
d)
to give increased confidence that the structure of the costing system developed for MPTE could be applied in other companies;
to attempt to replicate our findings on crew costs in two other PTEs;
to attempt to identify differences in weekday offpeak crew costs at different offpeak times of day, in MPTE;
to develop methods of analysing weekday peak and offpeak crew costs which will be simpler to apply than the method described in the main report.
1.2 Reasons for addendum format All of these purposes except
the first were identified by
the Steering Committee at a late stage in the study, when the main
report structure was basically complete. The central theme of the
main report - development of an overall cost structure and the
identification of major differences between peak and offpeak crew
costs - is not affected by the results of these further
investigations, and it therefore seemed more appropriate to report
them in the form of an addendum.
Because fulfilment of the second purpose b) required
analysis of data from the two PTEs visited, it was felt appropriate
by the Steering Committee to include also our other findings from
our visits to these PTEs in the addendum, responding to purpose a).
128
r
1.3 Structure of the addendum Section 2 of the addendum
summarises the extent to which
the purposes of the additional work were fulfilled.
The achievement of the first purpose is covered in the
summary. Sections 3 and 4 expand on the Summary for the purposes b)
and c) respectively, and Appendix 2 describes the simpler method of
analysis which we have developed in response to purpose d).
r
129
2. ADDENDUM SUMMARY
2.1 Applicability of cost structure to other PTEs Based on our analysis of
schedules data provided by
Greater Glasgow and Selnec* PTEs we were able to confirm our
Merseyside finding of consistently higher crew costs in weekday
peak periods, and hence the need for the cost structure to
recognise different effective crew costs in peak and offpeak periods.
Our discussions with officers in these PTEs indicated
no reason to expect that other aspects of our cost structure
would be difficult in principle to apply to their operations.
On two specific issues which had given us concern in
Steering Committee discussions, the treatment of some engineering
costs, and the problems of allocating the costs of duties worked
on several routes to the routes concerned, the two PTEs had similar
practices to those in use in MPTE:
a)
b)
Cleaning, servicing and routine maintenance are performed on an elapsed time basis in all three PTEs.
Both Glasgow and Selnec have route structures which also exhibit the pattern of one duty working on several routes which we found in MPTE, and which led us to our method of finding standard unit costs per bus hour of different types in order to apportion the costs of dutyrosters to routes.
Fewer duty sheets/rosters are operated in the other PTE's
than in Merseyside. The crew cost analysis method we used in MPTE
which depended on the availability of data from a large number (63)
Now Greater Manchester Transport
130
of rosters would therefore be more difficult (or impossible) to
apply and interpret in these other PTEs.
We have taken account of this observation in the
development of the simpler method of crew cost analysis reported
in this addendum.
2.2 Peak and offpeak crew costs: Selnec and Greater Glasgow PTE Analysis of existing weekday
duty sheets in Selnec and
Greater Glasgow indicates an effective rate of about two crew hours
paid per bus hour in peak periods, versus about one crew hour paid per
bus hour offpeak. This result is similar to what we obtained in
MPTE.
2.3 Weekday offpeak costs: MPTE We found indications in MPTE
that evening work may incur
somewhat higher costs than other weekday offpeak work (about
10-20%), mainly because fewer bus hours seem to be scheduled in
evening duties than in other non-spreadover duties. However,
this finding cannot necessarily be taken at face value. There
may be some(possibly informal)interaction between the lengths
of day and evening duties which would be upset if evening duties
were changed, so that the present (apparently different) costs
of evening duties are not necessarily attributable solely to
evening work.
131
We did not find any evidence in existing duty schedules
that particularly high utilization of 'hours paid for' is actually
being achieved for the operation of buses during daytime hours
only, as the Steering Committee had suggested might be the case.
We cannot, however, entirely rule out the possibility that
particularly effective use of crew time might be possible for daytime-
only buses. If it occurred, this would allow the addition of offpeak
bus hours between the peaks at very low extra cost over and above
the existing payment for the same bus, operated only during the
peaks.
2.4 Simplified method of analysis Our analysis of crew costs
for Selnec and Glasgow PTEs
was successfully performed on individual duties, not (as in our
original MPTE analyses) on whole duty sheets. This opens the
possibility of extending the crew cost analysis method for
differentiating peak and offpeak crew costs to the operations of
small as well as large companies, or to companies like Selnec and
Greater Glasgow PTEs which operate larger rosters, and hence have
fewer of them on which to base analysis.
We believe that the simple method can be applied with
a degree of confidence which is considerably enhanced by our earlier
method's success, and vice-versa.
132
We envisage that it would be applied to as much of the
company's operations as it is desired to cost. Before using the
results of the simpler method to calculate the different crew costs of
peak and offpeak work, it is important to check that the conditions
of Chapter 4 for validity of the results are fulfilled. In particular,
it would be dangerous to base results on the study of individual
duties without checking-
a)
b)
c)
that the results are compiled for sets of duties worked by a group of men who usually work those duties between them;
that analysis of different groups shows reasonable consistency in the peak and offpeak coefficients between groups,• and that the average mixture of peak and offpeak work is sufficiently different between groups to give confidence that the coefficients deduced from the analysis would be valid for significant changes to the mix in any one group;
that the system of penalty payments for spreadover working has not been consolidated or partially consolidated to the extent that peak/offpeak mix changes could not be implemented without changes to the form of payment and/or the union agreement. This will be particularly important to check if the system of spreadover payment is very different from that which was found in the three PTEs studied.
133
3. PEAK AND OFFPEAK CREW COSTS
3.1 Comparison between the three PTEs Table I shows the coefficients we estimate
for the hours paid per bus hour in each of
the three PTEs. The results indicate a perhaps surprisingly close
correspondence, with the peak coefficient roughly twice the offpeak
in all cases, except for Glasgow's Partick garage for which the
number of duties, and the range in the proportion of peak working,
are too limited to allow satisfactory estimation of a peak
coefficient.
The results are obviously dependent in each company on
both the nature of the union operating agreements, which determin~
the amount paid for duties worked, and on the amount and timing of
peak working, which in conjunction with scheduling practice gives
rise to the duties themselves. Some relevant features of the
union agreements in Selnec and Greater Glasgow are summarised in
Appendix 1.
We have not attempted to relate differences in
coefficients to characteristics of the peaking pattern and the
union agreements, on the basis of such a small sample, but this
might be a suitable subject for further research based on a
wider range of observations.
134
o2 +~
0 ~o
0
,%
2 m
m
g m
~ . ~
%
g .,-i
÷~
E3
O3
O3
03
0
g~
0~
w~ oo
o
~v
:: -,-4 0
"~=o ~ v
o ~
r~ ~-~0
0 0" , ' 4
0 0
~; o
A
o g ~ ~. % ~ ~; ~ ~ .2 o o
. g o g ~ ~ ~ ~ o 0 =-¢
,-.4 0 0 0 ,..4
o ~ ~ ~
d d d
¢q
,.¢:;
0 ~ !
=o
0
"g "2 0
E E
.,.4
°,-4
o *~
¢0
• . 0 4-~
o • r,O
. , q +~
,%
.,.-I
q) °,.-i o3 ~ ~
~ v . ' 4 ~
o l
~ 2 • ,4 ~'1
,...1
m ~
~ g 0 ,% = ,%
. + *
135
3.2 Method of analysis Figures 1 to 4 show graphically the
observations from which the coefficients
for Selnec and Greater Glasgow were deduced. The underlying model
assumed is:
crew hours paid
total bus hours operated = (A - B)xpeak bus hours
total bus hours + B + residual
This model was applied to the observations to estimate (A - B) and B.
The coefficients A and B have the same meaning as those described in
Chapter 4 of the main report: they are respectively the crew hours
paid per peak bus hour and per offpeak bus hour: i.e.,
crew hours paid = A x peak bus hours + B x offpeak bus hours
The graphs for Selnec and Greater Glasgow PTEs show the way in which
the amount paid per bus hour for a duty increases with the
proportion of peak working, and the tendency for high proportions
of peak work to be associated with more spreadover working.
3.3 Conclusion The similarity of results between PTEs and their
similarity also to LTEs and MoT results* give
increased confidence in the validity of our MPTE findings. However,
the three companies in which the methods of analysis have been
applied are somewhat similar: all are PTEs, all operate mainly stage
carriage services in urban areas, and all have union agreements
permitting spreadover working subject to penalty payment.
* referenced in the main report at the end of Chapter 4.
136
We expect that the simple method of analysing peak and
offpeak crew costs, based on analysis of individual duties, can be
applied in most companies with unconsolidated union agreements.
However, only further application in a wider variety of companies can
establish the wider generality of the results.
137
4. WEEKDAY OFFPEAK COSTS IN MERSEYSIDE PTE
4.1 Analysis of buses' operation It was suggested by members
of the Steering Committee that
the effective crew cost per bus hour might differ not only between
peak, offpeak and weekend work, but also at different weekday offpeak
periods of the day. In particular it was suggested that a bus
operated "daytime-only" from before the morning peak to just after
the evening peak (but not throughout the evening) might make
particularly economical use of the time available from two full
crew duties. If this were the case, then additional offpeak work
between the peaks could be obtained very cheaply by converting
the operation of a bus working at present only in the peaks, into
a full daytime-only bus operating as just described. Substantial
additional bus hours would be obtained at relatively low cost, by
replacing payment for one (expensive) spreadover duty by payment for
two (relatively cheap) ordinary duties.
In order to examine this question, we analysed the staffing
of bus running boards at the pilot garage. That is to say, we drew
time diagrams (see Figure 5 as an example) showing the operation of
each bus, the duties which covered that bus's operation, and the
"excess" amount paid for its operation.
The "excess" amount paid is the difference 0etween crew
hours paid and bus hours operated, for the operation of eac~ bus
running board.
138
If the hypothesis were correct then the "excess" amounts
of payment per bus should be lower for daMtime-onlY buses than for
peak-only buses.
4.2 Results of this analysis We found no evidence at the pilot
garage that the suggested economies
are being achieved in practice in existing MPTE schedules.
The average peak-only bus provides 5.5 bus hours* at •an
average excess of 3.0 hours paid per bus.
The four existing daytime-only buses, staffed by two full
duties, provide i 13~ bus hours each, for an average excess of 2.9
hours per bus. Five other daytime-only buses are run, staffed by
a mixture of ordinary and spreadover duties,• which incur a slightly
higher average excess of 3.1 hoUrs. ....
Conversion from peak-only to daytime-only would therefore
provide an extra 7¼ bus hours, but at an additional cost of 7.9 [
hours paid (payment for one whole additional duty, less the saving
in excess hours of O.1 hour). This is not significantly different
from the offpeak cost previously derived.
4.3 Higher costs of evening duties We have analysed two of MPTE's
duty sheets in the same way
as was done for Selnec and Greater Glasgow PTEs - i.e.,by plotting
"crew hours paid per bus hour" versus the "ratio of peak to total bus
hours" .
* For operations in both peaks. Several boards only run in one peak, and have been excluded from these calculations.
139
These analyses (see Figures 6 and 7) show an apparently
higher cost per crew hour £or evening duties; about 10-20% higher
than that for offpeak work as a whole deduced from our former
method of analysis. However, as described in the Summar~ this
result cannot necessarily be taken at face value.
0
.D
0 ).,-
" 0
Q..
0 t -
O
(/)
3 0 ¢.-
(/)
" 0
O.
0 t -
O
2-0
1"8
1-6
1"4
1"2
1.0
0 0
2"0
1"8
1-6
1"4
1"2
1"0
0 0
SELNEC "C" ROTA (2- MAN)
I
DUTY TYPE !
• Ordinary
O Spreadover
• C
• og • " j Y I
0
0 0 0
O
0
Io
0.1 0"2 0"3 0"4 0"5
Peak bus hours /Total bus hours
0"6
ADDENDUM Fig.1
SELNEC
" O " ROTA (O.M.O.) I
DUTY TYPE
• Ordinary
0 Spreadover
• OoC~ ~
0"7
0-1 0"2 0"3 0"4 0"5
Peak bus hours / Total bus hours
0.6 0 .7
A D D E N D U M F ig .2
141
0 e -
(13
0 r "
r . . )
P 0 e -
e-J
~o
0 .
.-s 0 e -
P ¢.)
2"0
1-8
1"6
1"4
1-2
1-0 I I I I I I
0 o
2-0
1.8
1.6
1-4
1"2
GR~T~R ~'~SGOW PAI~TICK (O.1~.O.)
I I
I DUTY TYPE
• Ordinary
O Spread over
O •
• e . o 9 • . - - - , • v U
0"1
a O
0"2 0"3 0'4 0-5
Peak bus hours / Total bus hours
0-6 0-7
A D D E N D U M F i g . 3
GRE~TER G'A~GOW GARTCRAIG (2 ' MAN)
I I
1.0 !
I I I I I
0 ' 0 0"1
• DUTY T Y P E
• Ordinary
O Spread over |
)
0 ~ • •
CI 0 _.,
J
I •
O J
0"2 0"3 0"4 0"5
Peak bus hours /Total bus hours
0-6 0-7
A D D E N D U M F i g . 4
1 4 2
0
X W 0 . . ~
0
0
0
X
0
_.1
Z 0 V
LU
i:~ ,o
E
~_ 1"- 0') ~ 0
UJ
i - " C~ - J ..J
I I I ill " I. ' I ° I ' II II ii~irJli~Jiiiiii • , . 0 ° • .
• ~ i i i . . ~ . : ! . ! i I i i l e . ,
I i ' " " i;I i.i Jii I II, I! I! ~ , ~ J . . . . !"! .!i! "~ g . ~ ,o .o ~ ~ ~ ~ ® ~ ® ~ , o o ,.. - ~ ~ ~ ~ . , - , ~ ,,-; .o o ,,. o. , - . . o ® ~ ,,-, ,-, - . .
' . . ,
g
O"
0
- ~1~ ....... ~I ~L~ ',,0
I i
n~
m
o - -
c,,,~ o).
,o .o
,o
.o .o
m
"6
I : : .
Z
1 4 3
0 ¢-
. 0
Q .
0 t -
c)
0
. 0
"10
C). (/)
. 0 t -
O
2-0
1 - 8
1-6
1.4
1"2
1-0
M'ERSEYSI I~E 85 DUTY SHEET
f I Least squares regression line
.°S excluding evening duties
D
DUTY TYPE
A
- - A J l 0
0
n
z~'
Through (daytime) •
Evening
Spreadover
Extra Duty
Overtime
• I : -I
0 0"2 0"4 0"6 0-8 1"0
Peak bus hours/Total bus hours
1-2
A D D E N D U M F i g . 6
2-0
1"8
I-6
| i
MERSEY, SI DE
86/87 DUTY SHEET
"Least squares re clression line - excluding evening duties
1-4 . J , '
~ e , A • • A • • A 9 _
1-2
A
D U T Y T Y P E
• Through (daytime)
1:0 i i i i i i
0 0
f 0 • Evening
0 Spreadover
n Extra Duty
z~ Overtime
I I
0 2 0 4 0 6 0-8 1-0 1"2
Peak bus hours/Total bus hours
A D D E N D U M F ig .7
144
ADDENDUM APPENDIX I
SOME RELEVANT FEATURES OF THE UNION AGREEMENTS
IN SELNEC AND GREATER GLASGOW PTEs
SELNEC
Basic payment 8 hours per duty worked; 40-hour week.
Maximum hours worked in a duty: 8¼ hours.
Spreadover duties For duties with spreadover in excess of
9h 06m, 0.2 hours is paid at basic rate for
every 12 minutes or part of 12 minutes in excess of 9h 06m;
maximum 13h.
To start and finish between 0600 and 2000.
Travelling time: now consolidated into the basic rate.
Sign on/sign off allowance: varies according to location
and type of relief. Could range
in theory from a minimum of 15 minutes for an ordinary duty
relieving on the road at both ends of the duty, using a farebox,
to a maximum of 69 minutes for a spreadover duty relieving
entirely at the depot, for an OMO driver using a ticket machine.
* Based on our interpretation of the operating agreement in force from October 1973, with later amendments as described to us on our visit.
145
GREATER GLASGOW
Types of duty All duties worked in Greater Glasgow PTE are called
"split" duties - that is, there is an (unpaid) meal
break in the middle of every duty.
Spreadover duties are those for which the time between
first starting and finally finishing work during the day exceeds
nine hours and six minutes.
Normal duties The standard work week is five days of eight hours
each. These are paid regardless of the actual hours
worked. Duties must average eight hours or less, and cannot exceed
eight hours fifteen minutes in "weight". The weight of the duty
corresponds to MPTE's definition of "hours worked" - i.e. the time
between sign on and sign off, less lhe unpaid meal b~eak, less any
interval between pieces of duty.
Premium rates Extra is paid for overtime, spreadover working,
Saturday afternoon after 1.O0 p.m., and all day
on Sunday. Former payments for early start, late finish, and
travelling time have been consolidated into the basic rate.
146
S~readover payments Spreadover is paid for if it is in excess of
nine hours s~x minutes, and must not exceed
twelve hours and thirty minutes. Spreadover time in excess of nine
hours and six minutes is paid for according to the following scale:
Up to 24 minutes
Every additional 12 minutes or part of 12 minutes
0.2 hours
0.2 hours additional
Up to a maximum of 3 hours 24 minutes (12 h 30m overall spread) 3.2 hours extra
Saturday after 1300 For any duties started before 1.00 p.m.
a 50% extra for that part of the duty after
1.O0 p.m. is paid, rounded to the nearest tenth of an hour.
For duty started after 1.O0 p.m. four hours extra is paid, or
50% for a duty piece which is less than a full day's work~
Sunday A four hour allowance is paid extra for any full Sunday duty. I
Overtime: scheduled Very little scheduled overtime is workedln small•
pieces. However, "red days" are included in the
duty roster, and are worked (voluntarily) at overtime rates. They
average approximately one day in every eigh t duties. The basic
additional payment for overtime is 50%. However, the details of its
application are somewhat complicated.
Overtime: unscheduled, and method of payment Unscheduled overtime can
be worked either as rest
days, or in addition to other duties. It is subject to a minimum
payment for two hours work plus 50% overtime penalty - i.e., a minimum
of three hours has to be paid for.
On weekdays any full duty worked as overtime pays twelve
hours (eight hours normal plus 50% overtime premium). Any duty
piece less than a full day's work has a 50% penalty added, rounded
to the nearest tenth of an hour, subject to the minimum payment for
two hours basic plus overtime premium.
On Saturdays, for a duty worked entirely after 1 p.m.
as overtime, a four-hour penalty is paid. For a Saturday worked
as a rest day double time applies, and is applied to the eight hours
normal duty plus four-hour premium for Saturday afternoon working
(equals 12 hours) plus 12 hour penalty for Saturday rest day working -
i.e., 24 hours is paid for a full Saturday duty worked as a rest day.
On Sundays, overtime is paid at 50% rate. A full duty pays
eight hours basic, plus four hours Sunday allowances, plus 50% of 12
hours (i.e.,six hours) as overtime penalty - i.e., 18 hours is paid
for a full Sunday duty worked as a rest day.
ADDENDUM APPENDIX 2
ESTIMATING PEAK AND OFFPEAK CREW
COSTS IN OTHER COMPANIES
This appendix describes a method which can be applied in any
company which has an "unconsolidated,' union agreement -- i.e., one
in which different men are paid according to the duties they
actually work, and where there is a significant element of extra
allowance for spreadover working to cover peak periods of
operation.
First, define the "peak" period for the company as a
whole, or for smaller parts of it if these have significantly
different peak periods. A working definition of the peak period
is the period during •which the number of bhses in service exceeds
the midday number by at least half the amount by which the peak
number exceeds the midday number. (See Figure 8.)
Second, group together the scheduled duties which are
worked on weekdays by the same group of men under the same agreement.
Third, for each of these groups, calculate for each duty:
a) the number of crew hours paid (or the duty- related pay, if this is calculated directly);
b) the bus hours operated in the peak period, as previously defined;
c) the totsl bus hours operated;
d) the two quantities
C = crew hours paid (or duty-related pay) per (total) bus hour = (a) ~ (c)
P = proportion of peak bus hours to total : (b)
Fourth, draw a graph for each group of duties, plotting
vertically, and P horizontally, one point for each duty.
149
G) ._o P
C: . m
::3 J ~
, D
E Z /
a.m. peak period
/ Equal
J
Time of day
p.m. peak period ,,= =,J
\
A D D E N D U M Fig .8 DEFINING THE PEAK PERIODS
150
i.
Fifth, examine the resulting graph. If the points tend
t o form a s t r a i g h t l i n e , , t e n d i n g u p w a r d s t o t h e r i g h t , . t h e n t h e r e
exists a simple relationship between crew hours paid and bus hours
operated in peak and offpeak periods. The way of estimating the
r e l a t i o n s h i p i s d e s c r i b e d i n l a t e r s t e p s . I f t h e s t r a i g h t - l i n e
trend is not found, more complicated analysis will be required
than can be described here. . -
To . e s t i m a t e t h e c o e f f i c i e n t s C o r r e s p o n d i n g t o t h e p e a k
and offpeak coefficients 0f Table 4.2 (or of Table 4.1, if duty-
related pay is calculateddirectly), proceed as follows:
EITHER :
Draw a line by eye which best fits the collection of points;
OR :
Perform a simple linear regression analysis of the relation between C and ~, and plot the resulting line on the graph.
The value of C where the line crosses the vertical axis
gives the offpeak coefficient.
To find the peak coefficient , draw a vertical line at ~ = I
(i.e., where peak bus hours = 100% of total bus hours) to meet the
line through the points. The value of C where these lines cross
gives the peak coefficient.
See Figure 9 for these steps.
Before the results can be appliedwith confidence, it is
important to check that the condition s for validity described in
Chapter 4 of the main report, Vol. I, are adequately fulfilled, and
that the checks described in this addendum, (Summar~ section 2.4)
have been made.
7
C
¢ -
a ~
t -
Value of C • • J l . . . . • m I
= peak co e'tticient . " J ~ _ . _ Line f i t t e d ~ ~ • ~ . ' ; through points
. i • o .,,,,,, , ' ' '~ • I
• I O J o • . I I
• • l Vertical line
I
Value of C I
= offpeak coefficient I I I I
I I ~ P
0 1
Peak bus hours/Total bus hours
ADDENDUM Fig. 9 DETERMINING THE PEAK AND OFFPEAK COEFFICIENTS
Printed in England by the Transport and Road Research Laboratory
152
![BUS BUS BUS BUS BUS BUS BUS BUS BUS · Sunday 15 May 2016 Liverpool Street to Colchester, Ipswich, Norwich and branches BUS BUS BUS BUS BUS BUS BUS BUS BUS] 1 1 1 1 1 1 1 1 1 1 1](https://img.pdfslide.net/doc/110x75/5fab4ce2477d2d3adf21016a/bus-bus-bus-bus-bus-bus-bus-bus-sunday-15-may-2016-liverpool-street-to-colchester.jpg)
![BUS BUS BUS BUS BUS BUS - Greater Anglia...London Liverpool Street to Hertford East, Stansted Airport and Cambridge Saturday 3rd December 2016 BUS BUS BUS BUS BUS BUS]]]] ]]]] ]]]]](https://img.pdfslide.net/doc/110x75/5e6fa285aaf29f59f73bda17/bus-bus-bus-bus-bus-bus-greater-anglia-london-liverpool-street-to-hertford.jpg)
![€¦ · Web view2009. 4. 23. · [Cr2O72-] Reverse Rate. A. increases increases. B. increases decreases. C. decreases decreases. D. decreases increases. 31. A small amount of H2SO4](https://img.pdfslide.net/doc/110x75/608f2c47b9e3f5096f2e5efc/web-view-2009-4-23-cr2o72-reverse-rate-a-increases-increases-b-increases.jpg)