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Chapter 9 Resource Allocation 1
Chapter 9Resource Allocation
Chapter 9 Resource Allocation 2
Introduction This chapter addresses:
Trade-offs involved to crash cost Relationship between resource
loading and leveling Some approaches used to solve
allocation problem
Chapter 9 Resource Allocation 3
Critical Path Method – Crashing a Project
One important difference between CPM & PERT: CPM included a way of relating the project
schedule to the level of physical resources trade time for cost, or vice versa Can specify 2 activity times and 2 costs 1st time/cost combination- called normal 2nd combination called crash Normal – usual ‘average’ time, resources Crash – expedite by applying additional resources
Chapter 9 Resource Allocation 4
Allocation problem requires more careful consideration-additional resources?
Many things make crashing a way of life on some projects (i.e last minutes changes in client specification, without permission to extend the project deadline by an appropriate increment)
Careful planning is critical when crashing project – need to consider feasibility of expediting work (e.g equipment availability)
Critical Path Method – Crashing a Project
Chapter 9 Resource Allocation 5
Slope = crash cost – normal cost crash time – normal time
Critical Path Method – Crashing a Project
Where: slope = cost per day of crashing a project
When slope is negative : indicate the time
required for a project is decreased, the cost is increased
Chapter 9 Resource Allocation 6
The dollars per day slope of activities is relevant only if the whole crash increment is useful
Crashing may involve a relatively simple decision to increase groups of resources (labor-shovel, Ditch-Witch Technology)
If do changes in technology tend to produce discontinuities in outcomes and also in cost.
Chapter 9 Resource Allocation 7
Principles to crash a project
1. Focus on the critical path when trying to shorten the duration [resource ready]
1. Select the least expensive way to do it
Chapter 9 Resource Allocation 8
Crashing a Project (E.g Two-Time CPM)
Activity Precedence
Duration, Days
(normal,crash)
Cost, $ (normal,cras
h)
Slope ($/day)
a - 3,2 40, 80 40/-1 = -40
b a 2,1 20, 80 60/-1 = -60
c a 2,2 20, 20 Cannot be expedited
d* a 4,1 30, 120 90/-3 = -30
e** b 3,1 10, 80 -70 (2 days)
*Partial crashing allowed**Partial crashing not allowed
Chapter 9 Resource Allocation 9
A CPM Example
1 2 3 4 5 6 7 8
a c
b
d
e
Normal Schedule, 8 days, $120
Chapter 9 Resource Allocation 10
1 2 3 4 5 6 7 8
ac
b
d
e
1 2 3 4 5 6 7 8
a c
b
d
e
1 2 3 4 5 6 7 8
a cb
d
e
7-day schedule, $160 6-day schedule. $220
5-day schedule, $2601 2 3 4 5 6 7 8
a cb
d
e
4-day schedule, $350
Chapter 9 Resource Allocation 11
Network critical path is a-b-e, project duration is 8 days, normal total cost is $120
The decision about which activities to crash depends on how much to reduce the duration
On the benefit side, some projects have penalty clauses that make the parent organization liable for late delivery- sometimes bonuses for early delivery
Chapter 9 Resource Allocation 12
On the cost side, figure below shows the time/cost relationship of crashing the project
0
50
100
150
200
250
300
350
400
0 1 2 3 4 5 6 7 8 9
Total duration (days)
Co
st (
$)
All crasha + b + 2d + 2e
a + d + 2e - ba + b
a
All normal
Chapter 9 Resource Allocation 13
Fast Tracking
Another way to expedite a project Term used for construction projects Refers to overlapping design and build
phases Design completed before construction
starts,so overlapping will result shortening the project duration
Build before design completed-more design changes
Loss productivity, increased cost, loss time
Chapter 9 Resource Allocation 14
Studies revealed that: more design changes in fast tracking – the
number of project change orders not significantly different than not fast-tracked project
Dependent on effective feed-back and feed-forward communication
Fast Tracking (cont.)
Chapter 9 Resource Allocation 15
SOLVED PROBLEM
Activity
Crash Time,Cost
Normal Time,Cost
Partial crashing
a 3,$60 3,$60
No
b 6,80 7,30 Yes
c 2,90 5,50 No
d 5,50 6,30 No
e 2,100 4,40 Yes
1
2
3
4
a
be
c
d
Find the lowest cost to complete the project in 10 days
Chapter 9 Resource Allocation 16
AnswerCurrent time and cost: 12 days and $210
3
1
2
3
4
a
be
cd0
3
74
5
6
8
12
Since the critical path is a-c-e, we only initially need consider these 3 activities:
a: cannot be crashed
c: can cut 3 days at an extra cost of $40 but only results in project completion by day 11, due to b. To reach 10 days, cut b by 1 day, total extra cost $90
e: can cut e by 2 days for an extra cost of $60 and results in project completion by day 10.
Thus, cut e 2 days at a cost of $60.
Chapter 9 Resource Allocation 17
RESOURCE ALLOCATION PROBLEM
A fundamental measure of the PM’s success in project mgmt is the skill with which the trade-offs among performance, time and cost are managed
The extreme points of the relationship between time use and resource are: Time limited Resource limited
Chapter 9 Resource Allocation 18
RESOURCE LOADING
The amount of individuals resources an existing schedule requires during specific time periods
Resource loading can be illustrated by: Resource usage calendar Modified PERT/CPM AOA diagram (similar
with Gantt Chart) PM responsibility:
Demand for resources does not exceed resource capacities
Ensure that the required resources, in the required amounts
Chapter 9 Resource Allocation 19
Resource Usage Calendar
Chapter 9 Resource Allocation 20
Modified PERT/CPM AOA Diagram(Refer Ch 08 Slide 26)
0 5 10 15 20 25 30 35 40 45
4
1
1 2
3
3
3
5
6 7
1 4
a
(4,0)
b
(2,1)c
(3,1)
dummy
h
(0,2)
d
(0,2)
j
(0,6)
e
(2,1)f
(1,1)
i
(6,3)
g
(1,0)
Chapter 9 Resource Allocation 21
RESOURCE LEVELING Aims to minimize the period-by-period
variations in resource loading by shifting tasks within their slack allowances
Purpose to create a smoother distribution of resource usage
Advantages; Much less hands on management Be able to use ‘just in time’ inventory policy
with right quantity delivered If the resource being leveled is people, it
improves morale and results in fewer problems in the personnel and payroll offices
Chapter 9 Resource Allocation 22
E.g: Network
1
2
3
4
a, 2[2]
c, 5
[4]b, 3
[2]
The activity time is shown above the arc, and resource usage (one resource, workers) is in brackets below the arc.
Chapter 9 Resource Allocation 23
Before Resource Leveling
1 2 3 4 5
10
8
6
4
2
b b
c c
a
c
Days1 2 3 4 5
c
b
a
Days
Work
ers
Act
ivit
y
Chapter 9 Resource Allocation 24
After Resource Leveling
1 2 3 4 5
10
8
6
4
2
a
c
b
Days1 2 3 4 5
c
b
a
Days
Act
ivit
y Work
ers
Chapter 9 Resource Allocation 25
RESOURCE LOADING/LEVELING AND UNCERTAINTY
If happens excess capacity,the alternative that we can consider: Try to level the demand, moving some of it forward and some backward Try to alter the supply of working hours-trade off time between periods of over capacity and
periods of under capacity Might expend additional resources-contract worker for overload period, subcontract the
workload Which cheaper?Delay or subcontract?