Topic No. 9 Facility Location Planning and Environment Thorsten Noss Ulrich Lindner Facility Location Planning

Topic No. 9

Facility Location Planning

and Environment

Thorsten Noss

Ulrich Lindner

Facility Location Planning

Contents

1. Introduction and Overview

2. Model: Uncapacitated Facility Location Problem and Environment

3. Model: Airline Networks and Environment

4. Transportation Planning and Environment

5. Summary

Facility Location Planning and Environment

1. Introduction and Overview

2. Model: Uncapacitated Facility Location Model: Uncapacitated Facility Location Problem and EnvironmentProblem and Environment

3. Model: Airline Networks and EnvironmentModel: Airline Networks and Environment

4. Transportation Planning and EnvironmentTransportation Planning and Environment

5. SummarySummary


Introduction:

Introduction and Overview

Only a small proportion of the location literature deals with environmental problems

Environmental problems often include uncertainty

Complexity

Multi-objective models

Not only minimization of cost

Hazardous Materials:


Hazardous materials ...

• include toxic ingredients (explosives,radioactive materials)

• require special treatment

• include a considerable risk for accidents

• can cause significant damage to humans and environment

Multitude of objectives

• asymmetrically distributed risks

• equity as an objective

• different viewpoints and priorities of stakeholders

Planning Hazardous Facilities (1):


Hazardous facilities

• Nuclear power plants

• disposal sites

• chemical processing plants

Single objective models

• focus on distance between facility and population centers

• maximization of the sum of distances

• maximization of minimum distance

Planning Hazardous Facilities (2):


Multi objective models

• minimization of costs

• minimization of public opposition against facility

• minimization of risks

• maximization of equity

• models can include new ways of technology

• tradeoffs between objectives

Planning Hazardous Materials Transport:


Transport mode and vehicle selection problems

• solved with risk assessment studies

• no best mode for all settings

Route planning problems

• minimization of risks, lenghts, costs etc

• again multi-objective problems

Integrated models

• include location and transport problems

• e.g. management of hazardous waste

Reservation Sites:


Selection of natural area reserves

• 1980s: - Simple scoring and ranking procedures

- highest ranked site not always the best

• 1990s: - Integer optimization models

- based on formulations from location science

- identify and evaluate entire sets of sites

- include uncertainty

- not always possible to predict species occurrence

Oil Spills:


Locating capability to respond to disasters / oil spills

• Problem of locating levels and types of cleanup capability

• Allocation problem (points of high spill potential)

• Occurrence of oil spills is uncertain (place, time)

• Large variability in volumes of these spills

• Different cleanup technologies

• Efficiency of the equipment

• Costs of damage to the environment

1. Introduction and OverviewIntroduction and Overview

2. Model: Uncapacitated Faclity Location Problem and Environment



5. SummarySummary


The Uncapacitated Facility Location Problem

- discrete location problem (the number of potential sites is finite).

- related to the field of networks.

- a set of nodes is considered, which are connected to each other.

- the nodes represent given locations of customers on the one hand, on the other hand potential facility sites.

Model: UFLP and Environment

- the sets of nodes share no elements underneath the other.

- the transportation costs of supplying customer i (i I) with a demand

of bn units with shipments from an established facility at a

potential site j (j J) are cIJ money-units.

- If a facility is located at a potential site (j J), fixed costs of fj units

(measured in terms of money) arise.


Assumptions of the model:

- every located facility is of unlimited capacity

- the customer demand can be satisfied by any potentially established

facility

Single-assignment property: Existence of an optimal solution in which no customer is serviced by more than one faciltiy

Decision variables are of binary type, only able to take on values 0 or 1


c11

cIJ

potential facility sites customers

f1

fJ

b1

bi

Type of Problem: How many facilities have to be established and where should they be located, when by satisfying total customer demand

the summation of fixed and transportation costs are to be minimised.


not if 0,

jfacility by serviced is icustomer if ,1ijy

Decision Variables

not if 0,

located is jfacility if ,1jx

Other constituents of the model:

fJ is recognised as fixed cost for locating facility j, for all j J

cIJ represent transportation cost to supply customer i with shipments for eachpair of (i,j)


Ii Jj Jjjjijij xfycmin

IiytosubjectJj

ij

,1

JjIixy jij ,,

JjIiyx iyj ,,1,0,1,0


An extension of the model:

The UFLP with additive noxious effects

- the terms obnoxious and noxious describe detrimental effects caused by operations of a facility

- a differentiation of objectives is made in 'pull' and 'push' objectives

pull-objectives apply to the attractiveness of a facility

push- objectives to their undesirable counterpart


- the undesirable part of a facility will be expressed in a set of K subjects, which push the facilities away from, for example population centers.

- these subjects are affected negatively by the work of a facility

Negative effects could be noise, heat, unpleasant odours, pollution ofair and water etc.

- to express beside attractions also possible repulsions of a facilitiy`s activities, the term ‘semi-obnoxious‘ is introduced


- semi-obnoxious facilities can have an attraction as well as a repulsion to both the customers I and the subjects K

- the set of customers and subjects are not disjoint and may coincidide

Therefore the term individual is introduced being of one or both sets

This leads to a finite set I K of individuals


- the objective-function is added by the term jKk Jj

kjxa

- the coefficient aKJ expresses the (ob)noxious effect on an individual caused by a facility

It is a nonnegative number equaling zero if the negative effect is below a certain distance

- for additive reasons, it is measured in units of money, to become compatible to the transportation costs cIJ


- the push-pull version of the UFLP assumes that each individual is affected by each facility and that these effects are expressed as costs

- also the assumptions of the UFLP in its original form continue to exist


IiytosubjectJj

ij

,1

JjIixy jij ,,


jKk Jj

kjIi Jj Jj

jjijij xaxfyc

min


- It is possible to include the (ob)noxious effect of facility j in the fixed costs of this facility

Kk

kjjj aff~

Defining

leads to the objective-function in its original form

Ii Jj Jjjjijij xfyc

~

min


IiytosubjectJj

ij

,1

JjIixy jij ,,


Ii Jj Jjjjijij xfyc

~

min


potential site j 1 2 3 4 fixed costs fj 4 10 12 14

potentia l site j ind ividual k

1 2 3 4

1 10 + 6 =

16 44 + 0 =

44 32+0 =

32 3 + 1 = 4

2 9 + 3 = 13 8 + 4 = 12 26+2 =

28 17 + 3 =

20

3 3 + 1 = 4 2 + 2 = 4 43+1 =

44 14 + 2 =

16

4 11 + 5 =

16 8 + 4 = 12 29+3 =

32 12 + 4 =

16

5 18 + 2 =

20 7+ 5 = 12 26+2 =

28 18 + 2 =

20

5

1

5

1ij

kkjij fac 72 94 176 90


potential site j individual k

2 3 4

1 0 0 12 2 0 0 0 3 0 0 0 4 4 0 0 5 8 0 0

ijw 12 0 12

jij fw 2 -12 -2


- the previous version of the UFLP assumes that the (ob)noxious effects are additive

- perhaps costs arising from polluting facilities are constant?

- this leads to the question if this assumption is reasonable

- do the negative effects depend on the number of facilities located closely to a subject (individual), or more on the fact whether a facility is sufficiently close to affect an individual?

The UFLP with minimal covering


IiytosubjectJj

ij

,1

JjIixy jij ,,

KkCjzx kkj ,,

KkJjIizyx kijj ,,,1,0,,1,0

Kkkk

Ii Jj Jjjjijij zaxfycmin


- the new binary variable zk expresses whether individual/subject k is affected by any facility

- the coefficient ak denotes the costs of the concerned subject

- the set Ck includes all facilities located close enough to affect subject k

If a facility j Ck is located, zk takes on the value 1 and ak is includedto the objective

If xJ equals 0 for all j Ck , the constraintis redundant

KkCjzx kkj ,,


IiytosubjectJj

ij

,1

JjIixy jij ,,

KkCjzx kkj ,,

KkJjIizyx kijj ,,,1,0,,1,0

Ii Jj Jjjjijij xfycmin

Kk

kk zamin




3. Model: Airline Networks and Environment


5. SummarySummary


Airline Networks (1):

Model: Airline Networks and Environment

International Airlines (Global Player)

• Extensive network

• Destinations all over the world

Hub-and-spoke system

• Extension of some airports to big hubs

• Reduction of non-profitable point-to-point connections

• More transfer-connections

• Higher load factors

• Lower unit cost

Airline Networks (2):


Example: normal Network Example: Hub-Network

Hub-Location and Environment (1):


Trade-Off for the Airline:

• Environmental aspect:

- Maximize distance between hub and population center

- Reduction of negative impacts on population (noise etc)

- Lower airport fees

• Economical aspect:

- Minimize distance between hub and population center

- More direct passengers, who pay more for a ticket

- Higher airport fees

Hub-Location and Environment (2):


Distance between Hub and other Cities:

• On routes to destinations which are relatively close to the hub it is hardly possible for an airline to operate these routes profitabily (e.g. FRA-CGN, FRA-STR)

• Introduction of high-speed railroad links:

• Increasing profits for the airline

• Better for the environment

The Model – Assumptions (1):


Assumptions:

• Airline with a big network: - long-haul network

- feeder network

• Amount of pax for long-haul network is fixed

• Set of potential hub-locations within an area (country)

• Airline has to decide where to locate its hub

• Dependig on chosen location airline has to operate feeder-connections to other locations to transport pax to hub

• When rail-link exists, no air-connection is necessary



Potential Hubs and train-links:

HAM

ZRH

STR

CGN

BER

MUC

BRU

VIE

FRA

AMS

PRG

Long-Haul Destinations:

PAR

ORD

JNB

TYO

NYC DEL

SIN

RIO

HUB



Hub FRA: train-and air-links:

HAM

ZRH

STR

CGN BER

MUC

BRU

VIE

FRA

AMS

PRG

Long-Haul Destinations:

PAR

ORD

JNB

TYO

NYC DEL

SIN

RIO

FRA

Train Link Air Link



• Notations (1):

•Pi = Population at location i

•xi = No. of total pax at hub i

•xL = No. of total pax for long-haul network (fix)

•xDi = No. of direct pax for long-haul-network at hub i

•xTi = No. of transfer-pax for long-haul-network at hub i

•xAi = No. of pax on feeder network (air travel) at hub i

•xRi = Number of pax on feeder network (railway) at hub i



Notations (2):

•fi = Fixed cost for establishing hub at location i

•mD = Contribution margin per direct pax on long-haul network (average)

•mT = Contribution margin per transfer pax on long-haul network (average)

•mA = Contribution margin per air travel-pax on feeder network (average)

•ci = airport fee per pax at hub i



Decision variable:

• zi = 1, if hub is established at site i, 0 otherwise

Relations:

• Airport fee is positively related to no. of population at site i:

• ci := ci (Pi) = α Pi , α > 0

• No. of direct pax is positively related to population around the airport:

xDi := xD

i (Pi) = β Pi , β > 0

• Direct pax pays more than an tranfer pax: mD> mT

• Losses on flights within feeder network: mA <0

The Model (1):


subject to:

1.

2.

3.

I

iiz

1

1

)(1

iiiAi

ATi

TI

i

Di

Di fxcxmxmxmzMax

Iixxx Ti

Ri

Ai ,...1

Iixxx LDi

Ti ,...1

4.

5.

6.

7.

8.

9.

The Model (2):


Iixxx iAi

L ,...1TD mm

Iicmm iAT ,...102

Iizi ,...11,0

IicmmfxxxxxxP iTD

iRi

Ai

Ti

Di

Lii ,...10,,,,,,,,,,,

0Am

Example (1):


Potential hubs i= 1,2,3,4

i=1 (DUS)

Train Link

i=2 (CGN) i=3 (FRA)

i=4 (MUC)

Given:

- margin per direct pax (long h.):

mD = 150 EUR

- margin per transfer pax (long h.):

mT = 120 EUR

- margin per air-feeder-pax:

mA = - 50 EUR

- Total pax for long-haul network:

xL = 300.000

Example (2):


i=1 i=2 i=3 i=4DUS CGN FRA MUC

Population (Tsd) Pi 5,000 3,000 3,000 4,000

Total Pax xi 440,000 380,000 400,000 460,000

Direct Pax ( = 0.02) xDi 100,000 60,000 60,000 80,000

Transfer Pax Long xTi 200,000 240,000 240,000 220,000

Feeder Pax Air xAi 140,000 80,000 100,000 160,000

Feeder Pax Rail xRi 60,000 160,000 140,000 60,000

Pax Long Haul xL 300,000 300,000 300,000 300,000

Airport fee (EUR/Pax) ( = 0.000005) ci 25 15 15 20

Fixed cost (TEUR) fi 5,000 5,000 5,000 5,000

Profit (TEUR) 16,000 23,100 21,800 16,200

Example (3):


Hub: i= 2 (CGN)i=1 (DUS)

i=2

(CGN) i=3 (FRA)

Air LinkTrain Link

i=4

(MUC)

100.000

60.000

80.000

xA2 80.000

+ xR2 160.000

= xT2 240.000

+ xD2 60.000

= xL 300.000

+ xA2 80.000

= x2 380.000

Long

Haul

Network300.000

Example (4):


Hub: i= 2 (CGN) – Calculation of Profit in TEUR:

Profit Direct Pax Long Haul mD * xD2 9.000

+ Profit Transfer Pax Long Haul mT * xT2 28.800

+ Profit Feeder Pax Air-Connection mA * xA2 - 4.000

+ Profit Feeder Pax Railroad 0 * xR2 0

- Cost Airport Fees c2 * x2 - 5.700

- Fixed Cost Airport Fees f2 - 5.000

= Profit Hub at Location 2 (CGN) 23.100

The Model – Conclusions:


The model optimizes both objectives:

• Maximization of profits for the airline

• Minimization of negative effects on population & evironment

Possible modifiations to the model:

• Include distances between potential hubs

• Possibility to allow new railroad-links to be established

• Include public opposition against the growth of an airport as an uncertainty parameter

higher costs or capacity cap




4. Transportation Planning and Environment

5. SummarySummary


Aspects and influences in the field of transport planning

- emissions (exhaust gases) of trucks

Co2-emissions are one aspect contributing to the change of climate

- decision is to be made: which means of transport is considered for the transportation?

are there alternatives for the transportation of shipments?

Transportation Planning and Environment

- also the shipments carried by a means of transport have to be taken into account

differentiation between harmless and hazardous materials

- in a 'normal' transport planning model, the objective is to move products from origins to destinations at minimal costs

these cost apply pricipally to the length of the route


- what happens in the case of an accidental release of hazardous material?

locating optimal routes for the transport of hazardous material has to deal with risks related to a possible release

- the aim is to minimize the exposure to the environment in case of an accident

- also new costs emerge

costs of compensation, costs related to the emission of pollutants






5. Summary


Documents

Topic No. 9 Facility Location Planning and Environment Thorsten Noss Ulrich Lindner Facility Location Planning