Topic No. 9 Facility Location Planning and Environment Thorsten Noss Ulrich Lindner Facility Location Planning
Dec 17, 2015
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
Facility Location Planning and Environment
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:
Introduction and Overview
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):
Introduction and Overview
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):
Introduction and Overview
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:
Introduction and Overview
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:
Introduction and Overview
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:
Introduction and Overview
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
3. Model: Airline Networks and EnvironmentModel: Airline Networks and Environment
4. Transportation Planning and EnvironmentTransportation Planning and Environment
5. SummarySummary
Facility Location Planning and Environment
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.
Model: UFLP and Environment
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
Model: UFLP and Environment
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.
Model: UFLP and Environment
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)
Model: UFLP and Environment
Ii Jj Jjjjijij xfycmin
IiytosubjectJj
ij
,1
JjIixy jij ,,
JjIiyx iyj ,,1,0,1,0
Model: UFLP and Environment
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
Model: UFLP and Environment
- 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
Model: UFLP and Environment
- 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
Model: UFLP and Environment
- 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
Model: UFLP and Environment
- 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
Model: UFLP and Environment
IiytosubjectJj
ij
,1
JjIixy jij ,,
JjIiyx iyj ,,1,0,1,0
jKk Jj
kjIi Jj Jj
jjijij xaxfyc
min
Model: UFLP and Environment
- 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
Model: UFLP and Environment
IiytosubjectJj
ij
,1
JjIixy jij ,,
JjIiyx iyj ,,1,0,1,0
Ii Jj Jjjjijij xfyc
~
min
Model: UFLP and Environment
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
Model: UFLP and Environment
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
Model: UFLP and Environment
- 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
Model: UFLP and Environment
IiytosubjectJj
ij
,1
JjIixy jij ,,
KkCjzx kkj ,,
KkJjIizyx kijj ,,,1,0,,1,0
Kkkk
Ii Jj Jjjjijij zaxfycmin
Model: UFLP and Environment
- 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 ,,
Model: UFLP and Environment
IiytosubjectJj
ij
,1
JjIixy jij ,,
KkCjzx kkj ,,
KkJjIizyx kijj ,,,1,0,,1,0
Ii Jj Jjjjijij xfycmin
Kk
kk zamin
Model: UFLP and Environment
1. Introduction and OverviewIntroduction and Overview
2. Model: Uncapacitated Facility Location Model: Uncapacitated Facility Location Problem and EnvironmentProblem and Environment
3. Model: Airline Networks and Environment
4. Transportation Planning and EnvironmentTransportation Planning and Environment
5. SummarySummary
Facility Location Planning and Environment
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):
Model: Airline Networks and Environment
Example: normal Network Example: Hub-Network
Hub-Location and Environment (1):
Model: Airline Networks and Environment
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):
Model: Airline Networks and Environment
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):
Model: Airline Networks and Environment
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
The Model – Assumptions (2):
Model: Airline Networks and Environment
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
The Model – Assumptions (3):
Model: Airline Networks and Environment
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
The Model – Assumptions (4):
Model: Airline Networks and Environment
• 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
The Model – Assumptions (5):
Model: Airline Networks and Environment
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
The Model – Assumptions (6):
Model: Airline Networks and Environment
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):
Model: Airline Networks and Environment
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):
Model: Airline Networks and Environment
Iixxx iAi
L ,...1TD mm
Iicmm iAT ,...102
Iizi ,...11,0
IicmmfxxxxxxP iTD
iRi
Ai
Ti
Di
Lii ,...10,,,,,,,,,,,
0Am
Example (1):
Model: Airline Networks and Environment
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):
Model: Airline Networks and Environment
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):
Model: Airline Networks and Environment
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):
Model: Airline Networks and Environment
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:
Model: Airline Networks and Environment
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
1. Introduction and OverviewIntroduction 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 Environment
5. SummarySummary
Facility Location Planning and Environment
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
Transportation Planning and Environment
- 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
Transportation Planning and Environment
1. Introduction and OverviewIntroduction 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. Summary
Facility Location Planning and Environment