SC Design
Facility Location
Sections 4.1, 4.2
Chapter 5 and 6
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1
Outline
 Frequency
decomposition of activities
 A strategic framework for facility location
 Multi-echelon networks
 Analytical methods for location
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2
Frequency Decomposition
 SCs
are enormous
 It is hard to make all decisions at once
 Integration by smart decomposition
 Frequency decomposition yields several sets of
decisions such that each set is integrated within
itself
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3
Frequency Decomposition
 Low
frequency activity, ~ once a year, high fixed cost
– R&D budget
– Capacity expansion budget
 Moderate frequency activity, ~ once a month
– Cancellation of specific R&D projects depending on
experimental outcomes
– Specific machines to purchase
 High frequency activity, ~ once a day, low fixed cost
– What experiments to start / continue today
– What to produce
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4
Facility Location: The Cost-Response Time Frontier
An inventory location based point of view
7-Eleven
Regional
Hi
Local Finished Goods (FG) Inventory
Regional FG Inventory
Cost
Local WIP (work-in-process)
Central
Sam’s Club
Central FG Inventory
Central WIP
Central Raw Material and Custom production
Custom production with raw material at suppliers
Low
Pull the inventory upstream
Low
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Response Time
Hi
5
Service and Number of Facilities
Response
Time
Number of Facilities
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Where inventory needs to be for a one week
order response time - typical results --> 1 DC
Customer
DC
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5 day order response time - typical results -> 2 DCs
Customer
DC
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3 day order response time - typical results -> 5 DCs
Customer
DC
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Next day order response time - typical
results --> 13 DCs
Customer
DC
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Same day / next day order response time typical results --> 26 DCs
Customer
DC
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Inbound and outbound shipping with more facilities
Supplier
Manufacturer
Inbound shipment
Customer
Outbound shipment
Add more facilities.
Supplier
Manufacturer
Distributor
Inbound shipment
Retailer
Customer
Outbound shipment
More inbound shipping and less outbound shipping with more facilities.
Less (inbound + outbound) shipping costs with more facilities,
12
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if economies of scale in transportation.
Costs and Number of Facilities
Total SC Inventory
Facility costs
Costs
Transportation
Number of facilities
No economies of scale in shipment size,
SC covers a larger portion with each facility.
With economies of scale in inbound shipping to retailers.
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Cost Build-up as a function of facilities
Cost of Operations
Total Costs
Percent Service
Level Within
Promised Time
Facilities
Inventory
Transportation
Labor
Number of Facilities
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14
Network Design Decisions

Facility function: Plant, DC, Warehouse:
What facility performs what function
– Packaging at the manufacturer or warehouse
– Should a rental computer return location run diagnostic tests on the returned
computers or should the testing be done at major warehouses?


Question arising from CRU Computer Rental Case done in OPRE6302
Facility location
– Starbucks opened up at UTD student apartments in 2005 but closed in 2006!
– Recall Japanese 7-eleven and their blanketing strategy
– SMU’s experimentation with Plano campus: http://www.smu.edu/legacy .

Capacity allocation
– SOM car park took 80 cars in 2005 and expanded in 2006 to take about 110 cars.

Supply and market allocation:
Who serves whom
– By location: UT Austin serves central Texas students
– By grade: UT Arlington serves undergraduate students
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Strategic Factors Influencing
Location Decisions

Strategic Facilities
Lead facility
Global Customers
Regional Customers
Server
<local-content>
Offshore
<reduced tariffs>
<for exports>
VW plants in Mexico
Serving Latin America
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Suziki’s Indian venture
Maruti Udyog
Source
<low-cost>
Nike plants in Korea
<advanced technology>
Lockheed Martin’s JSF in Dallas
Outpost facility
<Learn local skills>
Facilities in Japan; Toyota Prius
Contributor
<customization>
<development skills>
Maruti Udyog
16
Factors Influencing Location Decisions



Customer response time and local presence
Operating costs
Technological,
–
Availability and economies of scale (fixed operational costs)
»


Infrastructure, electricity, phone lines, suppliers
Macroeconomic,
–
–



Semiconductor manufacturing takes place only in 5-6 countries worldwide
Tariffs, exchange rate volatility, economic volatility
Economic communities: Nafta, EU, Pacific Rim, Efta
Politic, stability
Logistics and facility costs
Competitive
– Positive externalities
»
»
»
»
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Nissan in India develops car suppliers which can also supply Suziki in India.
Toyota City
Shopping Malls
DFW Telecom corridor hosting Alcatel, Ericsson, Nortel, …
– Negative externalities, see the next slide
17
Negative externality:
Market Splitting by Hotelling’s Model
0
a
a
b
1-a-b
1
b
Suppose customers (preferences, e.g. sugar content in coke)
are uniformly distributed over [0,1]
How much does firm at a get, how about firm at b?
If a locates first, where should b locate?
If a estimates how b will locate in response to a’s location,
where should a locate?
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A Framework for Global Site Location
Competitive STRATEGY
INTERNAL CONSTRAINTS
Capital, growth strategy,
existing network
PRODUCTION TECHNOLOGIES
Cost, Scale/Scope impact, support
required, flexibility
COMPETITIVE
ENVIRONMENT
GLOBAL COMPETITION
PHASE I
Supply Chain
Strategy
PHASE II
Regional Facility
Configuration
PRODUCTION METHODS
Skill needs, response time
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REGIONAL DEMAND
Size, growth, homogeneity,
local specifications
POLITICAL, EXCHANGE
RATE AND DEMAND RISK
PHASE III
Desirable Sites
FACTOR COSTS
Labor, materials, site specific
TARIFFS AND TAX
INCENTIVES
PHASE IV
Location Choices
AVAILABLE
INFRASTRUCTURE
LOGISTICS COSTS
Transport, inventory, coordination
19
Comparing Locations Objectively
According to McKinsey Global Institute on HBR Jun. 2006 p.91


Draw up a list of possible locations
Define the decision criteria
– Six common criteria used by companies
»
»
»
»
»
»


1. Cost of operating
2. Availability of the skills
3. Sales potential in the adjacent markets
4. Risk of doing the business
5. Attractiveness of living environments
6. Quality of infrastructure
Collect data for each location
Weight the criteria
» Fortisbank of Belgium, wants to enter new large markets, gives highest weight to 3.
» Citibank, wants a location for a captive IT center, gives the highest weight to 4.



Find risk data at
– Economist intelligence unit: www.eiu.com
– UN Development Program: http://hdr.undp.org/statistics/data/
Rank locations according to weighted sum of their scores
Assess the dynamics of the labor pool
» Availability of skilled labor
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– Top tier universities in the cities (How many top Business schools in Dallas?).
20
Analytical Models for SC Design

Objective functions
» Private sector deals with total costs

minimizes the sum of the distances to the customers
» Public sector deals with fairness and equity


minimizes the distance to the furthest customer
– Location of emergency response units
Demand allocation
» Distance vs. Price vs. Quality: Recall Hotelling model
Demand pattern over a geography: Discrete vs. Continuous
 Feasibility check

» Ante vs. Post

Distances
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» Euclidean vs. Rectilinear
» Triangular inequality
21
Network Optimization Models
 Allocating
demand to production facilities
 Locating facilities
 Determining capacity
Key Costs:
•Fixed facility cost
•Transportation cost
•Production cost
•Inventory cost
•Coordination cost
Which plants to establish? How to configure the network?
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A transportation network
Defined by data K, D and c
n supply points
m demand points
D1
c11
K1
D2
c12
c14
c22
K2
c23
D3
c31
K3
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c32
c34
D4
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Demand Allocation Model: Transportation Problem
Which market is served by which plant?
Which supply sources are used by a plant?
n
m
Min  cij xij
i 1 j 1
s.t.
Given m demand points, j=1..m
with demands Dj
Given n supply points, i=1..n
with capacity Ki
n
x  D
ij
j
x  K
i
i 1
m
Send supplies from supply points to demand points
xij = Quantity shipped from plant site i to customer j
j 1
x
ij
ij
0
Each unit of shipment from supply point i to demand
point j costs cij
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<See transportation.xls>
24
A transportation network
Defined by data K, D, c and f
Which supply n supply points
point operates?
m demand points
D1
c11
y1=yes or no f1,K1
D2
c12
c14
y2=yes or no f2,K2
c22
c23
D3
c31
y3=yes or no f3,K3
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c32
c34
D4
25
Plant Location with Multiple Sourcing
Which market is served by which plant?
Which supply sources are used by a plant?
None of the plants are open, a cost of fi is
paid to open plant i
n
Min 
i 1
yi = 1 if plant is located at site i, 0
otherwise
xij = Quantity shipped from plant site i to
customer j
m
f y   c x
i
i
i 1 j 1
ij
ij
s.t.
n
x  D
i 1
At most k plants will be opened
n
ij
j
m
x  K y
j 1
m
y
i 1
i
ij
i
i
k
y  {0,1}
i
How does cost change as k increases?
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Plant Location with Single Sourcing
Each customer has exactly one supplier
Which market is served by which plant?
Which supply sources are used by a plant?
n
None of the plants are open, a cost of fi is
paid to open plant i
Min 
i 1
n
m
f y   D c x
i
i
i 1 j 1
j
ij
ij
s.t.
n
x
i 1
yi = 1 if plant is located at site i,
0 otherwise
xij = 1 if market j is supplied by factory i,
0 otherwise
1
ij
m
Dx  K y
j 1
j
ij
i
i
yi , xi , j  {0,1}
Can a plant satisfy the demand of two or
more customers with this formulation?
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Case Study: Applichem Demand Allocation
To Mexico Canada Venezuela Frankfurt Gary Sunchem Capacity
From
Mexico
Canada
Venezuela
Frankfurt
Gary, Indiana
Sunchem
Demand
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$
$
$
$
$
$
81
147
172
115
143
222
30
$ 92
$ 78
$ 106
$ 71
$ 77
$ 129
26
$ 136
$ 135
$ 96
$ 110
$ 134
$ 205
160
$ 101
$ 98
$ 120
$ 59
$ 91
$ 145
200
$ 96
$ 88
$ 111
$ 74
$ 71
$ 136
264
$ 101
$ 97
$ 117
$ 77
$ 90
$ 116
119
220
37
45
470
185
50
28
Applichem Demand Allocation (1982)
Demand
Capacity
220 Mexico
37
Canada
45 Venezuela
30
32
11
45
Gary
50 Sunchem
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Canada
26
Latin America 160
115
200
470 Frankfurt
185
26
Mexico
36
185
119
Europe
200
U.S.A
264
Japan
119
29
Applichem Production Network 1982
(with duties)
Mexico
Mexico
Canada
Canada
Venezuela
Latin America
Europe
Frankfurt
Gary, Indiana
U.S.A
Sunchem
Japan
Annual Cost = $72,916,400
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Applichem Production Network 1982
(without duties)
Mexico
Mexico
Canada
Canada
Venezuela
Latin America
Europe
Frankfurt
Gary
U.S.A
Sunchem
Japan
Annual Cost = 66,328,100
Without duties, Venezuela and Canada plants are closed and
Frankfurt satisfies the excess Canada, Latin America and USA demand.
There is consolidation without duties.
31
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1981 Network
.
Mexico
Mexico
Canada
Canada
Venezuela
Frankfurt
Latin America
Europe
Gary
U.S.A
Sunchem
Japan
Annual Cost = $79,598,500
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1981 Network (Sunchem Closed)
Mexico
Mexico
Canada
Canada
Venezuela
Frankfurt
Latin America
Europe
Gary
U.S.A
Sunchem
Japan
Annual Cost = $82,246,800
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Value of Adding 0.1 M Pounds Capacity (1982)
Shadow (dual) prices from LP tells you where to invest.
Location
Mexico
Shadow price or
Lagrange multiplier
$0
Canada
$8,300
Venezuela
$36,900
Frankfurt
$22,300
Gary
$25,200
Sunchem
$0
Capacity should be evaluated as an option and priced accordingly.
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Gravity Methods for Location
Ton Mile-Center Solution
Given n delivery locations, i=1..n,
ai, bi : Coordinates of delivery location i
di : Distance to delivery location i
Fi : Annual tonnage to delivery location i
Locate a warehouse at (x,y)
<See gravitylocation.xls>
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di 
n
Min 
x, y
i 1
( x  ai)  ( y bi)
2
2
F i (ai  x) (bi  y)
2
n
ai Fi

i 1 d i
x n
Fi

i 1 d i
2
n
bi Fi

i 1 d i
y n
Fi

i 1 d i
36
Chapter 6
Network Design in an Uncertain Environment
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38
A tree representation of uncertainty


One way to represent Uncertainty is a binomial tree
Up by 1 down by -1 move with equal probability
Normal(0, T )
2
 2  (1) 2 (0.5)  (1) 2 (0.5)  1
<Show Applet balldrop.htm>
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T steps
39
Decision tree
– One column of nodes for each time period
– Each node corresponds to a future state
» What is in a state?

Price, demand, inflation, exchange rate, your OPRE 6366 grade
– Each path corresponds to an evolution of the states
into the future
– Transition from one node to another determined by
probabilities
– Evaluate the cost of a path starting from period T and
work backwards in time to period 0.
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40
Evaluating Facility Investments: AM Tires.
Section 6.5 of Chopra.
Plant
US
100,000
Mexico
50,000
Now
Dedicated Plant
Fixed Cost
Variable Cost
$1 M
$15
/year.
/tire
4 M pesos /
110 pesos
year
/tire
Flexible Plant
Fixed Cost
Variable Cost
$1.1 M
$15
/year
/tire
4.4 M pesos
110 pesos
/year
/tire
U.S. Demand = 100,000; Mexico demand = 50,000.
Demand is not to be met always. But selling more increases profit.
1US$ = 9 pesos.
Sale price $30 in US and 240 pesos in Mexico.
Future
Demand goes up or down by 20 percent with probability 0.5 and
Exchange rate goes up or down by 25 per cent with probability 0.5.
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AM
Tires
Period 0
Period 1
Period 2
DU=144
DM = 72
E=14.06
DU=120
DM = 60
E=11.25
DU=120
DM = 60
E=6.75
DU=120
DM = 40
E=11.25
DU=100
DM=50
E=9
DU=120
DM = 40
E=6.75
DU=80
DM = 60
E=11.25
DU=80
DM = 60
E=6.75
DU=80
DM = 40
E=11.25
DU=144
DM = 72
E=8.44
DU=144
DM = 48
E=14.06
DU=144
DM = 48
E=8.44
DU=96
DM = 72
E=14.06
How many states
in period 2?
Consider US demand
4 or 3 states
Consider the rest also
4x4x4 or 3x3x3
DU=96
DM = 72
E=8.44
DU=96
DM = 48
E=14.06
DU=96
DM = 48
E=8.44
DU=80
DM = 40
E=6.75
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AM Tires
Four possible capacity configurations:
•Both dedicated
•Both flexible
•U.S. flexible, Mexico dedicated
•U.S. dedicated, Mexico flexible
Consider the both flexible configuration
For each node solve the demand allocation model.
Plants
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Markets
U.S.
U.S.
Mexico
Mexico
43
AM Tires in period 2: Demand Allocation for
DUS = 144; DMex = 72, E = 14.06
Source
i
U.S.
U.S.
Mexico
Mexico
Destination
j
U.S.
Mexico
U.S.
Mexico
2
Max
2
m
i 1 j1
ij
x ij
Variable
cost
$15
$15
110 pesos
110 pesos
Shipping
cost
0
$1
$1
0
E
Sale price
14.06
14.06
14.06
14.06
$30
240 pesos
$30
240 pesos
Margin($)
mij
$15
$1.1
$21.2
$9.2
1.1=240/14.06-15-1
21.2=30-110/14.06-1
9.2=(240-110)/14.06
such that
2
x
i 1
2
x
j 1
 Dj
ij
ij
Compare this formulation to the Transportation problem.
We maximize the profit now.
 Ki
xij  0
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AM Tires: Demand Allocation for DU = 144;
DM = 72, E = 14.06; Cheap Peso
Plants
Markets
100K; $15
U.S.
U.S.
Profit =Revenue-Cost
Mexico
6K; $9.2
Mexico
US Production’s contribution=100,000*15-1,100,000=$400,000
Mex Production’s contribution=44,000*21.2+6000*9.2-4,400,000/14.06=$675,055
Profit(DU = 144; DM = 72, E = 14.06; Period 2; Both flexible)=$1,075,055
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AM Tires: Demand Allocation for DU = 144;
DM = 72, E = 8.44; Expensive Peso
Plants
Markets
100K; $15
U.S.
U.S.
Mexico
Mexico
6K; $15.4
US Production’s contribution=100,000*15-1,100,000=$400,000
Mex Production’s contribution=44,000*16+6000*15.4-4,400,000/8.44
=704000+92400-521327=$275,073
Profit(DU = 144; DM = 72, E = 8.44; Period 2; Both flexible)=$675,073
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AM Tires: Demand Allocation for DU = 144;
DM = 72, E = 5.06; Very Expensive Peso
Plants
Markets
78K; $15
U.S.
U.S.
Mexico
Mexico
50K; $25.7
US Production’s contribution=78000*15+22000*31.4-1,100,000=$760,800
Mex Production’s contribution=50000*25.7-4,400,000/5.06=$415,435
Profit(DU = 144; DM = 72, E = 8.44; Period 2; Both flexible)=$1,176,235
Cheap Peso profit=$1,075K; Expensive Peso profit=$675K;
Very Expensive Peso profit=$1,176K
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Facility Decision at AM Tires
Make profit computations for the first year nodes one by one:
Compute the profit for a node and add to that
(0.9)(1/8)(Sum of the profits of all 8 nodes
connected to the current one)
Plant Configuration
United States
Mexico
Dedicated
Dedicated
Flexible
Dedicated
Dedicated
Flexible
Flexible
Flexible
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NPV
$1,629,319
$1,514,322
$1,722,447
$1,529,758
48
Capacity Investment Strategies


Single sourcing is risky
Hedging Strategy
– Risk management?
» Too much capacity or too little capacity
» E.g. 200 leading financial services companies are examined from 19972002. Every other company struck at least once by a risky event.

Source: Running with Risk. The McKinsey Quarterly. No.4. 2003.
» Managers unfamiliar with risk often focus on relatively simple accounting
metrics as net income, earnings per share, return on investment, etc.
– Match revenue and cost exposure

Flexible Strategy
– Excess total capacity in multiple plants
– Flexible technologies

More will be said in aggregate planning chapter
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49
Summary
 Frequency
decomposition
 Factors influencing facility decisions
 A strategic framework for facility location
 Gravity methods for location
 Network-LP-IP optimization models
 Value capacity as a real option
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50
Location Allocation Decisions
Plants
Warehouses
Markets
1
2
Which plants to establish? Which warehouses to establish?
How to configure the network?
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51
p-Median Model
Inputs:
A set of feasible plant locations, indexed by j
A set of markets, indexed by i
Di demand of market i
No capacity limitations for plants
At most p plants are to be opened
dij distance between market i and plant j
yj = 1 if plant is located at site j,
0 otherwise
xij = 1 if market i is supplied from plant site j,
0 otherwise
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Min  Di  d ij xij
i
j
s.t.
y
j
j
p
xi , j  y j for all i, j
x
ij
 1 for all i
j
x ,y
ij
j
 {0,1} for all i, j
52
p-Center Model
Replace the objective function in p-Median problem with
Min Max {dijxij : i is a market assigned to plant j}
We are minimizing maximum distance between a market and a plant
Or say minimizing maximum distance between fire stations and all
the houses served by those fire stations. An example with p=3
stations and 9 houses:
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53
p-Covering Model
xi = 1 if demand point i is covered, 0
otherwise
yj = 1 if facility j is opened, 0 otherwise
Ni facilities associated with demand point
i
If j is in Ni, j can serve i
Can you read constraint (*) in English?
Max  Di xi
i
s.t.
y
jN i
y
j
j
 xi for all i (*)
p
j
x,y
i
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j
 {0,1} for all i, j
54
Other Models
 p-Choice
Models
– Criteria to choose the server: distance, price?
 Models
with multiple decision makers
– Franchise model
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