FACILITY LOCATION
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Introduction
Transportation / location tradeoffs
Types of location problems
Modes of transportation and routing
Location models
Sources: [1] Chapter 6,
[3] Chapter 7’s supplement
IE 323 Lecture Notes - 5
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FACILITY LOCATION –
introduction
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Product (with its characteristics): has been selected
(thru product selection and design + process design)
Production facility: its capacity (size as well) has
been determined to meet the demand
(thru capacity planning and forecasting)
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FACILITY LOCATION –
introduction
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Next: determine the most economical way to
obtain the product and deliver it to customers.
This includes considerations like:
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Location of the facility relative to locations of the
suppliers and potential customers, and possible
means of transportation
Layout of the facility
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FACILITY LOCATION –
introduction
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FACILITIES (tesisler): buildings and structures where operations
take place.
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Essential in operations planning, since facilities impact operations
due to many factors.
The topic of obtaining and distributing materials and products:
LOGISTICS.
LOGISTICS management: supply, storage, and movement of
materials, personnel, equipment and products within the
organization and between the organization and its
environment.
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Our focus will be: supply and distribution aspects of logistics
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FACILITY LOCATION –
introduction
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Distribution cost in sales: ranges from 10% (in mechanical
equipment industry) to 30 % (in food industry)
Hence
 Locate with care
 Operate supply and distribution with care
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FACILITY LOCATION –
transportation / location tradeoffs
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Logistics tradeoffs:
In service systems without a facilitating good:
 Locate in the vicinity of the customers (medical clinics,
parks, dry cleaners)
 Reach the customers by phone, internet (impact of ICT)
(banks): locate independent of the customers
 Transport the services (concerts, plays, blood donor
vehicles)
IE 323 Lecture Notes - 5
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FACILITY LOCATION –
transportation / location tradeoffs
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Logistics tradeoffs:
In service systems with a facilitating good:
 Product distributed to the customers (internet shopping,
express pizza delivery, Amazon.com)
 Locate in the vicinity of the customers (restaurants)
In goods manufacturing firms:
 Tradeoff between location and logistics costs (minimize
overall logistics costs) 
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FACILITY LOCATION –
transportation / location tradeoffs
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Locating the manufacturing facility closer to the inputs
 Processing natural resources as raw materials:
 Large loss in size / weight during processing.  inbound
transportation cost > outbound transportation cost to the
recipients (mining, steel production)
 Perishable inputs (fish processing, canning)
 Economies of scale for the product in terms of operating costs
 Locating the manufacturing facility closer to the customers
 Immobile product (projects: dams, roads, buildings, bridges). All
inputs carried to the construction site.
 To improve customer service primarily (tire manufacturers close to
car manufacturers)
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IE 323 Lecture Notes - 5
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FACILITY LOCATION –
transportation / location tradeoffs
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Example: Federal Express
Package delivery - in business for over 40 years
650 planes, 42,000 vans
Central hub concept
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Bring packages to Memphis from throughout the world going
to cities for which Federal Express does not have direct flights
Enables service to more locations with fewer aircrafts
Enables matching of aircraft flights with package loads
Reduces mishandling and delay in transit because there is
total control of packages from pickup to delivery
IE 323 Lecture Notes - 5
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FACILITY LOCATIONtypes of location problems
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Types of location problems:
Number and types of facilities
 Single facility vs Multiple facilities (the same type or not)
o Locating one additional facility with N existing facilities
o Locating or relocating N facilities at once (or thru time)
 Number of facilities in the multiple facilities case: known or
unknown (more complex)
Number of products
 Single product vs. multiple products
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Single-channel
multifacility case:
FWRC
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FACILITY LOCATIONtypes of location problems
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Types of location problems:
Alternative sites (select best N sites from M possible alternatives)
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Number of stages
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Specified site (discrete) alternatives vs. unspecified site alternatives
(usually continuous)
Multiple stages. Intervening stages between the production faciliy
and the recipients, as warehouses, distribution centers, wholesalers.
Single-channel vs. multi-channel wrt. the distribution pattern
Number of criteria
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Single vs. multiple
 Cost and service criteria
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FACILITY LOCATION modes of transportation and routing
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The five major modes of transportation:
 Water – least expensive mode, long trips with bulky,
nonperishable items; but slow and limited accessibility
 Rail – shorter hauls than water, small as well as large items,
good accessibility, specialized services (e.g. liquids, cattle,..),
inexpensive
 Truck – short hauls with small volumes to specialized locations
 Air – small, high-value and/or perishable items (e.g.
Electronic components, important paperwork), high speed of
delivery for long distances
 Pipeline (natural gas,..)
IE 323 Lecture Notes - 5
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FACILITY LOCATION modes of transportation and routing
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Transportation planning is complex, taking all pros and cons
of each mode of transportation into consideration.
Major considerations (factors) in transportation decisions
(Table 6.1):
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Cost/unit, total shipment cost, full truckload or less-thantruckload, shipping time, perishability of product during
shipment, risk of failure in delivery promises, protection of
goods from theft, weather conditions, size of the product,
availability of insurance..
Routing problem:
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Number of vehicles, types and their capacities (fleet of vehicles)
Route of each vehicle
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FACILITY LOCATION modes of transportation and routing
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Routing problem:
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One vehicle serving all recipients on one route: travelling
salesperson problem (TSP)
Fleet of vehicles: several vehicles serving all recipients thru
several routes - vehicle routing problem (VRP)
Usually minimize the distance travelled or the cost in VRP
and TSP
Other considerations: balancing the workload among the
vehicles; minimizing the idle or delay time.
IE 323 Lecture Notes - 5
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FACILITY LOCATION three-stage location process
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Regional/international stage:
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Community stage
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Factors to be considered: proximity to customers and suppliers,
labor supply, availability of inputs, environment
Many of the considerations at the regional / international
stage considered again at this stage
Site stage: the actual location of the facility is selected.
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Size, adjoining land, zoning, community attitudes, drainage,
soil, availability of water, sewer, and utilities, waste disposal,
transportation accessibility, local market, development costs.
Cash flow analysis of each candidate site is conducted: labor
cost, taxes, cost of land, cost of utilities and transportation.
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FACILITY LOCATION location models
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Some models may help in finding out better sites.
All models can be used for any of the stages.
Rate-Volume-Distance Transportation Cost Model
Simply the product of the transportation rate (T), the volume
(V), and the distance (D) over all locations (TVD model).
T: cost for the type of transportation needed: ₺/unit volume
(weight)/unit distance –e.g. 5 ₺/ ton-km.
V: volume (weight) being transported
D: distance from the facility to the recipients’ demand locations
i: recipient index. i=1,…, n
C: total cost
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FACILITY LOCATION location models
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Rate-Volume-Distance Transportation Cost Model
n
C   Ti Vi Di
i 1
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Example: Select the best location for a warehouse, among
alternative sites A and B, for supplying the demand of the
recipients below:
W/H site
A
B
recipient
1
2
3
1
2
3
IE 323 Lecture Notes - 5
Ti (₺/ton-km)
10
12
10
10
13
10
Vi (tons)
2
4
5
2
4
5
Di (km)
30
22
9
25
26
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FACILITY LOCATION location models
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Example (cont’d): TVD model
Cost (A) = 10 x 2 x 30 +12 x 4 x 22 + 10 x 5 x 9 = 2106 ₺
Cost (B) = 10 x 2 x 25 + 13 x 4 x 26 + 10 x 5 x 7 = 2202 ₺
Location A has the least cost.
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W/H Location recipient
A
1
2
3
B
1
2
3
IE 323 Lecture Notes - 5
Ti (₺/ton-km)
10
12
10
10
13
10
Vi (tons)
2
4
5
2
4
5
Di (km)
30
22
9
25
26
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FACILITY LOCATION location models
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If locating on a single line: Di dependent on the chosen facility
site on the straight line.
D2
1
V1
T1
2
V2
T2
4
3
V3
T3
D4
D3
V4
T4
D1
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FACILITY LOCATION location models
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The optimal is at one of the localities.
Find the jth location such that
1 n
Ti Vi   Ti Vi and

i 1
2 i 1
j 1
1 n
Ti Vi   Ti Vi .

i 1
2 i 1
j
D2
1
V1
T1
IE 323 Lecture Notes - 5
2
V2
T2
4
3
V3
T3
D1
D4
D3
V4
T4
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FACILITY LOCATION location models
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Example:
i
1
2
3
4
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 TiVi
TiVi
600
600
375
975
480
1455 *
864
2319
2319  1/2  TiVi = 1159.5
No distance was calculated.
2D Space: Make an incremental analysis: a hopeful initial site is
selected. Then it is moved slightly north, south, east and west. Total
cost comparison is made. The process is repeated until no more
improvement.
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Ti
3
2.5
3.2
2.7
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Vi
200
150
150
320
FACILITY LOCATION location models
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Center of gravity method : is another alternative method on 2-D,
finding the weighted average distance from some base point.
If there are no rate or volume weights, then the center of gravity
is just the average distance for the set of recipient locations.
If the volumes or the rates differ among recipient sites, then a
mean is calculated based on the volume or rate-weighted
distances.
If both the volumes and the rates differ among recipient sites,
then their products become the weights.
The mean is found by dividing by the sum of weights.
IE 323 Lecture Notes - 5
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FACILITY LOCATION location models
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Center of gravity method :
Assume xi and yi are the coordinates of the recipients.
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y1
T1V1
N
T2V2
y2
X* 
T3V3
y3
i 1
N
i
xi
i
T V
i 1
i
i
Y* 
T V
i 1
N
i
yi
i
T V
i 1
i
i
x2
x3
x1
T V
N
This optimizes the quadratic objective function:
T V  x  x *
N
Min
i 1
i
i
IE 323 Lecture Notes - 5
i
2
 yi  y *
2
.
Q: what is good about quadratic?
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FACILITY LOCATION location models
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Weighted Score Model : the most general approach of all.
offers a method to combine different concerns like cost
measures, profit measures, other quantitative and qualitative
measures in one combined model.
A weight is assigned to each factor (criterion) depending on its
importance to the manager.
 The more important the criterion, the higher its weight.
A score is assigned to each location alternative on each factor.
Higher score  better result.
Weight (Wi) x score (Si): weighted score on factor i.
Add up the weighted scores for each alternative.
IE 323 Lecture Notes - 5
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FACILITY LOCATION location models
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Weighted Score Model :
The location with the highest weighted score is the best location
site.
N
total weighted score   Wi S i
i 1
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example: Quebec city used the weighted score model in
relocating its blood bank.
How would you assign the importance weights?
IE 323 Lecture Notes - 5
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Example:
clinic location
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IE 323 Lecture Notes - 5
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