Facility Location
Class 2 and/or 3
1
Objectives






Identify some of the main reasons organizations
need to make location decisions
Explain why location decisions are important
Discuss the options that are available for
location decisions
Give examples of the major factors that affect
location decisions
Outline the decision process for making these
kinds of decisions
Use the techniques presented to solve typical
problems
2
Facility Location Problem
It is difficult to find a single location with all
required characteristics at the desired level
 For example:

◦ A location in Besiktas may offer a highly skilled labor
pool and proximity to customers but land costs may
be too high.
◦ Similarly, another location may offer low tax rates and
minimal government regulations but may be too far
from raw materials source or customer base.

Thus, facility location problem becomes one of
selecting site (among several available
alternatives) that optimizes a weighted set of
objectives.
3
Logistics Management
Logistics management is the management of a series
of macro-level transportation and distribution
activities with the main objective of delivering the
right amount of material (goods) at the right place at
the right time at the right cost using the right
methods.
 Goods:
Raw materials
Subassemblies obtained from suppliers
Products shipped from plants to warehouses or
customers
 Logistics management problems can be classified into
three categories:

4
What are these Categories:
Location Problems:
Location Problems involve determining the location of one or more new facilities
in one or more of several potential sites.
The cost of locating each new facility at each of the potential sites is assumed to
be unknown + operating and transportation cost of serving customers from this
facility-site combination.
 Allocation Problems:
Allocation Problems assume that the number and location of facilities are known
and attempt to determine how each customer is to be served. That is, given

◦
◦
◦
◦
◦
demand for goods at each customer center,
the production or supply
capacities at each facility, and
the cost of serving each customer from each facility,
the allocation problem determined how much each facility is to supply to each customer
center.
Location – Allocation Problems:
Location – Allocation Problems involve determining not only how much each
customer is to receive from each facility but also the number of facilities along
with their locations and capacities.

5
Response Time 1 week-> 1 Distribution Center
Clientes
Centro
distribución
6
Response Time 5 days-> 2 Distribution Center
Clientes
Centro
distribución
7
Response Time 3 days-> 5 Distribution Center
Clientes
Centro
distribución
8
Response Time 1 day-> 13 Distribution Center
Clientes
Centro
distribución
9
Same Day Response --> 26 Distribution
Centers
Customer
DC
10
Response
Time
Response time vs. Number of facilities
Number of Facilities
11
1st Classification of Facility Location Problems

Single-Facility Location Problems
Single-Facility location problems deal with the optimal determination of the location of
a single facility.

Multi-facility Location Problems
Multi-facility location problems deal with the simultaneous location determination for
more than one facility.
Generally, single-facility location problems are location problems, but Multi-facility
location problems can be location as well as location-allocation problems.
2nd Classification of Facility Location Problems
This classification of location problems is based on whether the set of possible
locations for a facility is finite or infinite:

Continuous Space Location Problem
If a facility can be located anywhere within the confines of a geographic area, then the
number of possible locations is infinite.

Discrete Space Location Problem
Discrete Space Location Problems have a finite feasible set of sites in which to locate a
facility.
12



Continuous Space Location Problem
If a facility can be located anywhere within the confines of a geographic area, then the
number of possible locations is infinite.

Because facilities can be located anywhere in a two-dimensional space, sometimes the optimal location
provided by the continuous space model may be infeasible. For example, a continuous space model may locate
13
a manufacturing facility on a lake!
3rd Classification of Facility Location Problems

Solution Technique:
◦ Minimization
 Total cost of setting up and operating the new facilities
(and serving the users)
 The sum of distances to be traveled by the items
 The number of facilities
◦ Maximization:
 Maximize the number of customers to be served
 Maximize the revenue of a facility
◦ Minimax:
 Minimize the maximum distance travelled (eg. emergency
facilities
14
Histogram Method
Cost
SuWater
Enerji
Energy
Vergi
Tax
Transportation
Ulaştırma
Labor
İşçilik
0
A
B
C
Alternatives
15
Weighted Factor Rating Method
Step 1: List all the factors that are important, i.e. have an impact
on the location decision.
Step 2: Assign appropriate weights (typically between 0 and 1) to
each factor based on the relative importance of each.
Step 3: Assign a score (typically between 0 and 100) for each
location with respect to each factor identified in Step 1.
Step 4: Compute the weighted score for each factor for each
location by multiplying its weight with the corresponding score
(which were assigned Steps 2 and 3, respectively).
Step 5: Compute the sum of the weighted scores for each
location and choose a location based on these scores.
16
Example 1:
Weighted Factor Method
A payroll processing company has recently won several major
contracts in the Midwest region of the United States and Central
Canada and wants to open a new, large facility to serve these areas.
Because customer service is so important, the company wants to be as
near its “customers” as possible. A preliminary investigation has shown
that Minneapolis, Winnipeg, and Springfield, Illinois are the three most
desirable locations, and the payroll company has to select one of these.
A subsequent thorough investigation of each location with respect to
eight important factors generated the raw scores and weights. Using
the location scoring method, determine the best location for the new
payroll processing facility.
17
Steps 1, 2 and 3.
Factors and weights for three locations
Score
Weight
Factor
Minneapolis
Winnipeg
Springfield
0.25
Proximity to customer
95
90
65
0.15
Land and construction prices
60
60
90
0.15
Wage rates
70
45
60
0.10
Property taxes
70
90
70
0.10
Business taxes
80
90
85
0.10
Commercial travel
80
65
75
0.08
Insurance costs
70
95
60
0.07
Office services
90
90
80
18
Steps 4 and 5.
Weighted scores for three locations
Weighted Score
Factor
Minneapolis
Winnipeg
Springfield
Proximity to customer
23.75
22.50
16.25
Land and construction prices
9.00
9.00
13.50
Wage rates
10.50
6.75
9.00
Property taxes
7.00
9.00
7.00
Business taxes
8.00
9.00
8.50
Commercial travel
8.00
6.50
7.50
Insurance costs
5.60
7.60
4.80
Office services
6.30
6.30
5.60
Sum of weighted scores
78.15
?
?
19
Example 2:
Weighted Factor Method
SCORES (0 TO 100)
LOCATION FACTOR
Labor pool and climate
Proximity to suppliers
Wage rates
Community environment
Proximity to customers
Shipping modes
Air service
WEIGHT
Site 1
Site 2
Site 3
.30
.20
.15
.15
.10
.05
.05
80
100
60
75
65
85
50
65
91
95
80
90
92
65
90
75
72
80
95
65
90
Sup
ple
men
t 720
Location Factor Rating
WEIGHTED SCORES
Site 1
Site 2
Site 3
24.00
20.00
9.00
11.25
6.50
4.25
2.50
77.50
19.50
18.20
14.25
12.00
9.00
4.60
3.25
80.80
27.00
15.00
10.80
12.00
9.50
3.25
4.50
82.05
Site 3 has the
highest factor rating
Sup
ple
men
t 721
Break-Even Analysis
Total cost = fixed costs + variable costs
(quantity):
TC  F  VC Q
Revenue = selling price (quantity)
R  SPQ
Break-even point is where total costs =
revenue:
TC  R or
or
Q
F  VC Q  SP Q
F
SP  VC
Example 1: Break-Even Analysis
A firm estimates that the fixed cost of producing
a line of footwear is $52,000 with a $9 variable
cost for each pair produced. They want to know:
◦ If each pair sells for $25, how many pairs must they
sell to break-even?
◦ If they sell 4000 pairs at $25 each, how much money
will they make?
23
Example 1: Break-Even Analysis cont`d…

Break-even point:
F
$52,000
Q

 3250 pairs
SP  VC $25  $9

Profit = total revenue – total costs
P  SP Q  F  VC Q 
 $254000  $52,000  $94000
 $12,000
24
Break-Even Analysis – Outsourcing
Total Cost of Outsourcin g :
TC Buy  FCBuy  VCBuy  Q 
Total Cost of Insourcing :
TC Make  FCMake  VCMake  Q 
Indifferen ce Point :
FCBuy  VCBuy  Q   FCMake  VCMake  Q 
25
Example: Break-Even Analysis – Outsourcing
Bill & Nancy plan to open a small bagel shop.
◦ The local baker has offered to sell them bagels at 40 cents
each. However, they will need to invest $1,000 in bread
racks to transport the bagels back & forth from the bakery
to their store.
◦ Alternatively, they can bake the bagels at their store for 15
cents each if they invest $15,000 in kitchen equipment.
◦ They expect to sell 60,000 bagels each year.
What should they do?
26
Example: Break-Even Analysis – Outsourcing
Indifferen ce Point Calculatio n :
FCBuy  VCBuy  Q   FCMake  VCMake  Q 
$1,000  $0.40  Q   $15,000  $0.15  Q 
Solve for Q : Q  56,000
Interpretation:
◦ They anticipate selling 60,000 bagels (greater than the
indifference point of 56,000).
◦ Therefore, make the bagels in-house.
27
Cost-Profit-Volume Analysis

Steps:
◦ 1.Determine the fixed and variable costs for each alternative
◦ 2.Plot the total-cost lines for all alternatives on the same
graph
◦ 3.Determine the location that will have the lowest total cost
(or highest profit) for the expected level of output

Assumptions
◦
◦
◦
◦
1.Fixed costs are constant for the range of probable output
2.Variable costs are linear for the range of probably output
3.The required level of output can be closely estimated
4.Only one product is involved
28
Cost-Profit-Volume Analysis, cont`d…

For a cost analysis, compute the total cost
for each alternative location:
29
Example: Cost-Profit-Volume Analysis

Fixed and variable costs for four potential plant
locations are shown below:
30
Example: Cost-Profit-Volume Analysis, cont`d…
31
Example: Cost-Profit-Volume Analysis, cont`d…
32
Minimum Cost Method
İSTANBU
L
ANKARA
BURSA
DEMAND
TRABZON
11
8
12
200
ADANA
10
7
9
400
KONYA
8
4
7
400
CAPACITY
400
300
300
1000
33
Minimum Cost Method
İSTANBU
L
ANKARA
BURSA
DEMAND
TRABZON
11
8
12
200
ADANA
10
7
9
400
KONYA
8
4
7
400
CAPACITY
400
300
300
1000
300
34
Minimum Cost Method
İSTANBU
L
ANKARA
BURSA
DEMAND
TRABZON
11
8
x
12
200
ADANA
10
7
x
9
400
KONYA
8
4
300
7
400
CAPACITY
400
300
300
1000
35
Minimum Cost Method
İSTANBU
L
ANKARA
BURSA
DEMAND
TRABZON
11
8
x
12
200
ADANA
10
7
x
9
400
KONYA
8
4
300
7
CAPACITY
400
300
300
100
400
1000
36
Minimum Cost Method
İSTANBU
L
ANKARA
BURSA
DEMAND
TRABZON
11
8
x
12
200
ADANA
10
7
x
9
400
KONYA
8
4
300
7
CAPACITY
400
x
300
300
100
400
1000
37
Minimum Cost Method
İSTANBU
L
ANKARA
BURSA
DEMAND
TRABZON
11
8
x
12
200
ADANA
10
7
x
9
200
400
KONYA
8
4
300
7
100
400
CAPACITY
400
x
300
300
1000
38
Minimum Cost Method
İSTANBU
L
ANKARA
BURSA
DEMAND
TRABZON
11
8
x
12
x
200
ADANA
10
7
x
9
200
400
KONYA
8
4
300
7
100
400
CAPACITY
400
x
300
300
1000
39
Minimum Cost Method
İSTANBU
L
ANKARA
BURSA
DEMAND
TRABZON
11
8
x
12
x
200
ADANA
10
200
7
x
9
200
400
KONYA
8
x
4
300
7
100
400
CAPACITY
400
300
300
1000
40
Minimum Cost Method
İSTANBU
L
ANKARA
BURSA
DEMAND
TRABZON
11
200
8
x
12
x
200
ADANA
10
200
7
x
9
200
400
KONYA
8
x
4
300
7
100
400
CAPACITY
400
300
300
1000
• TCBURSA =11*200+10*200+4*300+9*200+7*100=7900
41
Minimum Cost Method
İSTANBUL ANKARA
MERSİN
DEMAND
TRABZON
11
8
10
200
ADANA
10
7
1
400
KONYA
8
4
6
400
CAPACITY
400
300
300
1000
42
Minimum Cost Method
İSTANBUL ANKARA
MERSİN
DEMAND
TRABZON
11
8
10
x
200
ADANA
10
7
1
300
400
KONYA
8
4
6
x
400
CAPACITY
400
300
300
1000
43
Minimum Cost Method
İSTANBUL ANKARA
MERSİN
DEMAND
TRABZON
11
8
x
10
x
200
ADANA
10
7
x
1
300
400
KONYA
8
4
300
6
x
400
CAPACITY
400
300
300
1000
44
Minimum Cost Method
İSTANBUL ANKARA
MERSİN
DEMAND
TRABZON
11
200
8
x
10
x
200
ADANA
10
100
7
x
1
300
400
KONYA
8
100
4
300
6
x
400
CAPACITY
400
300
300
1000
• TCMERSİN =11*200+10*100+8*100+4*300+1*300=5500
45
Minimum Cost Method
İSTANBUL ANKARA
BURSA
DEMAND
TRABZON
11
200
8
x
12
x
200
ADANA
10
200
7
x
9
200
400
KONYA
8
x
4
300
7
100
400
CAPACITY
400
300
300
1000
• TCBURSA =11*200+10*200+4*300+9*200+7*300=7900
İSTANBUL ANKARA
MERSİN
DEMAND
TRABZON
11
200
8
x
10
x
200
ADANA
10
100
7
x
1
300
400
KONYA
8
100
4
300
6
x
400
CAPACITY
400
300
300
1000
• TCMERSİN =11*200+10*100+8*200+4*300+1*300=5500
46
Hybrid Analysis


A disadvantage of the Qualitative method discussed earlier is that
location decision is made based entirely on a subjective evaluation.
Although Quantitative method overcomes this disadvantage, it does
not allow us to incorporate unquantifiable factors that have a major
impact on the location decision.
Example:
The Quantitative techniques can easily consider:
◦ transportation cost, and
◦ operational costs,
but intangible factors such as;
◦ the attitude of a community toward businesses,
◦ potential labor unrest,
◦ reliability of auxiliary service providers are difficult to capture though
these are important in choosing a location decision.

Therefore, we need a method that incorporates subjective as well as
quantifiable cost and other factors.
47
Hybrid Analysis
A multi-attribute, single-facility location model
based on the ones presented by Brown and
Gibson (1972) and Buffa and Sarin (1987).
 This model classifies the objective and subjective
factors important to the specific location problem
being addressed as:
• critical,
• objective, and
• subjective.
 The meaning of objective and subjective factors is
obvious. The meaning of critical factors needs
some discussion.

48
Hybrid Analysis



In every location decision, usually at least
one factor determines whether or not a
location will be considered for further
evaluation.
For instance, if water is used extensively in a
manufacturing process (e.g. a brewery), then
a site that does not have an adequate water
supply now or in the future is automatically
removed from consideration.
This is an example of a critical factor.
49
Hybrid Analysis

After the factors are classified, they are
assigned numeric values:
50
Hybrid Analysis

Assume that we have m candidate locations and p critical, q
objective and r subjective factors. We can determine overall critical
factor measure (CFMi), objective factor measure (OFMi), and Subjective
Factor Measure (SFMi) for each location i with these equations.
51
Hybrid Analysis

After LMi is determined for each
candidate location, the next step is to
select the one with the greatest LMi value
52
Example: Hybrid Analysis
Mole-Sun Brewing Company is evaluating six
candidate location; Montreal, Plattsburgh, Ottawa,
Albany, Rochester, and Kingston for a new
brewery.
 The two critical, three objective and four
subjective factors that management wishes to
incorporate in its decision making are
summarized in the table (next slide).
 The weights of the subjective factors are also
provided in the table. Determine the best
location if the subjective factors are to be
weighted 50% more than the objective factors.

53

Questions?
54