2. 8 - 2
Summary
The Strategic Importance of Location
Factors That Affect Location Decisions
Labor Productivity
Exchange Rates and Currency Risks
Costs
Political Risk, Values, and Culture
Proximity to Markets
Proximity to Suppliers
Proximity to Competitors (Clustering)
3. 8 - 3
Outline
Methods of Evaluating Location
Alternatives
The Factor-Rating Method
Locational Break-Even Analysis
Center-of-Gravity Method
Transportation Model
4. 8 - 4
Factor-Rating Method
Popular because a wide variety of factors
can be included in the analysis
Six steps in the method
1. Develop a list of relevant factors also called key
success factors
2. Assign a weight to each factor
3. Develop a scale for each factor
4. Score each location for each factor
5. Multiply score by weights for each factor for
each location
6. Recommend the location with the highest point
score
5. 8 - 5
Factor-Rating Example
Key Scores
Success (out of 100) Weighted Scores
Factor Weight France Denmark France Denmark
Labor
availability
and attitude .25 70 60 (.25)(70) = 17.5 (.25)(60) = 15.0
People-to-
car ratio .05 50 60 (.05)(50) = 2.5 (.05)(60) = 3.0
Per capita
income .10 85 80 (.10)(85) = 8.5 (.10)(80) = 8.0
Tax structure .39 75 70 (.39)(75) = 29.3 (.39)(70) = 27.3
Education
and health .21 60 70 (.21)(60) = 12.6 (.21)(70) = 14.7
Totals 1.00 70.4 68.0
Table 8.4
6. 8 - 6
Locational
Break-Even Analysis
Method of cost-volume analysis used for
industrial locations
Three steps in the method
1. Determine fixed and variable costs for each
location
2. Plot the cost for each location
3. Select location with lowest total cost for
expected production volume
7. 8 - 7
Locational Break-Even Analysis Example
Three locations:
Akron $30,000 $75 $180,000
Bowling Green $60,000 $45 $150,000
Chicago $110,000 $25 $160,000
Fixed Variable Total
City Cost Cost Cost
Total Cost = Fixed Cost + (Variable Cost x Volume)
Selling price = $120
Expected volume = 2,000 units
9. 8 - 9
Center-of-Gravity Method
Finds location of distribution center
that minimizes distribution costs
Considers
Location of markets
Volume of goods shipped to those
markets
Shipping cost (or distance)
10. 8 - 10
Center-of-Gravity Method
Place existing locations on a
coordinate grid
Grid origin and scale is arbitrary
Maintain relative distances
Calculate X and Y coordinates for
‘center of gravity’
Assumes cost is directly proportional
to distance and volume shipped
11. 8 - 11
Center-of-Gravity Method
x - coordinate =
∑dixQi
∑Qi
i
i
∑diyQi
∑Qi
i
i
y - coordinate =
where dix = x-coordinate of location i
diy = y-coordinate of location i
Qi = Quantity of goods moved to
or from location i
13. 8 - 13
Center-of-Gravity Method
Number of Containers
Store Location Shipped per Month
Chicago (30, 120) 2,000
Pittsburgh (90, 110) 1,000
New York (130, 130) 1,000
Atlanta (60, 40) 2,000
x-coordinate =
(30)(2000) + (90)(1000) + (130)(1000) + (60)(2000)
2000 + 1000 + 1000 + 2000
= 66.7
y-coordinate =
(120)(2000) + (110)(1000) + (130)(1000) + (40)(2000)
2000 + 1000 + 1000 + 2000
= 93.3
14. 8 - 14
Center-of-Gravity Method
North-South
East-West
120 –
90 –
60 –
30 –
–
| | | | | |
30 60 90 120 150
Arbitrary
origin
Chicago (30, 120)
New York (130, 130)
Pittsburgh (90, 110)
Atlanta (60, 40)
Center of gravity (66.7, 93.3)
+
Figure 8.3
15. 8 - 15
Transportation Model
Finds amount to be shipped from several
points of supply to several points of
demand
Solution will minimize total production and
shipping costs
A special class of linear programming
problems
16. 8 - 16
Outline - Quantitative Modules C
(Transportation Models)
Transportation Modeling
Developing an Initial Solution
The Northwest-Corner Rule
The Intuitive Lowest-Cost Method
The Stepping-Stone Method
17. 8 - 17
Transportation Modeling
An interactive procedure that finds
the least costly means of moving
products from a series of sources
to a series of destinations
Can be used to
help resolve
distribution
and location
decisions
18. 8 - 18
Transportation Modeling
A special class of linear
programming
Need to know
1. The origin points and the capacity
or supply per period at each
2. The destination points and the
demand per period at each
3. The cost of shipping one unit from
each origin to each destination
19. 8 - 19
Transportation Problem
Fort Lauderdale
(300 units
capacity)
Albuquerque
(300 units
required)
Des Moines
(100 units
capacity)
Evansville
(300 units
capacity)
Cleveland
(200 units
required)
Boston
(200 units
required)
Figure C.1
20. 8 - 20
Transportation Problem
To
From Albuquerque Boston Cleveland
Des Moines $5 $4 $3
Evansville $8 $4 $3
Fort Lauderdale $9 $7 $5
Table C.1
21. 8 - 21
Transportation Matrix
From
To
Albuquerque Boston Cleveland
Des Moines
Evansville
Fort Lauderdale
Factory
capacity
Warehouse
requirement
300
300
300 200 200
100
700
$5
$5
$4
$4
$3
$3
$9
$8
$7
Cost of shipping 1 unit from Fort
Lauderdale factory to Boston warehouse
Des Moines
capacity
constraint
Cell
representing
a possible
source-to-
destination
shipping
assignment
(Evansville
to Cleveland)
Total demand
and total supply
Cleveland
warehouse demand
Figure C.2
22. 8 - 22
Northwest-Corner Rule
Start in the upper left-hand cell (or
northwest corner) of the table and allocate
units to shipping routes as follows:
1. Exhaust the supply (factory capacity) of each
row before moving down to the next row
2. Exhaust the (warehouse) requirements of
each column before moving to the next
column
3. Check to ensure that all supplies and
demands are met
23. 8 - 23
Northwest-Corner Rule
1. Assign 100 tubs from Des Moines to Albuquerque
(exhausting Des Moines’s supply)
2. Assign 200 tubs from Evansville to Albuquerque
(exhausting Albuquerque’s demand)
3. Assign 100 tubs from Evansville to Boston
(exhausting Evansville’s supply)
4. Assign 100 tubs from Fort Lauderdale to Boston
(exhausting Boston’s demand)
5. Assign 200 tubs from Fort Lauderdale to
Cleveland (exhausting Cleveland’s demand and
Fort Lauderdale’s supply)
24. 8 - 24
To (A)
Albuquerque
(B)
Boston
(C)
Cleveland
(D) Des Moines
(E) Evansville
(F) Fort Lauderdale
Warehouse
requirement 300 200 200
Factory
capacity
300
300
100
700
$5
$5
$4
$4
$3
$3
$9
$8
$7
From
Northwest-Corner Rule
100
100
100
200
200
Figure C.3
Means that the firm is shipping 100
bathtubs from Fort Lauderdale to Boston
25. 8 - 25
Northwest-Corner Rule
Computed Shipping Cost
Table C.2
This is a feasible solution
but not necessarily the
lowest cost alternative
Route
From To Tubs Shipped Cost per Unit Total Cost
D A 100 $5 $ 500
E A 200 8 1,600
E B 100 4 400
F B 100 7 700
F C 200 5 $1,000
Total: $4,200
26. 8 - 26
Intuitive Lowest-Cost Method
1. Identify the cell with the lowest cost
2. Allocate as many units as possible to
that cell without exceeding supply or
demand; then cross out the row or
column (or both) that is exhausted by
this assignment
3. Find the cell with the lowest cost from
the remaining cells
4. Repeat steps 2 and 3 until all units
have been allocated
27. 8 - 27
Intuitive Lowest-Cost Method
To (A)
Albuquerque
(B)
Boston
(C)
Cleveland
(D) Des Moines
(E) Evansville
(F) Fort Lauderdale
Warehouse
requirement 300 200 200
Factory
capacity
300
300
100
700
$5
$5
$4
$4
$3
$3
$9
$8
$7
From
100
First, $3 is the lowest cost cell so ship 100 units from
Des Moines to Cleveland and cross off the first row as
Des Moines is satisfied
Figure C.4
28. 8 - 28
Intuitive Lowest-Cost Method
To (A)
Albuquerque
(B)
Boston
(C)
Cleveland
(D) Des Moines
(E) Evansville
(F) Fort Lauderdale
Warehouse
requirement 300 200 200
Factory
capacity
300
300
100
700
$5
$5
$4
$4
$3
$3
$9
$8
$7
From
100
100
Second, $3 is again the lowest cost cell so ship 100 units
from Evansville to Cleveland and cross off column C as
Cleveland is satisfied
Figure C.4
29. 8 - 29
Intuitive Lowest-Cost Method
To (A)
Albuquerque
(B)
Boston
(C)
Cleveland
(D) Des Moines
(E) Evansville
(F) Fort Lauderdale
Warehouse
requirement 300 200 200
Factory
capacity
300
300
100
700
$5
$5
$4
$4
$3
$3
$9
$8
$7
From
100
100
200
Third, $4 is the lowest cost cell so ship 200 units from
Evansville to Boston and cross off column B and row E
as Evansville and Boston are satisfied
Figure C.4
30. 8 - 30
Intuitive Lowest-Cost Method
To (A)
Albuquerque
(B)
Boston
(C)
Cleveland
(D) Des Moines
(E) Evansville
(F) Fort Lauderdale
Warehouse
requirement 300 200 200
Factory
capacity
300
300
100
700
$5
$5
$4
$4
$3
$3
$9
$8
$7
From
100
100
200
300
Finally, ship 300 units from Albuquerque to Fort
Lauderdale as this is the only remaining cell to complete
the allocations
Figure C.4
32. 8 - 32
Intuitive Lowest-Cost Method
To (A)
Albuquerque
(B)
Boston
(C)
Cleveland
(D) Des Moines
(E) Evansville
(F) Fort Lauderdale
Warehouse
requirement 300 200 200
Factory
capacity
300
300
100
700
$5
$5
$4
$4
$3
$3
$9
$8
$7
From
100
100
200
300
Total Cost = $3(100) + $3(100) + $4(200) + $9(300)
= $4,100
Figure C.4
This is a feasible solution,
and an improvement over
the previous solution, but
not necessarily the lowest
cost alternative
33. 8 - 33
To (A)
Albuquerque
(B)
Boston
(C)
Cleveland
(D) Des Moines
(E) Evansville
(F) Fort Lauderdale
Warehouse
requirement 300 200 200
Factory
capacity
300
300
100
700
$5
$5
$4
$4
$3
$3
$9
$8
$7
From
Northwest-Corner Rule
100
100
100
200
200
Figure C.3
Means that the firm is shipping 100
bathtubs from Fort Lauderdale to Boston
34. 8 - 34
Stepping-Stone Method
1. Select any unused square to evaluate
2. Beginning at this square, trace a
closed path back to the original square
via squares that are currently being
used
3. Beginning with a plus (+) sign at the
unused corner, place alternate minus
and plus signs at each corner of the
path just traced
