1. Supply Chains and Logistics Chapter 13

2. What is a Facility Location?
The process of determining geographic sites for a firm’s operations.
Distribution center (DC)
A warehouse or stocking point where goods are stored for subsequent distribution to manufacturers, wholesalers, retailers, and customers.

3. Factors Affecting Location Decisions
The Factor Must Be Sensitive to Location
The Factor Must Have a High impact on the Company’s Ability to Meet Its Goals

4. Factors Affecting Location Decisions
Dominant Factors in Manufacturing
Favorable Labor Climate
Proximity to Markets
Impact on Environment
Quality of Life
Proximity to Suppliers and Resources
Proximity to the Parent Company’s Facilities
Utilities, Taxes, and Real Estate Costs
Other Factors

5. Factors Affecting Location Decisions
Dominant Factors in Services
Proximity to Customers
Transportation Costs and Proximity to Markets
Location of Competitors
Site-Specific Factors

6. Load-Distance Method Load-Distance Method
A mathematical model used to evaluate locations based on proximity factors
Euclidean distance
The straight line distance, or shortest possible path, between two points
Rectilinear distance
The distance between two points with a series of 90- degree turns, as along city blocks

7. Application 13.1 What is the distance between (20, 10) and (80, 60)?
Euclidean distance:
dAB = (xA – xB)2 + (yA – yB)2 =
(20 – 80)2 + (10 – 60)2 = 78.1
Rectilinear distance:
dAB = |xA – xB| + |yA – yB| =
|20 – 80| + |10 – 60| = 110

8. Load-Distance Method Calculating a load-distance score
Varies by industry
Use the actual distance to calculate ld score
Use rectangular or Euclidean distances
Find one acceptable facility location that minimizes the ld score
Formula for the ld score
ld =  lidi i

9. Application 13.2
Management is investigating which location would be best to position its new plant relative to two suppliers (located in Cleveland and Toledo) and three market areas (represented by Cincinnati, Dayton, and Lima). Management has limited the search for this plant to those five locations. The following information has been collected. Which is best, assuming rectilinear distance?
Location
x,y coordinates
Trips/year
Cincinnati
(11,6) 15
Dayton
(6,10) 20
Cleveland
(14,12) 30
Toledo
(9,12) 25
Lima
(13,8) 40

10. Application 13.2 Location x,y coordinates Trips/year Cincinnati (11,6)15
Dayton
(6,10) 20
Cleveland
(14,12) 30
Toledo
(9,12) 25
Lima
(13,8) 40
Cincinnati =
Dayton =
Cleveland =
Toledo =
Lima =
15(0) + 20(9) + 30(9) + 25(8) + 40(4)
= 810
15(9) + 20(0) + 30(10) + 25(5) + 40(9)
= 920
15(9) + 20(10) + 30(0) + 25(5) + 40(5)
= 660
15(8) + 20(5) + 30(5) + 25(0) + 40(8)
= 690
15(4) + 20(9) + 30(5) + 25(8) + 40(0)
= 590

11. Center of Gravity li xi li yi li li Center of Gravity
A good starting point to evaluate locations in the target area using the load-distance model.
Find x coordinate, x*, by multiplying each point’s x coordinate by its load (lt), summing these products li xi, and dividing by li
The center of gravity’s y coordinate y* found the same way
x* =
li xi
li i
y* =
li yi
li i

12. Example 13.1
A supplier to the electric utility industry produces power generators; the transportation costs are high. One market area includes the lower part of the Great Lakes region and the upper portion of the southeastern region. More than 600,000 tons are to be shipped to eight major customer locations as shown below:
Customer Location
Tons Shipped
x, y Coordinates
Three Rivers, MI
5,000
(7, 13)
Fort Wayne, IN
92,000
(8, 12)
Columbus, OH
70,000
(11, 10)
Ashland, KY
35,000
(11, 7)
Kingsport, TN
9,000
(12, 4)
Akron, OH
227,000
(13, 11)
Wheeling, WV
16,000
(14, 10)
Roanoke, VA
153,000
(15, 5)

13. Example 13.1
Customer Location
Tons Shipped
x, y Coordinates
Three Rivers, MI
5,000
(7, 13)
Fort Wayne, IN
92,000
(8, 12)
Columbus, OH
70,000
(11, 10)
Ashland, KY
35,000
(11, 7)
Kingsport, TN
9,000
(12, 4)
Akron, OH
227,000
(13, 11)
Wheeling, WV
16,000
(14, 10)
Roanoke, VA
153,000
(15, 5)
What is the center of gravity for the electric utilities supplier?
The center of gravity is calculated as shown below:
li = i
= 607
li xi = i
5(7) + 92(8) + 70(11) + 35(11) + 9(12) + 227(13)
+ 16(14) + 153(15) = 7,504
x* = =
li xi
li i
= 12.4
7,504
607

14. Example 13.1
Customer Location
Tons Shipped
x, y Coordinates
Three Rivers, MI
5,000
(7, 13)
Fort Wayne, IN
92,000
(8, 12)
Columbus, OH
70,000
(11, 10)
Ashland, KY
35,000
(11, 7)
Kingsport, TN
9,000
(12, 4)
Akron, OH
227,000
(13, 11)
Wheeling, WV
16,000
(14, 10)
Roanoke, VA
153,000
(15, 5)
What is the center of gravity for the electric utilities supplier?
li yi = i
5(13) + 92(12) + 70(10) + 35(7) + 9(4) + 227(11)
+ 16(10) + 153(5) = 5,572
x* = =
li yi
li i
= 9.2
5,572
607

15. Example 13.1
Customer Location
Tons Shipped
x, y Coordinates
Three Rivers, MI
5,000
(7, 13)
Fort Wayne, IN
92,000
(8, 12)
Columbus, OH
70,000
(11, 10)
Ashland, KY
35,000
(11, 7)
Kingsport, TN
9,000
(12, 4)
Akron, OH
227,000
(13, 11)
Wheeling, WV
16,000
(14, 10)
Roanoke, VA
153,000
(15, 5)
Using rectilinear distance, what is the resulting load–distance score for this location?
The resulting load-distance score is
ld =  lidi = i
5( ) + 92( ) + 70( ) + 35( ) + 90( ) + 227( ) + 16( ) + 153( )
= 2,662.4
where
di = |xi – x*| + |yi – y*|

16. Application 13.3 li xi li li yi li
A firm wishes to find a central location for its service. Business forecasts indicate travel from the central location to New York City on 20 occasions per year. Similarly, there will be 15 trips to Boston, and 30 trips to New Orleans. The x, y-coordinates are (11.0, 8.5) for New York, (12.0, 9.5) for Boston, and (4.0, 1.5) for New Orleans. What is the center of gravity of the three demand points?
x* = =
li xi
li i
[(20  11) + (15  12) + (30  4)]
( )
= 8.0
y* = =
li yi
li i
[(20  8.5) + (15  9.5) + (30  1.5)]
( )
= 5.5

17. Break-Even Analysis
Compare location alternatives on the basis of quantitative factors expressed in total costs
Determine the variable costs and fixed costs for each site
Plot total cost lines
Identify the approximate ranges for which each location has lowest cost
Solve algebraically for break-even points over the relevant ranges

18. Variable Costs per Unit
Example 13.2
An operations manager narrowed the search for a new facility location to four communities. The annual fixed costs (land, property taxes, insurance, equipment, and buildings) and the variable costs (labor, materials, transportation, and variable overhead) are as follows:
Community
Fixed Costs per Year
Variable Costs per Unit A
$150,000
$62 B
$300,000
$38 C
$500,000
$24 D
$600,000
$30

19. Example 13.2
Step 1
Plot the total cost curves for all the communities on a single graph. Identify on the graph the approximate range over which each community provides the lowest cost.
Step 2
Using break-even analysis, calculate the break-even quantities over the relevant ranges. If the expected demand is 15,000 units per year, what is the best location?

20. (Cost per Unit)(No. of Units)
Example 13.2
To plot a community’s total cost line, let us first compute the total cost for two output levels: Q = 0 and Q = 20,000 units per year. For the Q = 0 level, the total cost is simply the fixed costs. For the Q = 20,000 level, the total cost (fixed plus variable costs) is as follows:
Community
Fixed Costs
Variable Costs
(Cost per Unit)(No. of Units)
Total Cost
(Fixed + Variable) A
$150,000 B
$300,000 C
$500,000 D
$600,000
$62(20,000) = $1,240,000
$1,390,000
$38(20,000) = $760,000
$1,060,000
$24(20,000) = $480,000
$980,000
$30(20,000) = $600,000
$1,200,000

21. Example 13.2 A is best for low volumes B for intermediate volumes
The figure shows the graph of the total cost lines.
| | | | | | | | | | | |
1,600 –
1,400 –
1,200 –
1,000 –
800 –
600 –
400 –
200 – –
Annual cost (thousands of dollars)
Q (thousands of units) A
(20, 980)
(20, 1,390)
(20, 1,200)
(20, 1,060) D B
A is best for low volumes
B for intermediate volumes
C for high volumes.
We should no longer consider community D, because both its fixed and its variable costs are higher than community C’s. C
C best
6.25
14.3
Break-even point
B best
A best
Figure 13.3

22. Example 13.2
The break-even quantity between A and B lies at the end of the first range, where A is best, and the beginning of the second range, where B is best.
(A)
(B)
$150,000 + $62Q =
$300,000 + $38Q
Q = 6,250 units
The break-even quantity between B and C lies at the end of the range over which B is best and the beginning of the final range where C is best.
(B)
(C)
$300,000 + $38Q =
$500,000 + $24Q
Q = 14,286 units

23. Example 13.2
The break-even quantity between A and B lies at the end of the first range, where A is best, and the beginning of the second range, where B is best.
No other break-even quantities are needed. The break-even point between A and C lies above the shaded area, which does not mark either the start or the end of one of the three relevant ranges.
(A)
(B)
$150,000 + $62Q =
$300,000 + $38Q
Q = 6,250 units
The break-even quantity between B and C lies at the end of the range over which B is best and the beginning of the final range where C is best.
(B)
(C)
$300,000 + $38Q =
$500,000 + $24Q
Q = 14,286 units

24. Hint: In this problem, lease length is analogous to volume.
Application 13.4
By chance, the Atlantic City Community Chest has to close temporarily for general repairs. They are considering four temporary office locations:
Property Address
Move-in Costs
Monthly Rent
Boardwalk
$400
$50
Marvin Gardens
$280
$24
St. Charles Place
$360
$10
Baltic Avenue
$60
Use the graph on the next slide to determine for what length of lease each location would be favored?
Hint: In this problem, lease length is analogous to volume.

25. Application 13.4
| | | | | | | | |
Months →
Total Cost →
500 – –
400 –
300 –
200 –
100 –
Boardwalk
St Charles Place
Marvin Gardens
Baltic Avenue
Fs + csQ = FB + cBQ
Q =
FB – Fs
cs – cB =
$60 – $360
$10 – $60
= = 6 months
– 300
– 50
The short answer: Baltic Avenue if 6 months or less, St. Charles Place if longer

26. Transportation Method
Transportation method for location problems
A quantitative approach that can help solve multiple-facility location problems

27. Transportation Method
Setting Up the Initial Tableau
Create a row for each plant (existing or new) and a column for each warehouse
Add a column for plant capacities and a row for warehouse demands and insert their specific numerical values
Each cell not in the requirements row or capacity column represents a shipping route from a plant to a warehouse. Insert the unit costs in the upper right- hand corner of each of these cells.
The sum of the shipments in a row must equal the corresponding plant’s capacity and the sum of shipments in a column must equal the corresponding warehouse’s demand.

28. Transportation Method
Initial Tableau
Plant
Warehouse
Capacity
San Antonio, TX (1)
Hot Spring, AR (2)
Sioux Falls, SD (3)
Phoenix
5.00
6.00
5.40
400
Atlanta
7.00
4.60
6.60
500
Requirements
200
300
900
Figure 13.4

29. Transportation Method
Dummy plants or warehouses
The sum of capacities must equal the sum of demands
If capacity exceeds requirements we add an extra column (a dummy warehouse)
If requirements exceed capacity we add an extra row (a dummy plant)
Assign shipping costs to equal the stockout costs of the new cells
Finding a solution
The goal is to find the least-cost allocation pattern that satisfies all demands and exhausts all capacities.

30. Example 13.3
The optimal solution for the Sunbelt Pool Company, found with POM for Windows, is shown below and displays the data inputs, with the cells showing the unit costs, the bottom row showing the demands, and the last column showing the supply capacities.
Figure 13.5a

31. Example 13.3
Below shows how the existing network of plants supplies the three warehouses to minimize costs for a total of $4,580.
All warehouse demand is satisfied:
Warehouse 1 in San Antonio is fully supplied by Phoenix
Warehouse 2 in Hot Springs is fully supplied by Atlanta.
Warehouse 3 in Sioux Falls receives 200 units from Phoenix and 100 units from Atlanta, satisfying its 300-unit demand.
Figure 13.5b

32. Example 13.3
Below shows the total quantity and cost of each shipment. The total optimal cost reported in the upper-left corner of the previous table is $4,580, or 200($5.00) + 200($5.40) + 400($4.60) + 100($6.60) = $4,580.
Figure 13.5c

33. Example 13.3
Figure 13.6

34. GIS – Geographical Information System
What is a GIS?
GIS – Geographical Information System
A system of computer software, hardware, and data that the firm’s personnel can use to manipulate, analyze, and present information relevant to a location decision.

35. The GIS Method for Locating Multiple Facilities
A five step GIS framework
Step 1: Map the data
Step 2: Split the area
Step 3: Assign a facility location
Step 4: Search for alternative sites
Step 5: Compute ld scores and check capacity

36. Inventory Placement Centralized placement Inventory pooling
Keeping all the inventory of a product at a single location such as at a firm’s manufacturing plant or a warehouse and shipping directly to each of its customers
Inventory pooling
A reduction in inventory and safety stock because of the merging of variable demands from customers
Forward placement
Locating stock closer to customers at a warehouse, DC, wholesaler, or retailer

37. A Systematic Location Selection Process
Step 1: Identify the important location factors and categorize them as dominant or secondary Step 2: Consider alternative regions; then narrow to alternative communities and finally specific sites Step 3: Collect data on the alternatives Step 4: Analyze the data collected, beginning with the quantitative factors Step 5: Bring the qualitative factors pertaining to each site into the evaluation

38. Example 13.4
A new medical facility, Health-Watch, is to be located in Erie, Pennsylvania. The following table shows the location factors, weights, and scores (1 = poor, 5 = excellent) for one potential site. The weights in this case add up to 100 percent. A weighted score (WS) will be calculated for each site. What is the WS for this site?
Location Factor
Weight
Score
Total patient miles per month 25 4
Facility utilization 20 3
Average time per emergency trip
Expressway accessibility 15
Land and construction costs 10 1
Employee preferences 5

39. Example 13.4
Location Factor
Weight
Score
Total patient miles per month 25 4
Facility utilization 20 3
Average time per emergency trip
Expressway accessibility 15
Land and construction costs 10 1
Employee preferences 5
The WS for this particular site is calculated by multiplying each factor’s weight by its score and adding the results:
WS =
(25  4) + (20  3) + (20  3) + (15  4) + (10  1) + (10  5) =
= 340
The total WS of 340 can be compared with the total weighted scores for other sites being evaluated.

40. Application 13.5
Management is considering three potential locations for a new cookie factory. They have assigned scores shown below to the relevant factors on a 0 to 10 basis (10 is best). Using the preference matrix, which location would be preferred?
Location Factor
Weight
The Neighborhood
Sesame Street
Ronald’s Playhouse
Material Supply
0.1 5 9 8
Quality of Life
0.2 4
Mild Climate
0.3 10 6
Labor Skills
0.4 3 7
0.5
1.8
3.0
1.2
6.5
0.9
1.6
1.8
5.9
0.8
2.4
2.8
6.8

41. Population  Longitude
Solved Problem 1
The new Health-Watch facility is targeted to serve seven census tracts in Erie, Pennsylvania, whose latitudes and longitudes are shown below. Customers will travel from the seven census-tract centers to the new facility when they need health care. What is the target area’s center of gravity for the Health-Watch medical facility?
LOCATION DATA AND CALCULATIONS FOR HEALTH WATCH
Census Tract
Population
Latitude
Longitude
Population  Latitude
Population  Longitude 15
2,711
42.134
–80.041
114,225.27
–216,991.15 16
4,161
42.129
–80.023
175,298.77
–332,975.70 17
2,988
42.122
–80.055
125,860.54
–239,204.34 25
2,512
42.112
–80.066
105,785.34
–201,125.79 26
4,342
42.117
–80.052
182,872.01
–347,585.78 27
6,687
42.116
281,629.69
–535,113.80 28
6,789
42.107
–80.051
285,864.42
–543,466.24
Total
30,190
1,271,536.04
–2,
This is Figure 9.10 to support Solved Problem 2.
Table 13.1

42. Solved Problem 1
Next we solve for the center of gravity x* and y*. Because the coordinates are given as longitude and latitude, x* is the longitude and y* is the latitude for the center of gravity.
x* = =
1,271,536.05
30,190
y* = = –
– 2,416,462.81
30,190
The center of gravity is (42.12 North, West), and is shown on the map to be fairly central to the target area.

43. Solved Problem 1
Figure 13.9

44. Solved Problem 2
The operations manager for Mile-High Lemonade narrowed the search for a new facility location to seven communities. Annual fixed costs (land, property taxes, insurance, equipment, and buildings) and variable costs (labor, materials, transportation, and variable overhead) are shown in the following table.
a. Which of the communities can be eliminated from further consideration because they are dominated (both variable and fixed costs are higher) by another community?
b. Plot the total cost curves for all remaining communities on a single graph. Identify on the graph the approximate range over which each community provides the lowest cost.
c. Using break-even analysis, calculate the break-even quantities to determine the range over which each community provides the lowest cost.

45. Solved Problem 2 FIXED AND VARIABLE COSTS FOR MILE-HIGH LEMONADE
Community
Fixed Costs per Year
Variable Costs per Barrel
Aurora
$1,600,000
$17.00
Boulder
$2,000,000
$12.00
Colorado Springs
$1,500,000
$16.00
Denver
$3,000,000
$10.00
Englewood
$1,800,000
$15.00
Fort Collins
$1,200,000
Golden
$1,700,000
$14.00
Table 13.2

46. Solved Problem 2 Location costs (in millions of dollars)
Barrels of lemonade per year (in hundred thousands)
10 –
8 –
6 –
4 –
2 – –
| | | | | | |
2.67
Break-even point
Golden
Break-even point
Fort Collins
Boulder
Denver
Figure 13.10

47. Solved Problem 2
Aurora and Colorado Springs are dominated by Fort Collins, because both fixed and variable costs are higher for those communities than for Fort Collins. Englewood is dominated by Golden.
Fort Collins is best for low volumes, Boulder for intermediate volumes, and Denver for high volumes Although Golden is not dominated by any community, it is the second or third choice over the entire range. Golden does not become the lowest-cost choice at any volume.

48. Solved Problem 2
c. The break-even point between Fort Collins and Boulder is
$1,200,000 + $15Q = $2,000,000 + $12Q
Q = 266,667 barrels per year
The break-even point between Denver and Boulder is
$3,000,000 + $10Q = $2,000,000 + $12Q
Q = 500,000 barrels per year

49. Solved Problem 3
The Arid Company makes canoe paddles to serve distribution centers in Worchester, Rochester, and Dorchester from existing plants in Battle Creek and Cherry Creek.
Arid is considering locating a plant near the headwaters of Dee Creek.
Annual capacity for each plant is shown in the right-hand column of the tableau.
Transportation costs per paddle are shown in the tableau in the small boxes.
For example, the cost to ship one paddle from Battle Creak to Worchester is $4.37.
The optimal allocations are also shown. For example, Battle Creek ships 12,000 units to Rochester.
What are the estimated transportation costs associated with this allocation pattern?

50. Solved Problem 3 Source Destination Capacity Worchester Rochester
Dorchester
Battle Creek
$4.37
$4.25
$4.89
12,000
Cherry Creek
$4.00
$5.00
$5.27
10,000
Dee Creek
$4.13
$4.50
$3.75
18,000
Demand
6,000
22,000
40,000
12,000
6,000
4,000
Figure 13.11

51. Solved Problem 3 The total cost is $167,000
Ship 12,000 units from Battle Creek
to $4.25
Cost =
$51,000
Ship 6,000 units from Cherry Creek
to $4.00
$24,000
Ship 4,000 units from Cherry Creek
to $5.00
$20,000
Ship 6,000 units from Dee Creek
to $4.50
$27,000
Ship 12,000 units from Dee Creek
to $3.75
$45,000
Total =
$167,000

52. Solved Problem 4
An electronics manufacturer must expand by building a second facility. The search is narrowed to four locations, all of which are acceptable to management in terms of dominant factors. Assessment of these sites in terms of seven location factors is shown in the following table. For example, location A has a factor score of 5 (excellent) for labor climate; the weight for this factor (20) is the highest of any. Calculate the weighted score for each location. Which location should be recommended?

53. Factor Score for Each Location
Solved Problem 4
FACTOR INFORMATION FOR ELECTRONICS MANUFACTURER
Factor Score for Each Location
Location Factor
Factor Weight A B C D
Labor climate 20 5 4
Quality of life 16 2 3 1
Transportation system
Proximity to markets 14
Proximity to materials 12
Taxes
Utilities 10

54. Weighted Score for each Location
Solved Problem 4
Based on the weighted scores shown below, location C is the preferred site, although location B is a close second.
CALCULATING WEIGHTED SCORES FOR ELECTRONIC MANUFACTURER
Weighted Score for each Location
Location Factor
Factor Weight A B C D
Labor climate 20
Quality of life 16
Transportation system
Proximity to markets 14
Proximity to materials 12
Taxes
Utilities 10
Totals
100
100 80 32 48 64 16 48 64 32 70 42 56 24 36 60 50 40 30
348
370
374
330