OPM case analysis

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Supply Chain Logistic Networks

Chapter 13

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What is a Facility Location?

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.

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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

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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

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Factors Affecting Location Decisions

Dominant Factors in Services

Proximity to Customers

Transportation Costs and Proximity to Markets

Location of Competitors

Site-Specific Factors

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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

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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

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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

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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

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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

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

15(0) + 20(9) + 30(9) + 25(8) + 40(4)

= 810

Cincinnati =

Dayton =

Cleveland =

Toledo =

Lima =

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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

y* =

li yi

li

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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)

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Example 13.1

What is the center of gravity for the electric utilities supplier?

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)

The center of gravity is calculated as shown below:

x* = =

li xi

li

li =

li xi =

5 + 92 + 70 + 35 + 9 + 227 + 16 + 153 = 607

5(7) + 92(8) + 70(11) + 35(11) + 9(12) + 227(13)

+ 16(14) + 153(15) = 7,504

= 12.4

7,504

607

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Example 13.1

x* = =

li yi

li

li yi =

5(13) + 92(12) + 70(10) + 35(7) + 9(4) + 227(11)

+ 16(10) + 153(5) = 5,572

= 9.2

5,572

607

What is the center of gravity for the electric utilities supplier?

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)

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Example 13.1

The resulting load-distance score is

ld =  lidi =

5(5.4 + 3.8) + 92(4.4 + 2.8) + 70(1.4 + 0.8) + 35(1.4 + 2.2) + 90(0.4 + 5.2) + 227(0.6 + 1.8) + 16(1.6 + 0.8) + 153(2.6 + 4.2)

= 2,662.4

where

di = |xi – x*| + |yi – y*|

Using rectilinear distance, what is the resulting load–distance score for this location?

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)

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Application 13.3

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

y* = =

li yi

li

[(20  11) + (15  12) + (30  4)]

(20 + 15 + 30)

= 8.0

[(20  8.5) + (15  9.5) + (30  1.5)]

(20 + 15 + 30)

= 5.5

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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

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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

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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?

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Example 13.2

$62(20,000) = $1,240,000

$1,390,000

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

$38(20,000) = $760,000

$1,060,000

$24(20,000) = $480,000

$980,000

$30(20,000) = $600,000

$1,200,000

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:

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A best

B best

C best

Example 13.2

The figure shows the graph of the total cost lines.

| | | | | | | | | | | |

0 2 4 6 8 10 12 14 16 18 20 22

1,600 –

1,400 –

1,200 –

1,000 –

800 –

600 –

400 –

200 –

–

Annual cost (thousands of dollars)

Q (thousands of units)

6.25

14.3

Break-even point

(20, 980)

(20, 1,390)

(20, 1,200)

(20, 1,060)

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.

Figure 13.3

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Example 13.2

(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

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.

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Example 13.2

(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

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.

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By chance, the Atlantic City Community Chest has to close temporarily for general repairs. They are considering four temporary office locations:

Application 13.4

Property Address	Move-in Costs	Monthly Rent
Boardwalk	$400	$50
Marvin Gardens	$280	$24
St. Charles Place	$360	$10
Baltic Avenue	$60	$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.

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Application 13.4

| | | | | | | | |

0 1 2 3 4 5 6 7 8

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

= = 6 months

– 300

– 50

$60 – $360

$10 – $60

The short answer: Baltic Avenue if 6 months or less, St. Charles Place if longer

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Transportation Method

Transportation method for location problems

A quantitative approach that can help solve multiple-facility location problems

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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.

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Transportation Method

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		400		300			900
							900

Initial Tableau

Figure 13.4

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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.

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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

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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

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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

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Example 13.3

Figure 13.6

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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.

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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

The GIS Method for Locating Multiple Facilities

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Inventory Placement

Centralized placement

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

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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

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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?

Example 13.4

Location Factor	Weight	Score
Total patient miles per month	25	4
Facility utilization	20	3
Average time per emergency trip	20	3
Expressway accessibility	15	4
Land and construction costs	10	1
Employee preferences	10	5

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The WS for this particular site is calculated by multiplying each factor’s weight by its score and adding the results:

Example 13.4

Location Factor	Weight	Score
Total patient miles per month	25	4
Facility utilization	20	3
Average time per emergency trip	20	3
Expressway accessibility	15	4
Land and construction costs	10	1
Employee preferences	10	5

WS =

(25  4) + (20  3) + (20  3) + (15  4) + (10  1) + (10  5)

= 100 + 60 + 60 + 60 + 10 + 50

= 340

The total WS of 340 can be compared with the total weighted scores for other sites being evaluated.

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0.9

1.6

1.8

1.6

5.9

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?

Application 13.5

0.5

1.8

3.0

1.2

6.5

0.8

2.4

2.8

6.8

Location Factor	Weight	The Neighborhood	Sesame Street	Ronald’s Playhouse
Material Supply	0.1	5	9	8
Quality of Life	0.2	9	8	4
Mild Climate	0.3	10	6	8
Labor Skills	0.4	3	4	7

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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	–80.023	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	–2,416.462.80

Table 13.1

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This is Figure 9.10 to support Solved Problem 2.

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* = = 42.1178

1,271,536.05

30,190

y* = = – 80.0418

– 2,416,462.81

30,190

The center of gravity is (42.12 North, 80.04 West), and is shown on the map to be fairly central to the target area.

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Solved Problem 1

Figure 13.9

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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.

Solved Problem 2

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.

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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	$15.00
Golden	$1,700,000	$14.00

Table 13.2

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Solved Problem 2

Location costs (in millions of dollars)

Barrels of lemonade per year (in hundred thousands)

10 –

8 –

6 –

4 –

2 –

–

| | | | | | |

0 1 2 3 4 5 6

Fort Collins

Boulder

Denver

Golden

Break-even point

2.67

Figure 13.10

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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.

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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

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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?

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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		12,000		40,000


	12,000

6,000	4,000

	6,000	12,000

Solved Problem 3

Figure 13.11

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Solved Problem 3

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

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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?

Solved Problem 4

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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	4	5
Quality of life	16	2	3	4	1
Transportation system	16	3	4	3	2
Proximity to markets	14	5	3	4	4
Proximity to materials	12	2	3	3	4
Taxes	12	2	5	5	4
Utilities	10	5	4	3	3

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CALCULATING WEIGHTED SCORES FOR ELECTRONIC MANUFACTURER

Weighted Score for each Location

Location Factor

Factor Weight

Labor climate

Quality of life

Transportation system

Proximity to markets

Proximity to materials

Taxes

Utilities

Totals

100

Solved Problem 4

100

48	64	48	32
70	42	56	56
24	36	36	48
24	60	60	48
50	40	30	30
348	370	374	330

Based on the weighted scores shown below, location C is the preferred site, although location B is a close second.

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This Week’s Discussions

Procter & Gamble (P&G) – What have we learned about P&G this semester?

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