Supply Chains and Logistics Chapter 13

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.

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

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

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

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

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

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

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

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

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

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)

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

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

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(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*|

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)] (20 + 15 + 30) = 8.0 y* = = li yi li i [(20  8.5) + (15  9.5) + (30  1.5)] (20 + 15 + 30) = 5.5

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

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

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?

(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

Example 13.2 A is best for low volumes B for intermediate volumes 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) 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

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

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

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.

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 = $60 – $360 $10 – $60 = = 6 months – 300 – 50 The short answer: Baltic Avenue if 6 months or less, St. Charles Place if longer

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

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.

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

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.

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

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

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

Example 13.3 Figure 13.6

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.

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

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

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

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

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) = 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.

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

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 –2,416.462.80 This is Figure 9.10 to support Solved Problem 2. Table 13.1

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.

Solved Problem 1 Figure 13.9

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.

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

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 2.67 Break-even point Golden Break-even point Fort Collins Boulder Denver Figure 13.10

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.

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

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?

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

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 $24,000 Ship 4,000 units from Cherry Creek to Rochester @ $5.00 $20,000 Ship 6,000 units from Dee Creek to Rochester @ $4.50 $27,000 Ship 12,000 units from Dee Creek to Dorchester @ $3.75 $45,000 Total = $167,000

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?

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

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