11 Location Power Point Slides by Jeff Heyl

11 Location Power. Point Slides by Jeff Heyl Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. For Operations Management, 9 e by Krajewski/Ritzman/Malhotra © 2010 Pearson 11 Education – 1

Location Decisions l Location decisions affect processes and departments u Marketing u Human resources u Accounting and finance u Operations u International operations 11 – 2 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Location Decisions l Many factors u Sensitive to location u High impact on the company’s ability to meet its goals u Divide location factors l Dominant factors in manufacturing u Favorable labor climate u Proximity to markets u Quality of life u Proximity to suppliers and resources u Proximity to the parent company’s facilities u Utilities, taxes, and real estate costs u Other factors 11 – 3 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Location Decisions l Dominant factors in services l Impact of location on sales and customer satisfaction u Proximity to customers u Transportation costs and proximity to markets u Location of competitors u Site-specific factors 11 – 4 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Geographic Information Systems l GIS is a system of computer software, hardware, and data l Use to manipulate, analyze, and present information relevant to a location decision u Create a visual representation of a firm’s location choices u Useful decision-making tool l Using GIS to identify locations and demographic customer segments u Identifying locations that relate to target market u Part of an array of decision-making tools 11 – 5 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Locating a Single Facility l Expand onsite, build another facility, or relocate to another site u Onsite expansion u Building a new plant or moving to a new retail or office space l Comparing several sites 11 – 6 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Selecting a New Facility 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 11 – 7 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Calculating Weighted Scores EXAMPLE 11. 1 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 20 3 Expressway accessibility 15 4 Land construction costs 10 1 Employee preferences 10 5 11 – 8 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Calculating Weighted Scores SOLUTION The WS for this particular site is calculated by multiplying each factor’s weight by its score and adding the results: 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 construction costs 10 1 Employee preferences 10 5 WS = (25 4) + (20 3) + (15 4) + (10 1) + (10 5) = 100 + 60 + 10 + 50 = 340 The total WS of 340 can be compared with the total weighted scores for other sites being evaluated. 11 – 9 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Application 11. 1 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 9 8 4 Mild Climate 0. 3 10 6 8 Labor Skills 0. 4 3 4 7 11 – 10 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Application 11. 1 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 Material Supply 0. 1 5 0. 5 9 0. 9 8 0. 8 Quality of Life 0. 2 9 1. 8 8 1. 6 4 0. 8 Mild Climate 0. 3 10 3. 0 6 1. 8 8 2. 4 Labor Skills 0. 4 3 1. 2 4 1. 6 7 2. 8 6. 5 Sesame Street Ronald’s Playhouse 6. 8 5. 9 11 – 11 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Load-Distance (ld) Method l Identify and compare candidate locations u Like weighted-distance method u Select a location that minimizes the sum of the loads multiplied by the distance the load travels u Time may be used instead of distance 11 – 12 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Load-Distance (ld) Method l Calculating a load-distance score u Varies by industry u Use the actual distance to calculate ld score u Use rectangular or Euclidean distances u Different measures for distance u Find one acceptable facility location that minimizes the ld score l Formula for the ld score ld = lidi i 11 – 13 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Application 11. 2 What is the distance between (20, 10) and (80, 60)? SOLUTION Euclidean distance: d. AB = (x. A – x. B)2 + (y. A – y. B)2 = (20 – 80)2 + (10 – 60)2 = 78. 1 Rectilinear distance: d. AB = |x. A – x. B| + |y. A – y. B| = |20 – 80| + |10 – 60| = 110 11 – 14 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Application 12. 3 Management is investigating which location would be best to position its new plant relative to two suppliers (located in Cleveland 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 11 – 15 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Application 12. 3 SOLUTION Calculations: 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 = 15(0) + 20(9) + 30(9) + 25(8) + 40(4) Dayton = 15(9) + 20(0) + 30(10) + 25(5) + 40(9) = 810 = 920 Cleveland = 15(9) + 20(10) + 30(0) + 25(5) + 40(5) = 660 Toledo = 15(8) + 20(5) + 30(0) + 25(0) + 40(8) = 690 Lima = 15(4) + 20(9) + 30(5) + 25(8) + 40(0) = 590 11 – 16 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Center of Gravity Method l A good starting point u Find x coordinate, x*, by multiplying each point’s x coordinate by its load (lt), summing these products li xi, and dividing by li u The center of gravity’s y coordinate y* found the same way u Generally not the optimal location x* = i li xi i li y* = i li yi i li 11 – 17 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Finding the Center of Gravity EXAMPLE 11. 2 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 Three Rivers, MI Tons Shipped x, y Coordinates 5, 000 (7, 13) Fort Wayne, IN 92, 000 (8, 12) Columbus, OH 70, 000 (11, 10) Ashland, KY 35, 000 (11, 7) 9, 000 (12, 4) 227, 000 (13, 11) Wheeling, WV 16, 000 (14, 10) Roanoke, VA 153, 000 (15, 5) Kingsport, TN Akron, OH 11 – 18 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Finding the Center of Gravity What is the center of gravity for the electric utilities supplier? Using rectilinear distance, what is the resulting load–distance score for this location? SOLUTION Customer Location Three Rivers, MI Tons Shipped x, y Coordinates 5, 000 (7, 13) Fort Wayne, IN 92, 000 (8, 12) Columbus, OH 70, 000 (11, 10) Ashland, KY 35, 000 (11, 7) 9, 000 (12, 4) 227, 000 (13, 11) Wheeling, WV 16, 000 (14, 10) Roanoke, VA 153, 000 (15, 5) Kingsport, TN Akron, OH The center of gravity is calculated as shown below: li = 5 + 92 + 70 + 35 + 9 + 227 + 16 + 153 = 607 i li xi = 5(7) + 92(8) + 70(11) + 35(11) + 9(12) + 227(13) i + 16(14) + 153(15) = 7, 504 li xi x* = i li i 7, 504 = 12. 4 = 607 11 – 19 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Finding the Center of Gravity What is the center of gravity for the electric utilities supplier? Using rectilinear distance, what is the resulting load–distance score for this location? Customer Location Three Rivers, MI Tons Shipped x, y Coordinates 5, 000 (7, 13) Fort Wayne, IN 92, 000 (8, 12) Columbus, OH 70, 000 (11, 10) Ashland, KY 35, 000 (11, 7) 9, 000 (12, 4) 227, 000 (13, 11) Wheeling, WV 16, 000 (14, 10) Roanoke, VA 153, 000 (15, 5) Kingsport, TN Akron, OH li yi = 5(13) + 92(12) + 70(10) + 35(7) + 9(4) + 227(11) i + 16(10) + 153(5) = 5, 572 li yi x* = i li i 5, 572 = 9. 2 = 607 11 – 20 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Finding the Center of Gravity What is the center of gravity for the electric utilities supplier? Using rectilinear distance, what is the resulting load–distance score for this location? Customer Location Three Rivers, MI Tons Shipped x, y Coordinates 5, 000 (7, 13) Fort Wayne, IN 92, 000 (8, 12) Columbus, OH 70, 000 (11, 10) Ashland, KY 35, 000 (11, 7) 9, 000 (12, 4) 227, 000 (13, 11) Wheeling, WV 16, 000 (14, 10) Roanoke, VA 153, 000 (15, 5) Kingsport, TN Akron, OH The resulting load-distance score is ld = lidi = 5(5. 4 + 3. 8) + 92(4. 4 + 2. 8) + 70(1. 4 + 0. 8) + i 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*| 11 – 21 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Application 11. 4 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? SOLUTION li xi i x* = li i li yi y* = i li i [(20 11) + (15 12) + (30 4)] = 8. 0 = (20 + 15 + 30) [(20 8. 5) + (15 9. 5) + (30 1. 5)] = 5. 5 = (20 + 15 + 30) 11 – 22 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Using Break-Even Analysis l Compare location alternatives on the basis of quantitative factors expressed in total costs u Determine each site u Plot the variable costs and fixed costs for total cost lines u Identify the approximate ranges for which each location has lowest cost u Solve algebraically for break-even points over the relevant ranges 11 – 23 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Break-Even Analysis for Location EXAMPLE 11. 3 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 11 – 24 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Break-Even Analysis for Location 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 breakeven quantities over the relevant ranges. If the expected demand is 15, 000 units per year, what is the best location? 11 – 25 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Break-Even Analysis for Location SOLUTION 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 A $150, 000 B $300, 000 C $500, 000 D $600, 000 Variable Costs (Cost per Unit)(No. of Units) Total Cost (Fixed + Variable) 11 – 26 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Break-Even Analysis for Location SOLUTION 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 $62(20, 000) = $1, 240, 000 $1, 390, 000 B $300, 000 $38(20, 000) = $760, 000 $1, 060, 000 C $500, 000 $24(20, 000) = $480, 000 $980, 000 D $600, 000 $30(20, 000) = $600, 000 $1, 200, 000 11 – 27 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Break-Even Analysis for Location A 1, 600 – Annual cost (thousands of dollars) Figure 11. 1 shows the graph of the total cost lines. The line for community A goes from (0, 150) to (20, 1, 390). The graph indicates that community A is best for low volumes, B for intermediate volumes, and 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. (20, 1, 390) 1, 400 – 1, 200 – B (20, 1, 060) C 1, 000 – (20, 980) 800 – Break-even point 600 – Break-even point 400 – 200 – |– 0 C best B best A best | | | | 2 4 6 8 10 12 14 16 18 20 22 | | | 6. 25 14. 3 Q (thousands of units) Figure 11. 1 – Break-Even Analysis of Four Candidate Locations 11 – 28 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. D (20, 1, 200)

Break-Even Analysis for Location Step 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. We find it by setting both communities’ total cost equations equal to each other and solving: (A) (B) $150, 000 + $62 Q = $300, 000 + $38 Q 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. It is (B) (C) $300, 000 + $38 Q = $500, 000 + $24 Q Q = 14, 286 units 11 – 29 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Break-Even Analysis for Location No other break-even quantities are needed. The break-even point between A and C lies Step 2: The break-even quantity between A and B lies at the above the shaded area, which end of the first range, where A is best, and the does not mark the start beginning of the second range, whereeither B is best. We or the end of onetotal of the three find it by setting both communities’ cost relevant ranges. equations equal to each other and solving: (A) (B) $150, 000 + $62 Q = $300, 000 + $38 Q 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. It is (B) (C) $300, 000 + $38 Q = $500, 000 + $24 Q Q = 14, 286 units 11 – 30 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Application 11. 5 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 $350 $10 $60 Baltic Avenue 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. 11 – 31 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Application 11. 5 SOLUTION 500 – Fs + cs. Q = FB + c. BQ FB – Fs Q= c –c s B $60 – $360 $10 – $60 – 300 = = 6 months – 50 St Charles Place 400 – – Total Cost → = Boardwalk – Marvin Gardens 300 – – Baltic Avenue 200 – – The short answer: Baltic Avenue if 6 months or less, St. Charles Place if longer 100 – – | – 0 | | | 1 2 3 | | 4 5 Months → 11 – 32 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. | | | 6 7 8

Locating Within a Network l When a firm with a network of existing facilities plans a new facility, one of two conditions exists u Facilities operate independently u Facilities interact l The GIS method for locating multiple facilities u The transportation method 11 – 33 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Locating Within a Network l 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 l Other methods of location analysis u Heuristics u Simulation u Optimization 11 – 34 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Locating Multiple Facilities EXAMPLE 11. 4 l Witherspoon Automotive remanufactures automotive components and subassemblies l Full truckloads of parts to and from customers l Two locations: Spartanburg, SC and Orlando, FL l Locations have a remanufacturing facility and a warehouse l Spartanburg covers a total of 362 customers l Orlando facility covers a total of 66 customers l Spartanburg DC shipped 17, 219 and Orlando DC shipped 4, 629 full truckloads last year l Operating regions and customer locations are shown in Figure 11. 2. 11 – 35 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Locating Multiple Facilities Figure 11. 2 – Operating Regions and Customer Location for Witherspoon Automotive 11 – 36 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Locating Multiple Facilities The senior management decided to close the Spartanburg facility and split the region into two each with its own manufacturing and distribution center Five important location factors: 1. The new facilities should be located in a major metropolitan area 2. Total load–distance score should be minimized 3. Size of the two new facilities should not exceed a maximum of 9, 500 truckloads of output per year 4. Customer truckloads allocated between the two facilities should be fairly balanced 5. New distribution network should be able to accommodate up to 1, 000 full truckload shipments per year from the Alabama 11 – 37 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Locating Multiple Facilities Where should the two new facilities be opened, assuming that the Orlando DC will stay where it is, and that fixed cost differences in opening a new facility are comparable across most potential sites in the region? SOLUTION Using the data in their system and Map. Point, the managers at Witherspoon automotive overlaid the locations and the number of full truckload shipments delivered last year for each customer in the Spartanburg region onto a map. The Witherspoon Automotive video on myomlab shows how to perform this analysis using Map. Point. To achieve a greater degree of aggregation in customer base and to also give due consideration to the quality of life location factor, the map was changed from displaying data for each street address (customer) to an aggregate view that displays data for each Metropolitan Statistical Area (MSA). 11 – 38 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Locating Multiple Facilities Figure 11. 3 – Truckload Concentration for Witherspoon 11 – 39 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Locating Multiple Facilities The darker the shade, the greater the number of truckloads in the MSA. It was visually clear that Atlanta and Charlotte were the major markets, with Columbia, South Carolina; Greenville, South Carolina; and Richmond, Virginia, also having a heavy concentration of customers. From this map in Figure 11. 3, it was easy to see that the dark green shaded area in Atlanta has a heavy customer-trips concentration. It represents 4, 475 full truckloads, which would easily support half a facility. It seems reasonable for the management to locate one of the two new facilities near Atlanta. This decision will also achieve two other management objectives, in that the facility is near a major metropolitan area and is also well placed to serve the proposed expansion of the northern Alabama market. Management stated that if it decides to locate a facility near the Atlanta area, it would be in Buford, Georgia. 11 – 40 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Locating Multiple Facilities The next step was to partition the customers into 2 regions, each with a total demand of less than 9, 500 truckloads. Because it seemed clear that the Atlanta area would have a facility, one region was circled around Atlanta as shown in Figure 11. 4. Furthermore, if the northern Alabama market develops as hoped, it will handle an additional 1, 000 truckloads. Because of this potential, the Atlanta region can only handle 8, 500 truckloads for current customers. After a careful look at the map data, it was decided that Georgia, Tennessee, Alabama, and the parts of South Carolina that were within 2. 5 hours of the Atlanta facility would be assigned to the Atlanta region. The Augusta/Aiken MSA that straddles the Georgia/South Carolina border was also added to this region to balance the two regions. This scenario results in the Atlanta region being assigned 8, 397 truckloads and the second region having 8, 822 trips, and achieving a 48. 8 percent to 51. 2 percent split while still allowing capacity in the Atlanta region for the proposed expansion of the northern Alabama market. 11 – 41 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Locating Multiple Facilities Figure 11. 4 – Witherspoon’s Facilities Areas 11 – 42 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Locating Multiple Facilities In order to identify a good location for the second facility, the center of gravity for the second region was determined to find a good starting point. Looking at the map in Figure 11. 4, it appears that the center of the second region is around Durham, North Carolina. However, the center of gravity for the second region is close to a National Forest in Randolph County, North Carolina—not too far from Charlotte but considerably south and west of Durham. Such an outcome is to be expected because the Charlotte and to a lesser extent Columbia, South Carolina, markets have such a large percentage of the truckload volume for this region. However, the center of gravity does not appear to be a promising site because it is only near one customer. Given this dilemma, the management of Witherspoon Automotive decided to pick a site next to the center of gravity as well as several sites in the general area of the center of gravity that are near Interstate I-85. 11 – 43 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Locating Multiple Facilities Load–distance scores were computed using driving mileage and driving time based on last year’s demand for each of the possible locations. The following results were obtained for load –distance calculations based on one-way trips: Site City Load-Distance Using One-Way Mileage Load-Distance Using One-Way Travel Hours 1 Albemarle 1, 331, 608 22, 194 2 Salisbury 1, 075, 839 18, 541 3 Greensboro 1, 222, 675 20, 378 4 Concord 1, 037, 424 17, 938 11 – 44 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Locating Multiple Facilities As the Witherspoon Automotive managers reviewed the results, they noted that Concord will provide the minimum mileage and drive time, and have the additional advantage of being near Charlotte—fulfilling the managerial objective of being located near a major city. Another attractive feature of this solution is that the Greenville, South Carolina, and Augusta, Georgia, markets are almost as close to the Concord facility as they are to the Buford facility. Management can reassign customers in these markets to the Charlotte region at little additional cost if the northern Alabama market grows faster than expected. 11 – 45 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Solved Problem 1 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 Table 11. 1. 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? 11 – 46 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Solved Problem 1 TABLE 11. 1 | FACTOR INFORMATION FOR ELECTRONICS MANUFACTURER Factor Score for Each Location Factor Weight A B C D 1. Labor climate 20 5 4 4 5 2. Quality of life 16 2 3 4 1 3. Transportation system 16 3 4 3 2 4. Proximity to markets 14 5 3 4 4 5. Proximity to materials 12 2 3 3 4 6. Taxes 12 2 5 5 4 7. Utilities 10 5 4 3 3 11 – 47 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Solved Problem 1 SOLUTION Based on the weighted scores shown in Table 11. 2, location C is the preferred site, although location B is a close second. TABLE 11. 2 | | CALCULATING WEIGHTED SCORES FOR ELECTRONICS MANUFACTURER Weighted Score for each Location Factor Weight 1. Labor climate 20 2. Quality of life 16 3. Transportation system 16 4. Proximity to markets 14 5. Proximity to materials 12 6. Taxes 12 7. Utilities 10 Totals A B C 100 11 – 48 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. D

Solved Problem 1 SOLUTION Based on the weighted scores shown in Table 11. 2, location C is the preferred site, although location B is a close second. TABLE 11. 2 | | CALCULATING WEIGHTED SCORES FOR ELECTRONICS MANUFACTURER Weighted Score for each Location Factor Weight A B C D 1. Labor climate 20 100 80 80 100 2. Quality of life 16 32 48 64 16 3. Transportation system 16 48 64 48 32 4. Proximity to markets 14 70 42 56 56 5. Proximity to materials 12 24 36 36 48 6. Taxes 12 24 60 60 48 7. Utilities 10 50 40 30 30 100 348 370 374 330 Totals 11 – 49 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

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 Table 11. 3. 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. 11 – 50 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Solved Problem 2 TABLE 11. 3 | 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 $12. 00 Colorado Springs $1, 500, 000 $16. 00 Denver $3, 000 $10. 00 Englewood $1, 800, 000 $15. 00 Fort Collins $1, 200, 000 $15. 00 Golden $1, 700, 000 $14. 00 11 – 51 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Location costs (in millions of dollars) Solved Problem 2 10 – 8– 6– Break-even point Golden 4– 2– |– 0 Break-even point Fort Collins Denver Boulder | | | 1 2 3 4 5 6 2. 67 Barrels of lemonade per year (in hundred thousands) Figure 11. 5 – Break-Even Analysis of Four Candidate Locations 11 – 52 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Solved Problem 2 SOLUTION a. 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. b. Figure 11. 5 shows that 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. 11 – 53 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Solved Problem 2 c. The break-even point between Fort Collins and Boulder is $1, 200, 000 + $15 Q =$2, 000 + $12 Q Q =266, 667 barrels per year The break-even point between Denver and Boulder is $3, 000 + $10 Q =$2, 000 + $12 Q Q =500, 000 barrels per year 11 – 54 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Solved Problem 3 The new Health-Watch facility is targeted to serve seven census tracts in Erie, Pennsylvania, whose latitudes and longitudes are shown in Table 11. 4. 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? TABLE 11. 4 Census Tract | LOCATION DATA AND CALCULATIONS FOR HEALTH WATCH 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 11 – 55 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Solved Problem 3 SOLUTION We use Map. Point in this solution, with coordinates represented in the form of latitude and longitude rather than an (x, y) grid, to calculate the center of gravity. First the target area is displayed on the map of Erie, Pennsylvania, using Map. Point. In Figure 11. 6 a pushpin is placed in the approximate geographical center of the census tracts. The location sensor is then turned on. By moving the cursor over the pushpin, the location sensor will register the longitude and latitude for the pushpin. The population of each census tract is added to the map using Map. Point’s built-in demographic data. Thus, we obtain the following table in which latitudes and longitudes for each of the seven census-tracts are given, along with their actual populations, in thousands. 11 – 56 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Solved Problem 3 Figure 11. 6 – Center of Gravity for Health-Watch 11 – 57 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Solved Problem 3 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. 1, 271, 536. 05 x* = = 42. 1178 30, 190 – 2, 416, 462. 81 y* = = – 80. 0418 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. Active Model 11. 2 in myomlab confirms these calculations for the center of gravity, and allows us to explore other alternative locations as well. 11 – 58 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

11 – 59 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.