Chapter 8 Location Strategies Problems

PROBLEMS 108. A manufacturing company preparing to build a new plant is considering three potential locations for it. The fixed and variable costs for the three alternative locations are presented below. a. Complete a numeric locational cost-volume analysis. b. Indicate over what range each of the alternatives A, B, C is the low-cost choice. c. Is any alternative never preferred? Explain. Costs Fixed ($) Variable ($ per unit) A 2,500,000 21 B 2,000,000 25 C 3,500,000 15 B is cheapest up to 125,000 units; C is cheapest after 166,667 units. A is cheapest in between. The B-C crossover is not relevant. Thus each alternative has an attractive range. Break-even points Units Dollars Option A vs. Option B 125,000 5,125,000 Option A vs. Option C 166,667 6,000,000 Option B vs. Option C 150,000 5,750,000 (Methods of evaluating location alternatives, moderate) {AACSB: Analytic Skills} 206 109. A farmers' cooperative association plans to build a new sugar mill in Southwestern Louisiana. The primary objective of the mill is to provide the farmers with a place to take their crop for processing that will reduce their transportation costs. The members of the coop believe that the center-of-gravity method is appropriate for this objective. While there are over 200 sugar cane farms in the region, they are tightly clustered around six villages. Using the data below, use the center-of-gravity method to calculate the coordinates of the best location for this mill. On the grid below, plot the location of the six farm clusters and the calculated mill location. All mileage references use the city of Lake Charles as (0,0). Village Arceneaux Boudreaux Cancienne Darbonne Evangeline Fontenot Miles East of Lake Charles 90 140 20 50 100 10 SEE NEXT PAGE FOR SOLUTION. 207 Miles North of Lake Charles 10 60 70 20 80 120 Sugar Cane tonnage 240,000 320,000 450,000 120,000 60,000 140,000 The center of gravity, weighted by the tonnage at each village cluster, is about 66.8 miles east of Lake Charles and 58.0 miles north of Lake Charles. North --> Sugar Mill and Villages 140 120 100 10, 120 80 60 40 100, 80 20, 70 20 0 140, 60 67, 58 50, 20 0 20 40 60 90, 10 80 100 120 140 160 East --> (Methods of evaluating location alternatives, moderate) {AACSB: Analytic Skills} 208 110. A clothing chain is considering two different locations for a new retail outlet. The organization has identified the four factors listed in the following table as the basis for evaluation, and has assigned weights as shown on the right side of this table. The manager has rated each location on each factor, on a 100-point basis (higher scores are better), as shown in the right-hand table. a. Calculate the composite score for each alternative location. b. Which site should be chosen? c. Are you concerned about the sensitivity and subjectivity of this solution? Comment. Factor 1 2 3 4 Factor Description Average community income Community growth potential Availability of public transportation Labor cost Weight .40 .25 .15 .20 Barclay 75 60 45 80 Chester 70 80 90 65 The higher rated site is Chester, 74.5 to 67.75. There is a margin of several points, which should overcome most levels of subjectivity. The site factor scores are quite different, so that a small swing in weights could produce swings in scores of a few points, but probably not the seven necessary to reverse the findings. Weight Barclay Chester 0.40 75 70 Factor 1 0.25 60 80 Factor 2 0.15 45 90 Factor 3 0.20 80 65 Factor 4 Total 1.00 Weighted sum 67.75 74.5 Weighted average 67.75 74.5 (Methods of evaluating location alternatives, moderate) {AACSB: Analytic Skills} 111. A manufacturing company is considering two alternative locations for a new facility. The fixed and variable costs for the two locations are found in the table below. For which volume of business would the two locations be equally attractive? If the company plans on producing 50,000 units, which location would be more attractive? Fixed Costs Variable Costs ($ per unit) Glen Rose $1,000,000 25 Mesquite $1,500,000 23 Crossover is at 250,000 units. Below the crossover, Glen Rose must be cheaper as it has the lower fixed cost. Thus, for an estimated unit volume of 50,000, Glen Rose should be chosen. 209 Break-even points Option 1 vs. Option 2 Units 250,000 Dollars 7,250,000 Volume analysis at 50,000 units Option 1 Option 2 total cost $2,250,000.00 $2,650,000.00 (Methods of evaluating location alternatives, moderate) {AACSB: Analytic Skills} 112. East Texas Seasonings is preparing to build one processing center to serve its four sources of seasonings. The four source locations are at coordinates shown below. Also, the volume from each source is provided. a. Calculate the volume-weighted center of gravity. b. Calculate the simple center of gravity (all cities weighted equally). c. Explain why the two calculations differ. Athens, Texas Beaumont, Texas Carthage, Texas Denton, Texas X-coordinate 30 20 55 20 Y-coordinate 40 15 60 70 Volume 100 400 150 250 The weighted center of gravity is located at X = 24,250 / 900 = 26.9, Y = 36,500 / 900 = 40.6. The simple center of gravity is located at X = 125 / 4 = 31.25. Y = 185 / 4 = 46.25. The simple center is more to the east and north than the weighted center of gravity. A partial explanation is that the heaviest tonnage is from Beaumont, which is far to the west and south. Its influence pulls the weighted center toward the west and south. (Methods of evaluating location alternatives, moderate) {AACSB: Analytic Skills} 113. Location A would result in annual fixed costs of $300,000 and variable costs of $55 per unit. Annual fixed costs at Location B are $600,000 with variable costs of $32 per unit. Sales volume is estimated to be 30,000 units per year. Which location has the lower cost at this volume? How large is its cost advantage? At what volume are the two facilities equal in cost? At 30,000 units, Location A has total costs of $1, 950,000, while Location B has total costs of $1,560,000. Location B is cheaper by $390,000. The crossover occurs where 600,000 + 32X = 300,000 + 55X, or at X = 300,000 / 23 = 13,043 units. (Methods of evaluating location alternatives, moderate) {AACSB: Analytic Skills} 210 114. Using the factor ratings shown below, determine which location alternative should be chosen on the basis of maximum composite score. Location Factor Weight A B C Easy access 0.15 86 72 90 Parking facilities 0.20 72 77 91 Display area 0.18 86 90 90 Shopper (walking) traffic 0.21 94 86 80 Neighborhood wealth 0.16 99 89 81 Neighborhood safety 0.10 96 85 75 A is best (87.96), followed by C (85.16). B is somewhat further behind (83.20). Weight A B C Easy access 0.15 86 72 90 Parking facilities 0.20 72 77 91 Display area 0.18 86 90 90 Shopper (walking) traffic 0.21 94 86 80 Neighborhood wealth 0.16 99 89 81 Neighborhood safety 0.10 96 85 75 Total 1.00 Weighted sum 87.96 83.20 85.16 Weighted average 87.96 83.20 85.16 (Methods of evaluating location alternatives, moderate) {AACSB: Analytic Skills} 115. A manager has received an analysis of several cities being considered for a new order fulfillment center (warehouse) for Shop at Home Network. The scores (scale is 10 points = best) are contained in the table below. a. If the manager weights the factors equally, how would the locations be ranked? b. If transportation costs and operating costs are given weights that are double the weights of the others, should the locations be ranked differently? Location Factor W X Y Z Business services 7 9 5 4 Community services 5 7 6 7 Real estate cost 7 3 8 6 Construction costs 8 6 6 5 Operating costs 5 4 7 6 Business taxes 6 9 6 4 Transportation costs 8 6 7 8 SEE SOLUTION ON NEXT PAGE. 211 The locations are ranked W, Y, X, Z with equal weights; but W and Y tie for highest, and Z and X tie for lowest as revised. Business services Community services Real estate cost Construction costs Operating costs Business taxes Transportation costs Total Weighted average Weight 1 1 1 1 1 1 1 7 W 7 5 7 8 5 6 8 46 6.579 X 9 7 3 6 4 9 6 44 6.286 Y 5 6 8 6 7 6 7 45 6.429 Z 4 7 6 5 6 4 8 40 5.714 Weight W X Y Z Business services 1 7 9 5 4 Community services 1 5 7 6 7 Real estate cost 1 7 3 8 6 Construction costs 1 8 6 6 5 Operating costs 2 5 4 7 6 Business taxes 1 6 9 6 4 Transportation costs 2 8 6 7 8 Total 9 Weighted sum 59 54 59 54 Weighted average 6.56 6 6.56 6 (Methods of evaluating location alternatives, moderate) {AACSB: Analytic Skills} 212 116. A telecommunications firm is planning to lay fiber optic cable from several community college distance learning sites to a central studio, in such a way that the miles of cable are minimized. Some locations require more than one set of cables (these are the loads). Where should the studio be located to accomplish the objective? College A B C D E F G Map Coordinate (x, y) (2,10) (6,8) (4,9) (9,5) (8,1) (3,2) (2,6) Load 3 2 4 1 3 2 1 This is a center of gravity problem, even though it is not about shipping tangible items. The center of gravity is at coordinates X = 4.69, Y = 6.25. Weight X coord Y coord 3 2 10 Location 1 2 Location 2 6 8 4 Location 3 4 9 1 Location 4 9 5 3 Location 5 8 1 2 Location 6 3 2 1 Location 7 2 6 Sum 16 34 41 Average 4.857 5.857 Weighted Average 4.6875 6.25 (Methods of evaluating location alternatives, moderate) {AACSB: Analytic Skills} 213 117. The owner of a millwork shop is considering three alternative locations for a new plant for building embossed-and-clad steel exterior doors for residences. Fixed and variable costs follow. Since the plant ships nationwide, revenue is assumed the same regardless of plant location. Plot the total cost lines in the chart provided below, and identify the range over which each location is best. Costs Fixed Variable A $700,000 $28 Location B $1,000,000 $18 C $1,100,000 $20 A is cheapest from 0 to about 30,000 units. B is cheapest thereafter. C can never be preferred. Break-even points Location A vs. Location B Location A vs. Location C Location B vs. Location C Units 30,000 50,000 -50,000 Dollars $1,540,000 $2,100,000 $100,000 (Methods of evaluating location alternatives, moderate) {AACSB: Analytic Skills} 214 118. A manufacturing firm is considering three potential locations for a new parts manufacturing facility. A consulting firm has assessed three sites based on the four factors supplied by management as critical to the location's success. Given the management-supplied factor weights and the consultant team scores, which location should be selected? Scores are based on 50 = best. Do the results surprise you in any way? Comment. Factor Labor Climate Taxes Utilities Wages Weight 10 30 20 40 A 35 30 25 10 Location B 45 40 20 25 C 20 40 45 25 C is clearly better than either A or B. This problem illustrates the importance of having good scores on important factors. B has scores that are about as high as those of C, but in the wrong places. Weight Location A Location B Location C Labor Climate 10 35 45 20 Taxes 30 30 40 40 Utilities 20 25 20 45 Wages 40 10 25 25 Total 100 Weighted sum 2150 3050 3300 Weighted average 21.5 30.5 33.0 (Methods of evaluating location alternatives, moderate) {AACSB: Analytic Skills} 119. Environmental Glass Products, Inc. wants to build a new centralized facility to receive household, commercial, and industrial glass for recycling. This center will be supplied by trucks coming from four "collection points," where recyclable glass is dropped off by individuals and businesses. The volume and the map coordinates for the four collection centers are shown below. Where should the collection center be located? Collection point A B C D Load 9,000 4,000 2,000 5,000 (X,Y) Coordinates (4,8) (7,2) (4,1) (7,3) The center should be built near coordinates (5.35, 4.85). Collection Point Weight X coord Y coord A 9,000 4 8 B 4,000 7 2 C 2,000 4 1 D 5,000 7 3 Sum 20,000 22 14 Average 5.5 3.5 Weighted Average 5.35 4.85 (Methods of evaluating location alternatives, moderate) {AACSB: Analytic Skills} 215 120. A manufacturer of stamped metal auto parts has four parts factories in one city at the location coordinates shown below. Each coordinate unit represents a city block (roughly 100 meters). The yearly demand at each factory is also given. Factories Rayburn Industrial Park Port of Zavalla Henderson Mfg. Center Wax Mills Site Demand 19,000 3,000 5,000 6,000 X-Coord. 20 60 70 90 Y-Coord. 130 40 100 30 Management has decided to build a new sheet metal mill, to supply these factories, at a location central to these plants. What should be the map coordinates of the new plant? On the grid below, graph the locations of the four parts factories and the proposed sheet metal mill. SEE SOLUTION ON NEXT PAGE. 216 The mill should be located near (44, 99). The center-of-gravity model does not favor any single data point; it is the weighted average of them all. In this case, being central does not mean being close to any single factory, but it is closer to the collection of all four than any other mill location could be. Mill and Auto Parts Factories 140 20, 130 120 100 44, 99 70, 100 80 Series1 60 40 60, 40 90, 30 20 0 0 20 40 60 80 100 (Methods of evaluating location alternatives, moderate) {AACSB: Analytic Skills} 121. A small producer of music boxes wants to move to a larger facility. Two alternative facilities have been found. Site 1 has a fixed cost of $500,000 per year, with a variable cost of $25 per unit. Site 2 has a fixed cost of $800,000 per year, but a variable cost of $22 per unit. a. Write out the equation for total cost for each site. b. At what volume of output would the two locations have the same total cost? c. For what range of output would Site 1 be superior? d. For what range of output would Site 2 be superior? (a) The equation for the total cost at site 1 is TC = 500,000 + 25X, where X is volume. The equation for total cost at Site 2 is TC = 800,000 + 22X. (b) Set these two equations equal and solve for X. 500,000 + 25X = 800,000 + 22X leads to 300,000 = 3X, then to X = 100,000. Site 1 is preferred for volumes up to 100,000 units, and site 2 is preferred after 100,000 units. (Methods of evaluating location alternatives, moderate) {AACSB: Analytic Skills} 217 122. A small manufacturer is considering several locations for a new facility. They have identified four factors that they consider to be important for their location decision. They have decided to assign scores to the four factors, with a higher score indicating a more favorable location. Use the information in the following table to perform a factor rating to select the best location. Wages Labor Climate Taxes Utilities Weight 40 30 15 15 Location A Location B Location C 30 75 90 40 70 40 80 40 90 75 60 10 Location B is the preferred location. Weight Location A Location B Location C Wages 40 30 75 90 Labor Climate 30 40 70 40 Taxes 15 80 40 90 Utilities 15 75 60 10 Total 100 Weighted sum 4725 6600 6300 Weighted average 47.25 66 63 (Methods of evaluating location alternatives, moderate) {AACSB: Analytic Skills} 123. A contractor for the military is looking for a new location for a supply depot. The depot will supply four bases whose tonnage (demand) and map coordinates are shown below. If management wants the depot to have a central location, what should be its map coordinates? Bases Fort Able Base Baker Camp Charlie Camp Delta (X,Y) Coordinates (40,110) (70,50) (90,20) (70,80) Tonnage 30,000 60,000 35,000 75,000 The depot should be located near X = 69, Y = 65. Bases Weight X coord Y coord X mult. Y mult. Fort Able 30,000 40 110 1,200,000 3,300,000 Base Baker 60,000 70 50 4,200,000 3,000,000 Camp Charlie 35,000 90 20 3,150,000 700,000 Camp Delta 75,000 70 80 5,250,000 6,000,000 Sum 200,000 270 260 13,800,000 13,000,000 Weighted Average 69 65 (Methods of evaluating location alternatives, moderate) {AACSB: Analytic Skills} 218 124. A highway contractor needs to locate a single supply point to provide road building materials to four projects. The four projects, which are all approximately the same magnitude, are located at the following coordinates. Coordinate units are in miles. Project A Project B Project C Project D X (East) 50 15 40 30 Y (North) 10 60 60 20 a. On the grid below, plot the locations of the four road-building sites. Properly label all points. b. What is the center of gravity? c. If a single truck were sent from center to each project and back (four round trips), how many miles would be traveled? (Hint: use the Pythagorean Theorem ). d. Add the calculated center of gravity to the grid. The supply point should be at (33.75, 37.50). Project A Project B Project C Project D Sum Average Weighted Average Weight 1 1 1 1 4 X coord 50 15 40 30 135 33.75 33.75 Y coord 10 60 60 20 150 37.5 37.5 Distance to COG Project A 31.94 Project B 29.29 Project C 23.35 Project D 17.90 (Methods of evaluating location alternatives, difficult) {AACSB: Analytic Skills} 125. Every month, a distribution center will deliver 14,000 units to Retailer A at coordinates (20, 10), 12,000 units to Retailer B at coordinates (30, -15), and 20,000 units to Retailer C at coordinates (4, 4). Assuming no constraints on location, at what coordinates should the distribution center be located (rounded to two decimal places)? (15.65, 0.87), where 15.65 = [20(14) + 30(12) + 4(20)]/(14 + 12 + 20), and 0.87 = [10(14) − 15(12) + 4(20)]/(14 + 12 + 20). (Methods of evaluating location alternatives, moderate) {AACSB: Analytic Skills} 219