Problem #2 (not from text) 21 pts (this is an asset selection problem that takes into consideration fixed costs) Utopia Company operates a plant in Avalon with a monthly capacity of 35,000 units and a plant in Bridgetown with a monthly capacity of 40,000 units. Product is shipped to regional distribution centers located in Riverdale, Seaside and Teatown. The long-range planning group at Utopia reevaluated their forecasts and determined that due to an anticipated increase in demand in the next 5 years, the company should consider increasing capacity by constructing a new plant in one or more of the following cities: Cedar, Daphne, Elm or Florence. The estimated monthly fixed cost and the monthly capacity for the four proposed plants are as follows: Proposed Plant Location of Monthly Fixed Monthly Plant Cost Capacity Cedar $20,000 10,000 D Daphne $30,000 20,000 E Elm $40,000 30,000 F Florence $60,000 40,000 The anticipated monthly demands at the distribution centers are as follows: Distribution Center (DC) Location of DC Monthly Demand Riverdale 45,000 2 Seaside 30,000 Teatown 35,000 The shipping cost per unit from each plant to each distribution center is shown below Distribution Center Plant Site 1 52 3 3 7 10 4 2 8 9 D F 7 8 9 A diagram of the network associated with the above problem is shown on the next page Let Xij = the units shipped from plant i to distribution center j, with i = A, B, C, D, E or F and j = 1, 2, 3. For example, XD1 designates the # of units shipped from Plant D to Distribution Center 1. Distribution Ctrs Demands in thousands of Units OOOOOO! (a) Why is the company considering opening at least one new plant? (b) How many shipment variables will the LP formulation have? (That is, how many Xij variables are included in the formulation?) (c) Why do we need to introduce binary variables YC, YD, YE and YF? Do we need a binary variables YA and YB? Why? (d) Formulate a linear programming model for minimizing total costs (shipping costs+fixed costs); you should have a total of 9 constraints. You can use steps (-(iv) below as a guide for writing the LP i Use suitable variables to express the objective function (minimize shipping costs + fixed costs) ii. Write the demand constraints for Distribution Centers 1.2 and 3. iii. Write the supply constraints for plants A and B. iv. Use suitable variables to write the supply constraints for plants C, D, E and F. (e) Write a constraint to express a requirement that the company will open only one new plant (1) If the company will open only one plant, which plant do you think it will be C, D, E or F? Why? (g) Write a constraint to express a requirement that the company will either open both plants C and D or neither of them (that is, if plant C opens then plant D has to open as well and if plant D is open then Plant C has to open too) Extra credit option I (2 points): Use Excel solver to solve the linear program formulated in part (d): Which plants will open and what is the shipping plan (ie, how many units will be shipped from each plant to each distribution center?) What is the associated costs of this plan
