Question

2. A company that manufactures compressors has plants in three locations: Cleveland, Chicago, and Boston. During a week, the total capacity of each plant to produce one type of special compressor is 25, 45, and 35 units, respectively. The company wants to ship at least 40, 10, 20 and 30 units to distribution centers in Dallas, Atlanta, San Francisco, and Philadelphia respectively. The unit production and distribution costs from each plant to each distribution center are given in the table below. How many of these compressors should be shipped from each manufacturing plant to each distribution center, if the companys goal is to minimize the total cost? (24pts) Table: Unit production and shipping costs, availability of compressors, and demand for compressor units Distribution centers an Plants Dallas Atlanta FranciscoPhiladelphia |Availabilit Cleveland 2 2 4 10 25 45 35 4 са 2 10 20 Boston Requirements 40 30

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Answer #1

Since the availability is more than the requirements, we will need to add a dummy distribution center

Let us put these values in solver -

fx =SUM PRODUCT(C5:67,C13:F15) Formula Bar Solver Parameters 0 Set Objective: To: O Max O Min O value Of By Changing Variable Cells Sheet80!SC$21 Distribution Centers Plants Cleveland Chicago Boston Requirements Dallas Atlanta San Fransisco Philadelphia Availability 25 35 SC$13:$G$15 Subject to the Constraints 10 SC$16:SF$16 SC$8:SF$8 SH$13:$H$15 $G$5:$G$7 Add Change Delete Distribution Centers 12 13 Plants Cleveland Chicago Boston Requirements Dallas Atlanta San Fransisco Philadelphia Dummy Availability Reset Al Load/Save Make Unconstrained Variables Non-Negative Total Cost Select a Solving Method: Simplex LP Options 23 Solving Method Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear. Select the LP Simplex engine for linear Solver Problems, and select the Evolutionary engine for Solver problems that are non- smooth. 28 Close Solve

The objective function in green cell has to be minimized by changing the values in blue cells.

The constraints are applied on total requirement and total availability.

Let us initially assume the requirement at each center to be 1. The solver will optimize this requirement to find the minimum cost.

Run the solver to get -

Distribution Centers Plants Cleveland Chicago Boston Requirements Dallas Atlanta San Fransisco Philadelphia Availability 25 35 Distribution Centers 12 13 14 15 Plants Cleveland Chicago Boston Requireme Dallas Atlanta San Fransisco Philadelphia Dummy Availability 15 25 35 17 18 19 21 Total Cost

Hence, the number of compressors shipped from manufacturing plants to distribution centers are -

Distribution Centers Atlanta San Fransisco Philadelphia Dummy Dallas Plants Cleveland Chicago Boston 10 15 40 0 0 0 30

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