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EM 513 April/May 2010- Panama Practice Problems Set 2

1. Consider the following transportation problem, where the cost to ship a unit from plant A, B,or C to customers 1, 2, or 3, is shown in the small box in the corners of each cell. Note thatan initial solution is given. Find the optimal solution using the stepping stone method.

1 2 3 Supply 10 5 14

A 100 100 200

6 9 11

B 300 300

12 8 7

C 200 200 400

Demand 100 600 200

2. Dorian Auto manufactures luxury cars. The company believes that its most likely customersare high-income women and high-income men. In order to reach these groups, Dorian isplanning to run commercials during two TV programs; a comedy show and a football game.The comedy show will be seen by 7 million high-income women and 2 million high-incomemen. The football game will be seen by 2 million high-income women and 12 million high-income men. Commercial time costs $50,000 per minute during the comedy show, and$400,000 per minute during the football game. Dorian can purchase a variable amount ofminutes of commercial time during each program. That is, they do not have to purchase aninteger number of minutes. However, Dorian wants the total exposure to be at least 28million women-minutes and at least 24 million men-minutes. (For example, if they run 1.5minutes of commercial time during the Football game they would gain 3 million women-

minutes and 18 million men-minutes of exposure.) How many minutes of commercialtime should Dorian purchase during the comedy show and the football game to minimize itsadvertising costs, but meet the total exposure requirements? Formulate this as a linearprogram and solve graphically.

3. Consider the following facility layout and flow matrix (loads per day).Each department is 50x50.

a) Find the total volume-distance product (VDP) of the current layout.b) Find an improved layout, (keep the same overall facility shape and use rectangular or

square departments) and show it has reduced VDP.

A B C

To

A B C

A - 2 17

From B 10 - 13C 5 7 -

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6.

a) Formulate the following as a linear program.b) Use Excel Solver to solve the problem and find the optimal solution.

7. Existing machines are located within a building at P1=(4, 4), P2=(4, 10), P3=(6, 5),P4=(10, 5), P5= (11, 9), P6= (12, 3). Each must access a new centralized mold storagearea that is being planned. The number of molds needed per day at each machine are,w1=4, w2=4, w3=2, w4=2, w5=5, and w6=7.

a) Find the optimal location for the new storage area using the rectilinear distance metricand evaluate the objective function.

b) Repeat part (a) but use the Euclidean distance metric. Use Excel Solver.

c) Repeat part (a) but use the minimax objective with rectilinear distance.

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8. A square warehouse is divided into nine equal bays. It is designed to hold six types ofparts, A, B, C, D, E, F. There are two input/output locations (P1 & P2) with thepercentage of flow as indicated. Using the information below, make an optimalassignment of parts to bays such that total distance is minimized.

9. Consider the actual sales data shown below.

Month Sales

1 127

2 1503 152

4 101

5 130

6 75

7 120

8 84

9 80

10 120

11 42

12 91

a. Develop a graph of the data using Excel.b. Find a 3-month moving average forecast for periods 2-13 and compute the sum of

squared error. Add this to your plot in (a).

c. Use exponential smoothing and find a forecast for periods 2-13 using =0.2 and findthe sum of squared error. Add this to your plot in (a)

d. Develop a linear regression model of the data (use Month as the independent variable,and Sales as the dependent variable). Add this line to your plot in (a)

e. What would the regression predict would happen to sales far into the future?

Bays Needed Flow (lds/mo)

A 2 20

B 1 9

C 1 5

D 3 33

E 1 14

F 1 16

P1=30%

P2=70%