MGS 8140 Management Science-infeasible production plans

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MGS 8140 Management Science

Task:

Part A

In evaluating linear programming solutions for March and April production, Mr. Russell is dissatisfied with the fractional values obtained. He suggests to Ms. Davis that they round the solutions to the nearest whole numbers. She objects, stating that doing so would not necessarily be optimal and might even lead to infeasible production plans.

Questions:

1.  American’s production quantities are to be decided for March.
a. Formulate and solve the problem as a linear program using Excel Solver. Then round the solutions to the nearest integer. Check the feasibility of your rounded solution and determine the corresponding total profit.

b. Formulate and solve the problem as an integer program. Determine which constraints are binding and what slack is available for those that are not binding. Does this solution have a higher total profit than the rounded LP solution in part (a)?

Part B

Ms. Davis is dissatisfied with the focus of the original linear and integer programs, all of which optimize a single goal – maximization of profit. Because American has several goals that are best considered simultaneously, she now wants to reevaluate the baseball bat production decisions by explicitly incorporating the following goals:

Goal 1: Achieve a profit of at least $3,000 for March and $4,000 for April.
Goal 2: Use not more than 4,000 minutes of lathe time, to allow for preventive maintenance scheduling. 
Goal 3: Use exactly 7,500 minutes of finishing time, to level out workforce scheduling.
Goal 4: Use no more than 7,000 inches of wood, to stabilize long-run inventories.

Ms. Davis chooses to evaluate the problem using goal programming. On her own, Ms. Davis decides to assign weights to the various goals. She assigns zero weight (no penalty) to bettering the targets for Goals 1, 2, and 4. For Goal 3, she chooses to give equal weight to falling below or above the target 

MGS 8140 Management Science

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