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Standard Pump Corporation recently won a $14 million contract with the U.S. Navy to supply 2000 custom-designed submersible pumps over a period of four months. The contract calls for the delivery of 200 pumps at the end of May, 600 pumps at the end of June, 600 pumps at the end of July, and 600 pumps at the end of August. Standard's production capacity is 500 pumps in May, 400 pumps in June, 800 pumps in July, and 500 pumps in August. Management would like to develop a production schedule that will keep monthly ending inventories low while at the same time minimizing the fluctuations in inventory levels from month to month. In attempting to develop a goal programming model of the problem, the company's production scheduler let xm denote the number of pumps produced in month m and sm denote the number of pumps in inventory at the end of month m. Here, m = 1 refers to May, m = 2 refers to June, m=3 refers to July, and m = 4 refers to August. In the interim, management has asked you to assist the production scheduler in model development.

a. Using these variables, develop a constraint for each month that will satisfy the following demand requirement: (Beginning Inventory) + (Current Production) - ( Ending Inventory) = (Month m Demand)

b. Develop goal equations that represent the fluctuations in the production level from May to June, June to July, and July to August.

c. Inventory carrying costs are high. Standard wishes to avoid carrying any monthly ending inventories over the scheduling period of May to August. Develop goal equations with a target of zero for the ending inventory in May, June, and July.

d. Assuming the production fluctuation and inventory goals are of equal importance, develop and solve a goal programming model to determine the best production schedule.

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This shows how to develop constraints, goal equations, and a goal programming model for a given situation.

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