An Introduction to Management Science 13th Edition by David Anderson,Dennis Sweeney ,Thomas Williams ,Jeffrey Camm, Kipp Martin

Exercise 13

Standard Pump recently won a $14 million contract with the U.S. Navy to supply 2000 custom-designed submersible pumps over the next 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 pimps 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 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 x m denote the number of pumps produced in month m and s m denote the number of pumps in inventory at the end of month m. Here, m = 1 refers to May, m = 2 refer to June, m = 3 refers to July, and m = 4 refers to August. Management asks 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:
b. Write goal equations that represent the fluctuations in the production level from May to June, June to July to August.
c. Inventory carrying costs are high. Is it possible for Standard to avoid carrying any monthly ending inventories over the scheduling period of May to August? If not, develop goal equations with a target of zero for the ending inventory in May, June, and July.
d. Besides the goal equations developed in parts (b) and (c), what other constraints are needed in the model?
e. Assuming the production fluctuation and inventory goals are of equal importance develop and solve a goal programming model to determine the best production schedule.
f. Can you find a way to reduce the variables and constraints needed in your model by eliminating the goal equations and deviation variables for ending inventory levels? Explain.