Developing and solving a goal programming model
Please state all your assumptions and show all your work. Define your decision variables clearly. Briefly explain your constraints and objective functions. Define all units of measure (e.g., hours, $, $/hour, etc.) Explain what software package you used (e.g., LINDO, LINGO, EXCEL solver, etc.)For EXCEL solver, be sure to give a separate statement of the formulation /input.
Use an equation editor for the equations. If you cannot get one, then use subscripts to indicate indexing. Graphs should be detailed and easy to read.
Q
Standard pump recently won a $14 million contract with the US 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 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 denotes 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. 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 requirements.
(Beginning Inventory) + (Current Production) - (Ending Inventory) = (This month's demand)
b) Write a goal equation that represents the fluctuations in the production level from May to June, June to July, and 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 the target of zero for the ending inventory in May, June and July.
d) Besides the goal equations developed in part 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 variable and constraints needed in your model by eliminating the goal equations and deviation variables for ending inventory levels? Explain.
Hint:
Constraint for June: s1 + x2 - s2 = 600
Constraint for July: s2 + x3 - s3 = 600