A plant produces two product families. You want to plan production for the next three months. Completed items can be stored at the plant or shipped to regional warehouses. The plant has unlimited storage capacity, but the warehouses can only hold 3,000 items each. Storage costs at the plant are $0.80 per item per month but only $0.60 per item per month at the warehouses. Family 1 requires 5 labor hours per unit to produce. Family 2 requires 6 labor hours per unit. Each worker can work 120 hours regular time per month and up to 20 hours overtime. Regular time wages are $20 per hour and overtime wages are $30 per hour. The initial workforce has 275 workers. Workers can be hired at a cost of $400 but are only 50% as productive in their first month as the experienced workers. One percent of the workforce quits each month. Workers can be fired at a cost of $500 each. Hiring and firing occurs at the start of the month. No workers were hired last month. Shortages are to be avoided whenever possible. There are no initial inventories at either the plant or warehouses, but the company would like to keep a safety stock of at least 500 units for each family at each warehouse. Demand occurs at the warehouses and is given in Table below. Define the decision variables and write out an optimization problem. Give the complete formulation explicitly stating objective function, all constraints and parameter values. Use Excel program to solve the formulated optimization problem. Show every details of your work. Analyze the results and comment on the optimization solutions.
|
Warehouse
|
Product Family
|
Month 1
|
Month 2
|
Month 3
|
|
1
|
1
|
1,100
|
1,500
|
2,000
|
|
1
|
2
|
900
|
1,500
|
2,000
|
|
2
|
1
|
1,200
|
2,000
|
2,000
|
|
2
|
2
|
1,300
|
1,000
|
2,000
|