A company produces refrigerators and dishwashers. During the coming year quarterly demand for these products is as shown in the following table:
|
Product
|
Q1
|
Q2
|
Q3
|
Q4
|
|
Refrigerators
|
1500
|
1000
|
2000
|
1200
|
|
Dishwashers
|
1000
|
2000
|
1500
|
2500
|
The company wants a production schedule that meets the demand requirements in each quarter. Management has also decided that the inventory level for each product must be at least 150 units at the end of each Quarter. There is no inventory on hand at the start of the first quarter. In any quarter the inventory plus the production quantity minus the demand equals the inventory amount for the next quarter.
During any quarter 12000 hours of production time are available. A refrigerator requires 2 hours and a dishwasher 3 hours of production time. Refrigerators cannot be manufactured in the fourth quarter because the company plans to modify tooling for a new product line.
Assume that each refrigerator left in inventory at the end of a quarter incurs a holding cost of $5 and that each dishwasher left in inventory at the end of a quarter incurs a holding cost of $7. The company wants to plan its production schedule over the year in such a way that it meets the quarterly demands and minimizes the total inventory cost. Formulate and solve this production planning problem. Assume the solution need not be integer. Without re-solving state what an extra hour of production time in Q3 is worth.