An electronics manufacturer makes video security systems for parking lots. Demand estimates for the next four quarters are 15, 9, 23, and 17 units

The company is preparing an aggregate plan that uses inventory, regular time, overtime, and back orders. Subcontracting is not allowed. Regular time capacity is 12 units for quarters 1 and 2, 15 units for quarters 3 and 4. Overtime capacity is 6 units per quarter. Regular time cost is $20,000 per system, while overtime cost is $30,000 per unit. Back order cost is $2000 per system per quarter; inventory holding cost is $500 per unit per quarter. Beginning inventory is zero.

Complete the table of data inputs for solving this aggregate planning problem with the transportation method. Specifically, how many sources are there, and how many destinations? What is the supply from each source, and the demand of each destination? What is the cost of each source-destination pair?

There are eight sources: regular time and overtime for each quarter. There are four destinations, one for each quarter. The four demands are the quarterly demand estimates. The eight supplies are the regular time and overtime capacities of each quarter. The cell costs for regular time begin at $20,000, and increase rightward by the carrying cost increment, and increase downward by the backorder increment. The data table appears below.

Video Security
Quarter 1 Quarter 2 Quarter 3 Quarter 4 SUPPLY
Regular time quarter 1 20,000 20,500 21,000 21,500 12
Overtime quarter 1 30,000 30,500 31,000 31,500 6
Regular time quarter 2 22,000 20,000 20,500 21,000 12
Overtime quarter 2 32,000 30,000 30,500 31,000 6
Regular time quarter 3 24,000 22,000 20,000 20,500 15
Overtime quarter 3 34,000 32,000 30,000 30,500 6
Regular time quarter 4 26,000 24,000 22,000 20,000 15
Overtime quarter 4 36,000 34,000 32,000 30,000 6
DEMAND 15 9 23 17