Answered Essay: Mike Blanford, master scheduler at General Avionics, has the following demand forecast for

Mike Blanford, master scheduler at General Avionics, has the following demand forecast for one line in his factory:

Quarter Unit Sales
1 10,000
2 22,000
3 11,000
4 12,000

At the beginning of quarter 1, there are 7,000 units in inventory. The firm has prepared the following data:

Hiring cost per employee = $500

Firing cost per employee = $1,000

Beginning workforce = 60 employees

Inventory carrying cost = $2 per unit per quarter (charged on ending inventory)

Stockout cost = $5 per unit per quarter of ending stockout quantity

Regular payroll = $5,200 per employee per quarter

Each employee can produce 200 units per quarter. If Mike produces exactly enough to meet demand each quarter with no inventories at the end of quarters, how much will he produce each quarter, and what is the overall cost? (Use a spreadsheet model for the calculations.)

Use the data in above question to calculate production quantities and costs for a level rate of output with no ending inventory at the end of quarter 4. In this case, you may allow items to be backordered (but all demand must be met by the end of quarter 4, i.e. no lost sales permitted).

Expert Answer

Answer
Case 1 no inventories at the end of quarters
Quarter 1 2 3 4
Unit Sales 10,000 22,000 11,000 12,000
Beginning Inv 7000 0 0 0
Production Req 3,000 22,000 11,000 12,000
Closing inv 0 0 0 0
Production rate @200/worker 200 200 200 200
Workers required 15 110 55 60
Beginning work force 60 15 110 55
Work force 15 110 55 60
workforce cost 78000 572000 286000 312000
Hiring 0 95 0 5
Firing 45 0 55 0
Hiring cost 0 47500 0 2500
Firing cost 45000 0 55000 0
Inv cost 0 0 0 0
Total cost 123000 619500 341000 314500
1398000
Option 2 No firing 312000
Rejected

So Hiring and Firing is the best option in each quarter

As the back order cost is 0.

If all items are produced as per the inventory to be zero and reduce the firing, except for the first month.

Case 1 no inventories at the end of quarters
Quarter 1 2 3 4
Unit Sales 10,000 3,000 3,000 39,000
Beginning Inv 7000 0 0 0
Production Req 3,000 3,000 3,000 39,000
Closing inv 0 0 0 0
Production rate @200/worker 200 200 200 200
Workers required 15 15 15 195
Beginning work force 60 15 15 15
Work force 15 15 15 195
workforce cost 78000 78000 78000 1014000
Hiring 0 0 0 180
Firing 45 0 0 0
Hiring cost 0 0 0 90000
Firing cost 45000 0 0 0
Inv cost 0 0 0 0
Total cost 123000 78000 78000 1104000
1383000
Option 2 No firing 312000
Rejected

So we see this is a better option, if back orders are permitted.

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