We are formulating an aggregate plan for an 8-quarter period. Our demand forecas

Question

We are formulating an aggregate plan for an 8-quarter period. Our demand forecast is as follows:

We will enter Quarter 1 with 0 units in inventory and the capacity to produce 200 units per quarter without overtime. Increasing regular-time capacity has been estimated to cost $30 per unit. Reducing regular-time capacity has been estimated to cost $20 per unit. Overtime production costs $10 per unit.

Carrying inventory (or having backorders) is not permitted. By policy, overtime production is limited to a maximum of 30 units per quarter. Idle time (i.e., having more regular-time capacity than is necessary) is not permitted.

If we used a chase planning approach (with overtime) in this situation, what would our minimum total (Capacity Increase + Capacity Decrease + Overtime) cost be?

Quarter 1 2 3 4 5 6 7 8 Forecast 200 340 390 300 240 360 440 320

Explanation / Answer

Using a chase plan, as he least cost is by OT, first OT capacity is exhausted and then other options are explored, so we get:

Rate Quarter 1 2 3 4 5 6 7 8 Demand 200 340 390 300 240 360 440 320 Beginning Inv 0 0 0 0 0 0 0 0 Production Regular 200 310 360 300 240 330 410 320 30 Increased capacity 0 110 50 0 0 90 80 0 20 Decreased capacity 0 0 0 60 60 0 0 90 10 OT 0 30 30 0 0 30 30 0 (Rate* units) Capacity increase cost 0 3300 1500 0 0 2700 2400 0 (Rate* units) Capacity Decrease cost 0 0 0 1200 1200 0 0 1800 (Rate* units) OT cost 0 300 300 0 0 300 300 0 Sum of all 3 Total cost 0 3600 1800 1200 1200 3000 2700 1800 Grand Total 15300

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