Question

Bart Incorporated manufactures rotary air fans and uses a production−planning horizon of on minus−half. It allows for regular​ time, part​ time, overtime, and subcontracting production to meet the demand but no more than 12 units may be made by each of these methods. Both anticipation inventory and backorders are allowed. The beginning​ (or current) inventory is 20 units. Their first attempt at a sales and operations plan has resulted in the following.

	1	2	3	4	5	6	Total
Inputs
Forecasted demand	100	125	120	80	75	70	570
Workforce Level	80	80	80	80	80	80	480
Part Time	12	12	12	12	12	12	72
Overtime	0	0	0	0	0	0	0
Subcontract	0	0	0	0	0	0	0
Derived
Beginning inventory	20	12	0	0	0	0
Ending inventory	12	0	0	0	0	2
Backlog	0	21	49	37	20	0	127
Calculated
Workforce level​ $5	400	400	400	400	400	400	​$2,400
Part Time​ $6	72	72	72	72	72	72	​$432
Overtime​ $7.5	0	0	0	0	0	0	​$0
Subcontract​ $8	0	0	0	0	0	0	​$0
Inventory holding​ $5	80	30	0	0	0	5	​$115
Back orders​ $20	0	420	980	740	400	0	​$2,540
Total	​$552	​$922	​$1,452	​$1,212	​$872	​$477	​$5,487

What would be the total plan cost if no more than five units each could be made each month by part−​time, ​overtime, and subcontracted​ workers?

A. ​$4,775

B. ​$4,550

C. ​$4,822

D. ​$4,920

Answer 1

If no more than five units each could be made each month by part−​time, ​overtime, and subcontracted​ workers, then the plan will change as below.

	1	2	3	4	5	6	Total
Inputs
Forecasted demand	100	125	120	80	75	70	570
Workforce Level	80	80	80	80	80	80	480
Part Time	5	5	5	5	5	5	30
Overtime
Subcontract
Derived
Beginning inventory	20	5	0	0	0	0
Ending inventory	5	0	0	0	0	0
Backlog	0	125-80-5-5=35	120-80-5+35=70	80-80-5+70=65	75-80-5+65=55	70-80-5+55=40	265
Calculated
Workforce level​ $5	400	400	400	400	400	400	​$2,400
Part Time​ $6	6*5=30	30	30	30	30	30	180
Overtime​ $7.5
Subcontract​ $8
Inventory holding​ $5	5*5=25	30	0	0	0	5	​$115
Back orders​ $20	0	20*35=700	20*70=1400	20*65=1300	20*55=1100	20*40=800	​$5300
Total							$​7995

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