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Using the following information, develop an optimum (minimum total cost) six-month aggregate plan 4 Total 1500 + n Month Forecast (units) 400 300 100 150 250 300 + n Beginning inventory of the first month-n Costs Output Regular time cost- S120 per unit Overtime cost $180 per unit Inventory holding cost $50 per unit per month on average inventory Back order cost = $200 per unit per month Average Inventory = (Beginning Inventory + Ending Inventory) / 2 Regular output 22 units per worker per month Overtime output maximum of 90 units per month for the entire company (all workers combined) Ending inventory for the sixth month 0 Strategy:Maintain workers and use ove ime Example: Sixth Month’s Forecasted Demand 300 + n = 300 45-345 units Total Forecasted Demand = 1500 + n = 1500 + 45 = 1545 units Beginning Inventory n- 45

Total cost calculation for this six-month aggregate plan:
If n=48
Total Cost calculation of the Plan Total
Month 1 2 3 4 5 6
Forecast 400 300 100 150 250 348 1,548
Beginning Inventory 48 0 0 88 158 128
Production Required (forecast -Inventory+ backorders of previous month) 352 342 132 62 92 220
Regular Production (10 workers *22 units) 220 220 220 220 220 220 1,320
Overtime Production (maximum 90 units/month) 90 90 0 0 0 0 180
Total Production (regular + Overtime) 310 310 220 220 220 220 1,500
Ending Inventory 0 0 88 158 128 0
Average Inventory (Beginning + Ending)/2 24 0 44 123 143 64
Ending Backorders 42 32 0 0 0 0
Cost:
Regular cost of production ($120/unit) $26,400 $26,400 $26,400 $26,400 $26,400 $26,400 $158,400
Overtime cost of production ($180/unit) $16,200 $16,200 $0 $0 $0 $0 $32,400
Inventory holding cost ($50/unit per period) $1,200 $0 $2,200 $6,150 $7,150 $3,200 $19,900
Backorder cost ($200/ unit per period) $8,400 $6,400 $0 $0 $0 $0 $14,800
Total Cost per Month $52,200 $49,000 $28,600 $32,550 $33,550 $29,600 $225,500
A. Back log for the second month = 32
B. Ending inventory for third month = 88
C. Average inventory for fifth month =143
D. Total cost of the third month = $28,600
E. Total inventory holding cost for this six-month aggregate plan = $19,900
F. Total cost for this six-month aggregate plan = $225,500
 
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