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Given the following demand forecasts, costs, and constraints for a company. Regular Prod. Capacity = 27,000...

Given the following demand forecasts, costs, and constraints for a company.

Regular Prod. Capacity = 27,000 units/qtr Regular Prod. Cost = $12/unit
Overtime Prod. Capacity = 3000 units/qtr Overtime Prod. Cost = $20/unit
Subcontracting Capacity = 16,000 units/qtr Subcontracting Cost = $25/unit
Inventory Capacity = 32,000 units/qtr Inventory Cost = $5/unit/qtr
Beginning Inventory = 0 Backorder Cost = $15/unit/qtr
Quarter Demand (units)
1 19,200
2 42,000
3 27,000
4 10,800

What is the cost if the company uses level production with overtime and subcontracting (no backorders) to meet demand?

Please do not use excel when solving.

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Answer #1

Manual solution is following:

Average demand per quarter = (19200+42000+27000+10800)/4 = 24750

Level production = 24750

Level production is more than demand in Q1 and Q4. Therefore, overtime and subcontract in Q1 and Q4 is 0 .

However, demand is more than level production rate in Q2 and Q3.

Ending Inventory in Q1 = 24750-19200 = 5550

Overtime in Q2 = 3000 (limited)

Subcontract in Q2 = 42000 - 24750 - 3000 - 5550 = 8700

Ending inventory in Q2 = 5550-42000+24750+3000+8700 = 0

Overtime in Q3 = 27000 - 24750 = 2250

Ending inventory in Q3 = 24750+2250-27000 = 0

Ending inventory in Q4 = 24750-10800 = 13950

Total Cost = 24750*4*12 + (3000+2250)*20 + 8700*25 + (5550+0+0+13950)*5 = $ 1,608,000

This is the not the optimal solution, because its total cost is higher than the optimal solution as determined by Solver as below:

The optimal level production plan using overtime and subcontracting with zero backorders is determined by Solver:

Cost Capacit SSolver Parameters 2 Regular production 3 Overtime production 4 Subcontract production 5 Invento 6 Backorder 12 27000 3000 16000 32000 SFS21 Set Objective: To: By Changing Variable Cells: 25 O Max (0) Min Value Of: 0 SBS15:SES16,SBS14 Subject to the Constraints: SBS13:SES130 9 Period 10 Demand 11 Beginning invento 12 Total 13 Ending invento 14 Regular production 15 Overtime production 16 Subcontract production 17 Production cost 18 Overtime cost 19 Subcontract cost 20 Inventory cost 21 Total Cost Total 99000 Add 19200 42000 10800 31200 27000 10800 SBS15:SES15SC$3 BS16:SES16SCS4 SBS13:SES13SCS5 Change uction 30000 10800 27000 3000 27000 27000 16200 27000 Delete 27000 108000 6000 1200 3240001296000 120000 30000 135000 27000 3000 1200 27000 Reset All Make Unconstrained Variables Non-Negative 324000 324000324000 3 60000 60000 Select a Solving Method: Simplex LP Options 30000 Solving Method 81000 438000 414000324000 405000 54000 Select the IPOPT Nonlinear engine for Solver Problems that are smooth nonlinear.Select the LP Simplex engine for linear Solver Problems. 1581 Solve Close 24 25

EXCEL FORMULAS:

Cost Capaci acity 2 Regular productiorn 3 Overtime production 4 Subcontract production 25 5 Invento 6 Backorder 12 27000 3000 16000 32000 20 15 9 Period 10 Demand 11 Beginning invento 12 Total production 13 Ending invento 14 Regular production 15 Overtime production 16 Subcontract production0 17 Production cost 18 Overtime cost 19 Subcontract cost 20 Inventory cost 21 Total Cost Q1 02 Total 19200 42000 -SUM(B10:E10) 27000 -C13 -SUM D14:D16) 10800 B13 D13 -SUM(B14:B16) -SUM(C14:C16) -SUM(E14:E16) B10+B11+B12 27000 3000 C10+C11+C12 -B14 3000 1200 -C14 $B2 -C15* $B3 -C16 $BA -C13 5 -SUM(C17:C20 E10+E11+E12 -SUM(B13:E13) -SUM(B14:E14) -SUM(B15:E15) -SUM(B16:E16) D10+D1+D12 C14 -D14 B14 $B2 B15 $B3 B16 $B4 B13 5 D14 $B2 D15*$B3 D16*$B4 D13 5 E14 $B2 E15 $B3 E16*$B4 E13 5 F14 $B2 F15 $B3 F16*$B4 F13*$B5 SUM(F17:F20) -SUM(B17:B20) -SUM(D17:D20) -SUM(E17:E20 23 24 25

Total cost of optimal plan = $ 1,581,000

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