Question

Given the following information set up the problem in a transportation table and solve for the minimum-cost plan:

	PERIOD
	1		2	3
Demand		550	700	750
Capacity
Regular		500	500	440
Overtime		50	50	50
Subcontract		120	120	100
Beginning inventory		100
Costs
Regular time	$	60 per unit
Overtime	$	80 per unit
Subcontract	$	90 per unit
Inventory carrying cost	$	1 per unit per month
Back-order cost	$	3 per unit per month

Suppose that an inventory carrying cost is increased $2 per unit per period. What will the additional cost of the optimal plan be? (Omit the "$" sign in your response.)

Additional cost           $

Answer 1

Solution

Optimal Plan	Month 1	Month 2	Month 3	Unused	Total	Capacity		Cost	Month 1	Month 2	Month 3
Beginning inventory	100	0	0	0	100	100		Beginning inventory	$0	$1	$2
Month 1 reg time	400	0	100	0	500	500		Month 1 reg time	$60	$61	$62
Month 1 overtime	50	0	0	0	50	50		Month 1 overtime	$80	$81	$82
Month 1 subcontracting	0	30	60	30	120	120		Month 1 subcontracting	$90	$91	$92
Month 2 reg time	0	500	0	0	500	500		Month 2 reg time	$63	$60	$61
Month 2 overtime	0	50	0	0	50	50		Month 2 overtime	$83	$80	$81
Month 2 subcontracting	0	120	0	0	120	120		Month 2 subcontracting	$93	$90	$91
Month 3 reg time	0	0	440	0	440	440		Month 3 reg time	$66	$63	$60
Month 3 overtime	0	0	50	0	50	50		Month 3 overtime	$86	$83	$80
Month 3 subcontracting	0	0	100	0	100	100		Month 3 subcontracting	$96	$93	$90
Total	550	700	750	30
Demand	550	700	750	30				Regular time cost	$60
								Overtime Cost	$80
Total Cost	$126,650							Subcontracting cost	$90
								Carrying cost	$1
								Back-order cost	$3

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It is told that the inventory carrying cost is increased ('by' or 'to'?) $2 per unit per period. We assumed that the increase is by $2 and the new carrying cost is 1+2 = $3.

Optimal Plan	Month 1	Month 2	Month 3	Unused	Total	Capacity		Cost	Month 1	Month 2	Month 3
Beginning inventory	100	0	0	0	100	100		Beginning inventory	$0	$3	$6
Month 1 reg time	400	0	100	0	500	500		Month 1 reg time	$60	$63	$66
Month 1 overtime	50	0	0	0	50	50		Month 1 overtime	$80	$83	$86
Month 1 subcontracting	0	30	60	30	120	120		Month 1 subcontracting	$90	$93	$96
Month 2 reg time	0	500	0	0	500	500		Month 2 reg time	$63	$60	$63
Month 2 overtime	0	50	0	0	50	50		Month 2 overtime	$83	$80	$83
Month 2 subcontracting	0	120	0	0	120	120		Month 2 subcontracting	$93	$90	$93
Month 3 reg time	0	0	440	0	440	440		Month 3 reg time	$66	$63	$60
Month 3 overtime	0	0	50	0	50	50		Month 3 overtime	$86	$83	$80
Month 3 subcontracting	0	0	100	0	100	100		Month 3 subcontracting	$96	$93	$90
Total	550	700	750	30
Demand	550	700	750	30				Regular time cost	$60
								Overtime Cost	$80
Total Cost	$127,350							Subcontracting cost	$90
								Carrying cost	$3
								Back-order cost	$3

So,

Additional cost = 127,350 - 126,650 = $700

If we assume the new carrying cost is $2 (i.e not 'by' but 'to'), the answer will be $350.