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           $

I've asked this question a couple of times and it has been incorrect. So.. the answer is not 440 haha.. good luck! Thanks for your help!

Answer 1

The transportation model for aggregate plan is as follows:

(the net demand in month 1 = 550 – 100 (inventory) = 450 units

The optimal Solution is as follows:

In month 1,

Regular production = 500 (340 units in month 1 and store 160 units to satisfy month 3 demand)

OT = 50 (30 in month 1 and store 20 units to satisfy month 2 demand)

Subcontract = 90 for month 1

In month 2,

Regular production = 500 (500 units in month 2)

OT = 50 in month 2)

Subcontract = 120 for month 2

In month 3,

Regular production = 440 units in month 3)

OT = 50 in month 3

Subcontract = 100 for month 3

Total optimal cost = $126,650

If the inventory cost is increased by $2 per unit, the optimal solution remain same, but the inventory holding cost will increase.

Additional cost = 160 units x 2 months x ($2 - $1) + 30 units x 1 month x ($2 - $1) = $350

Additional Cost = $350