Question

home / study / business / operations management / operations management questions and answers / given the following information set up the problem in a transportation table and solve for ...

Question: Given the following information set up the problem in a transportation table and solve for the mi...

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?

I have asked this question a couple times and it has been incorrect. The answer is not $440.... good luck!

Answer 1

Hi, first of all, I am using excel solver to optimize the solution. The assumption is that the production cannot exceed the mentioned capacity for a period.

Step 1

Setup the solution, define the regular, overtime and subcontract units as decision variables. Form the equations, constrains, and the “if” conditions. (I am assuming you know how to do this. In case if you don’t, let me know in the comment section and I will provide you with the formulas). Here, the total unis is the summation of total product across the 3 periods and the beginning inventory.

Step 2

Us the total cost as minimizing objective function and use the constraints as shown in the screenshot.

Step 3

Obtain the optimal solution by running solver. Shown in the screenshot. The total cost at this point is $126960

Step 4

Change the value of Carrying (B19) to 2 and rerun the solver. Record the total cost. The total cost at this point is $127050. Hence the difference of making carrying cost from $1 to $2 is $90.

Hope this helps. Cheers!