Given the following information set up the problem in a transportation table and

Question

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

PERIOD

Suppose that regular-time capacity will be reduced to 440 units in period 3 to accommodate a company wide safety inspection of equipment. An inventory carrying cost is $4 per unit per period. What will the additional cost of the optimal plan be?

PERIOD

1 2 3   Demand    550       700      750         Capacity                 Regular    500       500      500           Overtime    50       50      50           Subcontract    120       120      100         Beginning inventory    100            Costs           Regular time $   61 per unit     Overtime $   90 per unit     Subcontract $   93 per unit       Inventory carrying cost $   4 per unit per month         Back-order cost $   3 per unit per month  

Explanation / Answer

For first part, please find below the solution as below:

Explanation: With beginning inventory of 100, we would to need a total capacity of 1900 to meet the demand. As subcontracting costs the maximum/unit, we need to minimize the number of units which we subcontract. Also keeping in mind the inventory carrying cost, we need to minimize the number of units we subcontract in period 1.

Thus, number of units to be subcontracted in period 1 = Demand - Beginning inventory - Regular capacity of 3 periods - overtime capacity of 3 periods - max subcontracting capacity of period 2 & period 3

= 2000 - 100 - 1500 - 150 - 220

=30 units

Thus, optimal cost for first part is $129370

When regular capapcity in period 3 is reduced to 440, the optimal solution is as below:

In this case, we have regular capacity as 440 for period 3. Thus, subcontracting units for period 1

= 2000 - 100 - (500+500+440) - 150 - (120 + 100)

= 2000 - 100 - 1440 - 150 - 220

= 2000 - 1910

=90 units

Thus, optimal cost is equal to $131770

Period 1 2 3 Total Demand 550 700 750 2000 Capacity 580 670 650 1900 Regular 500 500 500 Over time 50 50 50 Subcontract 30 120 100 Excess Output forecast 30 - - Beginning inventory 100 130 100 Ending inventory 130 100 0 Average inventory 115 115 50 Backlog 0 0 0 Costs Regular 30500 30500 30500 Overtime 4500 4500 4500 Subcontract 2790 11160 9300 Inventory carrying cost 460 460 200 Backlog cost 0 0 0 38250 46620 44500 $129370

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