The factory´s main machine has broken down and the owners will incur costs of €3

Question

The factory´s main machine has broken down and the owners will incur costs of €3500 for each day the machine is out of action. The factory’s engineer has 3 immediate options. He can return the machine to the supplier who has agreed to collect, repair and return it all free of charge, but not to compensate the company for any losses of production while the repair is carried out. The supplier would not agree to repair the machine if any other person has previously attempted to repair it. If the machine is returned, the supplier will guarantee to return it in working order in 10 days’ time. Alternatively, the engineer can call in a specialist local engineering company. They will charge €30 000 to carry out the repair and they estimate a 60% chance they will be able to return the machine to working order in 3 days. There is, however, a 40% chance that repairs will delay by another day. Finally he could attempt to carry out the repair work himself, with an estimated 50% chance that the machine can be mended in 5 days. However, if the attempted repair hasn`t been successful at the end of the five days he will have to call in the engineering company for repair. It can be assumed that the probability distribution for the local engineering company’s repair times remains unaffected by any work the factory engineer has carried out previously. Assuming the firm´s objective is to minimize expected costs, what course of action should be taken? Show all your workings and calculations. There is uncertainty about downtime costs. Perform a Sensitivity Analysis to illustrate the robustness of your options against that parameter on a fluctuation in downtime costs between 3,500 and 7000 a day. Show your calculations in a table and comment on how strong the intial decision is. Also show your Sensitivity Analysis graphically.

Explanation / Answer

Solution

Option 1: Return the machine to the supplier.

Since the supplier’s repair work is free of cost, the only cost involved is the downtime cost for 10 days = 10 x 3500 = $35000

Option 2: Call in the specialized engineering company for repairing.

Down-time cost = 10500 for 3 days with probability 0.6 and 14000 for 4 days with probability 0.4. So, expected down-time cost = (10500 x 0.6) + (14000 x 0.4) = 11900.

In addition, the company would charge 30000 for the repair work. So, total expected cost = 11900 + 30000 = $41900

Option 3: Factory’s engineer does the repair work.

Since there is 50% chance of repairing within 5 days, the cost (only down-time cost is involved) is (5 x 3500) = 17500 with probability 0.5.

If the engineer is not able to set the machine right, whose probability is 0.5 again, the machine must be entrusted to the specialized engineering company whose total expected cost is 41900 as shown above, with probability 0.5. So, expected total cost = (17500 x 0.5) + (41900 x 0.5) = $29700

Since Option 3 has the least expected total cost,

the optimum decision is: Factory’s engineer does the repair work ANSWER

Sensitivity Analysis

Let uncertain down-time cost be x. Then, expected total cost is:

10x for Option 1; (3.4x + 30000) for Option 2 and (4.2x + 15000) for Option 3.

Comparing the above by inequalities,

Option 1 is best when x < $1875; Option 2 is best if $1875 < x < $2586 and Option 3 is best if x > $2586 ANSWER

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