A coin-operated dry-cleaning store has five machines. The operating characterist

Question

A coin-operated dry-cleaning store has five machines. The operating characteristics of the machines are such that any machine breaks down according to a Poisson process with mean breakdown rate of one per day. A repairman can fix a machine according to an exponential distribution with a mean repair time of one-half day. Currently, three repairmen are on duty. The manager has the option of replacing these three repairmen with a super-repairman whose salary is equal to the total of the three regulars, but who can fix a machine in one-third the time, that is, in one-sixth day. Should he be hired?

Explanation / Answer

Total no. of machines : 5

Machines that are broken down at any given time: L

So, total operational machines at any given time: 5 - L

According to the above given data, machibne breaks down (Possion process) with a mean breakdown rate of 1 per day

So, at the begining of any given day, operational machines = 5 -1 = 4

Case 1: three repairman

Case 2: Super repairman

Time taken for repair in case 1: 1/2 day, so at the end of half day, operational machines = 5

So in the above case, avg operational machines per day = 4.5 (4/2 + 5/2)

In case 2, at the end of 1/6th day, operational machines = 5

So in this case , avg operational machines = 4.83 (4/6 + 5/6 + 5/6 + 5/6 + 5/6 + 5/6)

So, case 2 maximizes the no. of operational machines, hence the super repairman should be hired.

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