3. A manager is facing the decision whether to use an automatic device to perfor

Question

3. A manager is facing the decision whether to use an automatic device to perform one of its production operations. Fortunately, the manager has taken this course in the past and she may quantify the benefits The automatic device would perform the operation in exactly 1.2 minutes. Currently, the operation is done manually. The duration of the manual operation is exponentially distributed; an average of 50 operations can be completed per hour. Units of the product arrive according to a Poisson proces with an arrival rate of 30 units per hou r. (a) Compare the average production rate between the new and the old system. What do you find? I claim there is a benefit from the new system, is this true? (1 point) (b) If the automatic device costs S 9,000, and each minute saved per product at the operation is worth $10, should the device be installed? If so, how long does it take to recoup the $9,000 investment? If not, what is the minimum rate of savings per hour that would change your decision? (4 points)

Explanation / Answer

Answer1:

arrival rate = 30 units/hour

lambda = arrival rate = 30/hr

For manual process , processing rate= mu =50 /hr

Therefore utilization = Rho = lambda /mu = 30/50= 0.6

For automatic process

processing rate =1 ops in 1.2 minute = 50 operations in an hour = mu '

Therefore the utilization now=( lambda /mu' )= Rho' = 30/50= 0.6

Even with automation the production rate does not change . So there is no additional benefit.

(b) For manual process system idle time proportion = (1-Rho) =(1-0.6) = 0.4

For automatic process system idle time proportion =(1-Rho') = (1-0.6) =0.4

There is no time savings of system idle time due to automation.

Hence it is not worth to invest in installation of automatic device

Say we operate 1000 hours in order to recover the cost then the new system should yield savings worth $9000 ie $ 9 per hour of savings for every hour of operations.

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