Question

BenT Shoes will open several new production facilities during the coming year. Each new production facility is designed to have one quality inspector. A concern is that during busy periods, the shipment of shoes to retailers may be delayed as they wait to be inspected. This concern prompted BenT Shoes to undertake a study of the flow of shoes into the quality inspection department as a waiting line. BenT Shoes vice president wants to determine whether one quality inspector per facility will be sufficient. The average delay waiting for quality inspection should be no more than one minute.

One random variable is the arrival times of shoes to the quality inspection department. For the quality inspection department being studied, the shoes interarrival times are assumed to be uniformly distributed between 2 and 9 minutes. Like the examples of your text-book, assume that the simulation run begins at time=0. Past data from similar quality inspection departments indicate that a normal probability distribution with a mean of 3 minutes and a standard deviation of 0.5 minutes can be used to describe service (inspection) times. Build the suitable simulation model, run it for 10 times, and decide if one inspector is enough.

Answer 1

the shoes interarrival times are assumed to be uniformly distributed between 2 and 9 minutes. We will use 2+(9-2)*RAND() to simulate the interarrival times

a normal probability distribution with a mean of 3 minutes and a standard deviation of 0.5 minutes can be used to describe service (inspection) times. We will use norm.inv(RAND(),3,0.5) to simulate the inspection time

Prepare the following sheet

get this

After 10 simulations, we can see that the average wait time (in this run of 10 trials) is 0.28 minutes.

This is meets the desired average delay waiting for quality inspection should be no more than one minute.

ans: one quality inspector per facility will be sufficient