The Rustbelt Manufacturing Company employs a maintenance crew to repair its machines as needed. Management now wants a simulation study done to analyze what the size of the crew should be, where the crew sizes under consideration are 2, 3, and 4. The time required by the crew to repair a machine has a uniform distribution over the interval from 0 to twice the mean, where the mean depends on the crew size. The mean is 4 hours with two crew members, 3 hours with three crew members, and 2 hours with four crew members. The time between breakdowns of some machine has an exponential distribution with a mean of 5 hours. When a machine breaks down and so requires repair, management wants its average waiting time before repair begins to be no more than 3 hours. Management also wants the crew size to be no larger than necessary to achieve this.

(a) Develop a simulation model for this problem by describing its basic building blocks listed in Sec. 22.1 as they would be applied to this situation.

R

(b) Consider the case of a crew size of 2. Starting with no machines needing repair, use next-event incrementing to perform the simulation by hand for 20 hours of simulated time.

R

(c) Repeat part (b), but this time with fixed-time incrementing

(with 1 hour as the time unit).

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(d) Use the interactive routine for simulation in your OR Courseware (which incorporates next-event incrementing)

to interactively execute a simulation run over a period of 10 breakdowns for each of the three crew sizes under consideration.

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(e) Use the Queueing Simulator to simulate this system over a period of 10,000 breakdowns for each of the three crew sizes.

(f) Use the M/G/1 queueing model presented in Sec. 17.7 to obtain the expected waiting time Wq analytically for each of the three crew sizes. (You can either calculate Wq by hand or use the template for this model in the Excel file for Chap. 17.)

Which crew size should be used?