AVI supplies vended food to a large university. Because students kick the machines at every opportunity, management has a constant repair problem. The machines break down on an average of three per hour, and the breakdowns are distributed in a Poisson manner. Downtime costs the company $25/hour per machine, and each maintenance worker gets $4/hour. One worker can service machines at an average rate of five per hour, distributed exponentially; two workers working together (as one team) can service seven per hour, distributed exponentially; and, a team of three workers can do eight per hour, distributed exponentially. What is the optimum maintenance crew size?

The optimum maintenance crew size is 2 workers.

Explanation:

M/M/1 model for all: -

With one worker: λ= 3 per hour.

µ= 5 per hour.

Average number in system = λ/µ-λ = = 1.5.

- With two workers: λ= 3 per hour µ= 7 per hour.

Average number in system = λ/µ-λ−==0.75.

- With three workers: λ= 3 per hour, µ= 8 per hour.

Average number in system = λ/µ-λ−==0.6.

# workers       λ      µ     (ns)    ($25*(ns))    ($4*(no.of workers)     Total cost

      1                3      5      1.5       37.50                         4                          $41.50

      2               3      7      0.75     18.75                         8                         $26.75

      3               3      8      0.6        15                             12                        $27.00

The optimum maintenance crew size is 2 workers.

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