Question

In: Operations Management

In the service department of the NAPA (National Auto Parts Association), mechanics requiring parts for auto...

In the service department of the NAPA (National Auto Parts Association), mechanics requiring parts for auto repair or service present their request forms at the parts department counter. The parts clerk fills a request while the mechanic waits. Mechanics arrive in a random (Poisson) fashion at the rate of 60 per hour, and a clerk can fill requests at the rate of 20 per hour (exponential). If the cost for a parts clerk is $20 per hour and the cost for a mechanic is $50 per hour, answer the following three questions (Because of the high arrival rate, an infinite source may be assumed.)

  • Please analyze the total cost per hour (clerks’ hourly cost and mechanics’ time spent in system) when there are 4 clerks to staff the counter?
  • Please analyze the total cost per hour (clerks’ hourly cost and mechanics’ time spent in system) when there are 5 clerks to staff the counter?
  • Is there a need to have 6 clerk to staff the counter? Please explain why with analysis.

Solutions

Expert Solution

Arrival rate, = 60 per hour

Service rate, = 20 per hour

Cost for parts clerk, Cs = $ 20 per hour

Cost for mechanic, Cw = $ 50 per hour

/ = 60/20 = 3

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1)

Number of clerks, M = 4

Look for /= 3 and M=4 n the following table:

For /= 3 and M=4, Lq = 1.528

Average number of mechanics in system, L = Lq+/ = 1.528+3 = 4.528

Total cost per hour = M*Cs + L*Cw = 4*20+4.528*50 = $ 306.4

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2)

Using 5 clerks

Look for /= 3 and M=5 n table 18.4

Lq = 0.354

Average number of mechanics in system, L = Lq+/ = 0.354+3 = 3.354

Total cost per hour = M*Cs + L*Cw = 5*20+3.354*50 = $ 267.7

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3)

Using 6 clerks

Look for /= 3 and M=6 n table 18.4

Lq = 0.099

Average number of mechanics in system, L = Lq+/ = 0.099+3 = 3.099

Total cost per hour = M*Cs + L*Cw = 6*20+3.099*50 = $ 275

Total cost per hour for 6 clerks is higher than 5 clerks.

Therefore, there is NO need to have 6 clerks.

keosha answered 1 year ago
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