question archive 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
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
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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.
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The step by step solution of the same is as follows:
Explanation
Arrival rate Lambda = 60 per hour
service rate mu = 20 per hour
Utilisation rho = 60/20 =3
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?
Lq with rho = 3
and
number of resources = 4 would be 1.5283
avg waiting time per person with 4 clerks = 1.5283/60
avg waiting time per hour = 60x 1.5283/60 =1.5283hours
Total cost = 1.5283*50 + 4 * 20 = $156.415
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?
In the similar way, Lq with rho =3 and 5 resources would be 0.3542
avg waiting time per hour = 60x0.3542/60 =0.3542 hours
Total cost = 0.3542*50+5*20 =$117.71
Is there a need to have 6 clerk to staff the counter? Please explain why with analysis.
There is no need of employing 6 clerks because the cost of 6 clerks = 6*20 = 120 is higher than the 5 clerks option.
