During the early morning hours, customers arrive at a branch post office at an a

Question

During the early morning hours, customers arrive at a branch post office at an average rate of 45 per hour (Poisson), while clerks can handle transactions in an average time (exponential) of 4 minutes each.

Suppose that the cost of a clerk is $30 per hour and customer waiting time represents a “cost” of $20 per hour. Fill in the following table:

M = 4
Ls = 4.528 Format x.xxx
Customer Cost = $90.56 Format x.xxx No $ Sign
Clerk Cost = $

Format xxx No $ Sign
Total Cost = $

Format xxx.xx No $ Sign

For M = 5
Ls =

Format x.xxx
Customer Cost = $

Format x.xxx No $ Sign
Clerk Cost = $

Format xxx No $ Sign
Total Cost = $

Format xxx.xx No $ Sign

For M = 6
Ls =

Format x.xxx
Customer Cost = $61.98 Format x.xxx No $ Sign
Clerk Cost = $

Format xxx No $ Sign
Total Cost = $

Format xxx.xx No $ Sign


To Keep Overall Cost at a Minimum, we should have

clerks.

Please show your work and/or show how you setup in Excel; I would greatly greatly appreciate it.

Explanation / Answer

A With 6 clerks, Lq is equal to 0.099. B Clerks Ws (hs) Ws (min) 4 0.1006 6.038 5 0.745 4.472 At least five clerks are needed if the average time in the system is to be less than 5 minutes. C Total cost equals clerk cost + waiting cost. Total cost for 4, 5 and 6 clerks is as follows: Clerks Ls Customer Cost Clerk Cost Total Cost 4 4.528 $          90.56 $       120.00 $       210.57 5 3.35 $          67.08 $       150.00 $       217.08 6 3.01 $          61.98 $       180.00 $       241.98 The optimum number of clerks is 4.

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