Question

In: Operations Management

A financial call center receives customer calls at every 15 seconds. The call center trains customer...

A financial call center receives customer calls at every 15 seconds. The call center trains customer

service representatives (CSRs) in a way that they take an average of 7.5 minutes to process a call.

Caller inter-arrival and processing times are exponentially distributed.

Currently, the call center employs 42 CSRs and pays each CSR $15 per hour including benefits.

The center estimates that it loses $1 for each minute a customer is on hold, in terms of the

negative impact on future business.

What is the optimal staffing level (i.e., number of CRSs employed) minimizing the total operating

cost? How much can the call center can save with adopting the optimal staffing level?

Hint:

Starting from the current number of CSRs, how does the total cost per hour change if we

hire one employee? What can you learn from this?

Expert Solution

Arrival rate, = 3600/15 = 240 calls per hour

Service rate, = 60/7.5 = 8 calls per hour

Number of CSRs (servers), s = 42

Service cost, Cs = $ 15 per hour

Waiting cost, Cw = $ 1 per minute = $ 60 per hour

/ = 240/8 = 30

Following Excel model is used,

EXCEL FORMULA:

Cell	Formula	Copy to
H3	=($D$4/$D$5)^G2/FACT(G2)+H2	H3:H44
D9	=1/((VLOOKUP(D6+1,$G$2:$H$44,2,0)-VLOOKUP(D6,$G$2:$H$44,2,0))/(1-D4/(D5*D6))+VLOOKUP(D6,$G$2:$H$44,2,0))
D10	=D4/D5/D6
D11	=(VLOOKUP(D6+1,$G$2:$H$44,2,0)-VLOOKUP(D6,$G$2:$H$44,2,0))D9D10/(1-D10)^2+D4/D5
D12	=D11-D4/D5
D13	=D11/$D$4
D14	=D12/$D$4
D19	=D16*D6
D20	=D12*D17
D22	=SUM(D19:D20)

In cell D6, start from number 42 and keep decreasing, as long as the total cost (cell D22) keeps decreasing.

We see that that cost decreases upto s=37, thereafter, it again starts increasing.

Therefore, optimal number of CSRs to be employed = 37

Total operating cost per hour = $ 594.93

keosha answered 2 weeks ago

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