Question

1. Agan Interior Design provides home and office decorating assistance to its customers. In normal operation, an average of 2.1 customers arrive each hour. One design consultant is available to answer customer questions and make product recommendations. Agan's management would like to evaluate two alternatives:

   • Use one consultant with an average service time of 8 minutes per customer.
   • Expand to two consultants, each of whom has an average service time of 10 minutes per customer.

   If the consultants are paid $16 per hour and the customer waiting time is valued at $23 per hour for waiting time prior to service, should Agan expand to the two-consultant system?

   No

   What is the total cost for each scenario? Round your answers to the nearest cent.

   The total cost for the first scenario where there is one consultant with an average service time of 8 minutes per customer is $________ . The total cost for the second scenario where there are two consultants with an average service time of 10 minutes per customer is $________ .

Answer 1

ANSWER:

Arrival rate , λ= 2.1 customers /hour

Service rate, u = 60 minutes/ Service time = 60/8 = 7.5 customers /hour

Utilization = λ / u

Waiting time in Queue = λ / u * 1 / (λ - u) = 2.1/7.5 * 1 / (7.5-2.1) = 0.0519 hours

Customer waiting time cost/ hour = Cost /hour * Arrival rate * Wait time

Total hourly cost of 1 consultant system (Current scenario) = Consultant pay + Customer waiting time cost = $18 + 2.1 * 0.0519*25 = $20.72

New Service rate, u2 = 60/10 = 6 /hour

Number of servers, s = 2

Now, = λ / u2 = 2.1/6 = 0.35 . Looking up λ / u ratio for 2 servers, P0 = 0.7021

Utilization = λ / u2 * s = 2.1 / 12 = 0.175

Customer waiting in line = Lq = 0.7021* (0.35)^2 0.175 / (2(1-0.175)^2) = 0.0111

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Wq = Lq / λ = 0.0111/2.1= 0.0053 hours

Total hourly cost of 2 consultant system = Consultant pay of 2 consultants+ Customer waiting time = $18 *2+ 2.1 * 0.0053*25= $36.28

Hence, 2 consultant system is expensive and should not be considered i.e. we should not expand to two consultant system