Agan Interior Design provides home and office decorating ass

Agan Interior Design provides home and office decorating assistance to its customers. In normal operation, an average of 2.5 customers arrive each hour. One design consultant is available to answer customer questions and make product recommendations. The consultant averages 10 minutes with each customer.

A. Compute the operating characteristics of the customer waiting line, assuming Poisson arrivals and exponential service times.

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B. Service goals dictate that an arriving customer should not wait for service more than an average of 5 minutes. Is this goal being met? If not, what acction do you recommend?

C. If the consultant can reduce the average time spent per customer to 8 minutes, what is the mean service rate? Will the service goal be met?

Solution

a) The operating characteristics include the length of the people in the waiting queue and also the waiting time for those person.

For the given problem, using the poisson\'s approximation, the waiting time is equal to

Waiting = 10 * e^{-2.5/10} = 7.14 minutes

b) No the goal is not met, since the person is waiting for 7.15 minutes which is more than 5 minutes

Recommendation:

1) Increase the service rate or the time spend with the particular person

2) Hire a second consultant in order to speed up with the process

c) Mean service time

=> 10 * (e^{-2.5/8)

=> 7.5 customers/hr

Waiting queue time will decrease to 4 minutes which met the previous condiiton of 5 minutes