Question

Agan Interior Design provides home and office decorating assistance to its customers. In normal operation, an average of 2.9 customers arrive each hour. One design consultant is available to answer customer questions and make product recommendations. The consultant averages 12 minutes with each customer.

1. Compute the operating characteristics of the customer waiting line, assuming Poisson arrivals and exponential service times. If required, round your answers to four decimal places.

	Lq	=
	L	=
	Wq	= hours
	W	= hours
	Pw	=

3. Service goals dictate that an arriving customer should not wait for service more than an average of 9 minutes. Is this goal being met? If not, what action do you recommend?
   
   
   • Yes
   • No. Firm should decrease the mean service rate µ for the consultant.
   • No. Firm should increase the mean service rate µ for the consultant or hire a second consultant.

5. If the consultant can reduce the average time spent per customer to 9 minutes, what is the mean service rate? If required, round your answer to one decimal place.
   

customer per hour

Will the service goal be met?

Yes or no

Answer 1

a) The arrival rate is 2.9 customers per hour. The consultant averages 12 minutes with each customer. Hence service rate is 5 customers per hour

Hence = 2.9 and = 5

b) We can see that the time for which the customer has to wait for service Wq is 0.2758*60 = 16.548 mins. Hence we can see that the average wait time for customer for service is 16.548 minutes which is more than 9 minutes. Hence the answer is No, the firm's goal is not met. If we decrease the mean service rate, then the customer will have to wait even more. Hence the firm should increase the mean service rate µ for the consultant or hire a second consultant so that more customers are serviced within the given time and the waiting time for customers decreases.

c) If the consultant can reduce the average time spent per customer to 9 minutes, the mean service rate is 60/9 = 6.7 customers per hour.

Now the waiting time Wq becomes as below

Hence we can see that the service goal is now met.