Question

Problem 15-11 (Algorithmic)

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.

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	=

2. 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 action do you recommend?
   
   No. Firm should increase the mean service rate µ for the consultant or hire a second consultant.
   
3. If the consultant can reduce the average time spent per customer to 8 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

Answer 1

a.

Arrival rate = 2.5 customers per hour

Service rate, = 1 customer per 10 minutes = 6 customers per hour

p = / = 2.5/6 = 0.4167

Lq = p . /( - ) = 0.4167 * 2.5 /(6 - 2.5) = 0.2976

L =   /( - ) = 2.5 /(6 - 2.5) = 0.7143

Wq = p/( - ) = 0.4167 /(6 - 2.5) = 0.1191 hours

W = 1/( - ) = 1 /(6 - 2.5) = 0.2857 hours

p = / = 2.5/6 = 0.4167

b.

Average waiting time in queue = 0.1191 hour = 0.1191 * 60 = 7.146 minutes

which is greater than target of 5 mins.

So, the goal was not met. Firm should increase the mean service rate µ for the consultant or hire a second consultant.

c.

Service rate, = 1 customer per 8 minutes = (60/8) customers per hour = 7.5 customers per hour

p = / = 2.5/7.5 = 0.3333

Wq = p/( - ) = 0.3333 /(7.5 - 2.5) = 0.06666 hours = 4 minutes

Thus, the service goal of 5 minutes of maximum average waiting time in queue is met.