Question

The following situation refers to Tom Opim, a first-year MBA student. In order to pay the rent, Tom decides to take a job in the computer department of a local department store. His only responsibility is to answer telephone calls to the department, most of which are inquiries about store hours and product availability. As Tom is the only person answering calls, the manager of the store is concerned about queuing problems. Currently, the computer department receives an average of one call every 3 minutes, with a standard deviation in this interarrival time of 3 minutes. Tom requires an average of 2 minutes to handle a call. The standard deviation in this processing time is 1 minute. The telephone company charges $5.00 per hour for the telephone lines whenever they are in use (either while a customer is in conversation with Tom or while waiting to be helped). Assume that there are no limits on the number of customers that can be on hold and that customers do not hang up even if forced to wait a long time.

a. For one of his courses, Tom has to read a book ( The Pole, by E. Silvermouse). He can read 1 page per minute. Tom’s boss has agreed that Tom could use his idle time for studying, as long as he drops the book as soon as a call comes in. How many pages can Tom read during an 8-hour shift?

b. How long does a customer have to wait, on average, before talking to Tom?

c. What is the average total cost of telephone lines over an 8-hour shift? Note that the department store is billed whenever a line is in use, including when a line is used to put customers on hold.

Answer 1

Answer A:

Idle time =(1-U)=(1-2/3)(1/3)*8hour=160min-Page read 160min *a1page/min=160pages

Answer B:

Waiting time=2 min*[2/3 / (1-2/3)]*[(12+0.52)/2]=2.5 min

Answer C:

The average total time a line is used per customer=average wait time + average processing time.

· in this case, the average total time per customer =2.5+2=4.5 minutes per customer.

· there is an average of 20 customers per hour so the average number of minutes per hour=20*4.5=90 minutes.

· thus, the total per hour chaege=(90/60)*$5=7.50 per hour or $60 for 8 hours.