The following situation refers to Sam Ops, a senior OM/IM student. In order to p
ID: 446899 • Letter: T
Question
The following situation refers to Sam Ops, a senior OM/IM student. In order to pay the rent, Sam decides to take a job in the computer department of a local department store. Sam’s only responsibility is to answer telephone calls to the department, most of which are inquiries about store hours and product availability. As Sam 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 inter arrival time of 3 minutes. Sam requires an average of 2 minutes to handle a call. The standard deviation in this processing time is l (one) minute. The telephone company charges $6.00 per hour for the telephone lines whenever they are in use (either while a customer is in conversation with Sam 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, Sam has to read a book (The Pole, by E. Silver mouse). He can read 1 page per minute. Sam's boss has agreed that Sam 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 Sam read during an 8-hour shift?
b.) How long does a customer have to wait, on average, before talking to Sam?
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.
d.) Calculate the average number of callers in the system (either waiting for service or being served).
e.) Calculate the value of cd^2, the SCV (squared coefficient of variation) of the inter-departure times from the system.
f.) Provide two potential ways of improving the computer department’s call center system.
Explanation / Answer
Given Calls arrival rate 1 call every 3 min means customer arrival rate = 60/3= 20 =
Servicing rate 2 min per call mean service rate = 60/2 = 30 =
a. Waiting in the system = / ( - ) = 20/30(30 - 20) = 4 minutes.
Sam is reading 1 page in I min, therefore 4 pages he will reading during the wait time
Means in 8 hour, he will read 8x 60 = 480 x4= 1920 pages.
b. the customer has to wait 4 min in one hour processing.
c. Ws = 1/ - = 1/ 30 -20 = 1/10 hour = 60/10= 6 min.
Cost is given $ 6 per hour that means for 6 min it will cost $ 0.6
d. Expected no of customers in the system = Ls= / 1-
= / = 20/30 = 0.66
Ls = 0.66 / 1 – 0.66 = 0.66/0.33 = 2
e. squared CV = 2/ sd = 2/1 = 2
f. One way to improve is use parallel serving system to avoid queues.
second way is recruit fast employees, who can handle the calls quickly.