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 interarrival 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 $5.00 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. Silvermouse). 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 interdeparture times from the system.
f. Provide two potential ways of improving the computer department’s call center system.
g. Suppose the call center operator, Sam, always works through a computer technology interface, which is prone to random, preemptive breakdown. [When the technology is down, the operator also cannot work.] The computer technology resource is subject to random failure with mean time to failure (MTTF or uptime), mf = 8 hours, and mean time to repair (MTTR or downtime), mr = 30 minutes. Repair time is exponentially distributed with SCV, cr 2 = 1. Calculate the mean and SCV of the effective call processing time, te and ce 2 , after incorporating computer technology breakdown.