8.4.3 A mail order company has one department taking customer orders and the other handling
customer complaints. Currently each department has a separate telephone number. Each
department has 7 Watts lines served by two customer service representatives. Calls come
into each department at the rate of 1 per minute. Each customer service representative
takes on average 1.5 minutes to serve a customer. A proposal has been put forward to
merge the to departments and cross train the workers. The new department would, as a
result, have 14 watts lines served by four customer service representatives. As the
operations manager, you know that
(a) The proportion of callers getting a busy signal will
(i) Increase
(ii) Decrease
(iii) Remained unchanged.
(b) The average utilization of customer service representatives will
(i) Increase
(ii) Decrease
(iii) Remained unchanged
Answers:
8.4.4 Star Brite Media (SBM), an independent video rental store, carries digital projection
systems that customers can rent out together with new, high-definition DVDs. The store
manager is forecasting that, in an average week, about 21 customers would ask to rent a
projection system, the exact number of requests per week being random and may be
assumed to be Poisson distributed. Their projection rental time is estimated to follow
exponential distribution with a mean of about 3 days. (SBM is open 7 days per week.)
a. What is the minimum number of projection systems Sandra should buy to ensure a
service level of 90%, i.e., that the probability that a projection system is available when a
customer requests to rent one is about 90%? (Assume that customers who are interested
in renting a projection system but do not find one available do not wait, but go to find one
at another store.)