Operation management

A Call Center for a retail merchandise company has 5 operators fielding customer-service calls. The average time required for each operator to process a call is 5 minutes. There are two categories of customers who are serviced by the center. Category I customers constitute the most loyal customers who purchase considerably more per year in total dollar amount from the company than the "regular" Category II customers. Management wants to provide good service to all of its customers, but it also knows that it must consistently provide excellent service to its Category I customers or risk losing them to competitors. The time spent waiting on the phone to speak with a customer-service representative is a significant factor in determining customers' perceived service quality (customers do not like having to wait a long time to speak with an operator). Calls arrive at the service center at a rate of 45 calls per hour. On the average 40% of these calls are from Category I customers. The time to service a call as well as the inter arrival time between calls each follow an exponential distribution. (Note: you may use OM Explorer (or equivalent) to assist you in answering this question; however, you must copy and paste the output into your Show Work. Be sure to also explain how you determined your final answer from the output.)

a. Assume that all of the operators are placed in a customer-service "pool," with each call routed to the first available operator on a first-come, first-served basis and that calls are placed in a common waiting line for the five operators. On the average, how long will a caller wait before an operator picks up on the line? Answer in minutes rounded to the nearest tenth.

b. Assume now that 2 of the operators are dedicated exclusively to Category I calls, and the remaining operators are dedicated exclusively to Category II calls. There are separate waiting lines for each category of caller (calls are not permitted to be shifted to an operator that is not assigned to its corresponding category; however, callers within the same category share a common waiting line). The automatic answering system is able to determine the category of the caller (using the callers account number) and routes the call automatically to the relevant waiting line/operator.

i. On the average, how long will a Category I caller wait before an operator picks up on the line? (Answer in minutes rounded to the nearest tenth.)

ii. On the average, how long will a Category II caller wait before an operator picks up on the line? (Answer in minutes rounded to the nearest tenth.

c. How do the waiting times in the "pooled" system in part a compare with the waiting times in the "partitioned" system in part b? Does the partitioned system with servers dedicated exclusively to each category of customers provide better service?