Queuing Theory (Waiting Line Management)

Notation (lambda) = average arrival rate (mu) = average service rate per server C = Number of Servers WQ = Expected wait time inline W = Expected total time in the system. Expected wait time plus expected service time. LQ = Expected number of people in line

Single Channel-Single Phase (C = 1) L = Expected number of people system (waiting in line or being serviced) Pn = Probability that there are n people in the system

Mona Lott works in the Customer Service Department at MediPlus Products and is solely responsible for handling customer phone complaints. Customer complaints recently increased when the company inadvertently put itching powder instead of talc in a batch of foot powder. The number of complaints she receives and must document is random and averages 4 per hour. It takes Mona an average of 10 minutes to record and process a complaint. a. What portion of the time is Mona busy taking complaint calls? b. What is the average time a complaining customer is on hold? c. What is the average time a complaining customer spends on the phone? d. On average, how many customers are on hold? e. Mona is paid $20 per hour. Customer time is valued at $30 per hour. What is the average total cost per hour (labor + customer)? Management is considering the purchase of a case management software package that will speed up the time it takes to document and record a complaint. The software will reduce the average time to process a complaint to 6 minutes. f. What is the average time a complaining customer is on the phone now? g. What is the average time that a complainer is on hold now? h. If the software has an amortized cost of $5 per hour, what is the average total cost per hour now? Suppose there is a company that produces complementary products to that of MedlinePlus. Also, assume that their complaint department has the exact same characteristics and costs as those of originally listed for Mediplus. What would be the benefit of cross-training the two phone complaint takers and combining the two complaint departments through phone technology so whoever is available takes the next complaint call. i. What is the average time that a complainer is on hold now (LQ = .0833)? j. What is the average total cost per hour to MediPlus of this option?