Question 1 (Queuing Models: Waiting Line Management)

Intent: This situation is intended to help managers see the tradeoffs between labor cost and cost of customer waiting. Managers often try to use resources at a very high utilization. But high utilization, at the expense of long customer wait, is not always helpful. This problem indicates how an optimal workforce staffing can be derived to minimize overall cost. This problem also illustrates how different designs may be necessary for the same service for different customer segments.

Part I:

A walk-in-clinic provides medical services to a college campus where most customers are students. The Director of the clinic is considering use of queuing formulas to determine the best level of staffing. On the basis of past record, the director finds that the clinic receives, at the average, 18 customers per hour, and service records estimate that each provider (doctor or nurse) takes 12 minutes to treat a patient. The hourly cost of a provider is $80 per hour. The cost of keeping a customer waiting in line is estimated to be $100 per hour (this includes patient's time, cost of inconvenience, bad word of mouth, loss of future business, etc). In order to use queuing models, assume that arrivals follow to a Poisson distribution and service times are exponentially distributed. Patients are treated by the first available provider on a first-come-first-serve basis from a single line. [Note: This is an M/M/C systems, use appropriate formula/table]. Determine the optimal number of providers (level of staffing) that minimizes the total cost of labor and customer waiting. What is the corresponding minimum total (hourly) cost?

Part II:

Now, assume that instead of students, the customers are top level business executives. The revised cost of keeping a customer waiting in line is estimated to be $1000 per hour (this includes executive's time, cost of inconvenience, bad word of mouth, loss of future business, etc). The arrival rate, service rate and other policies are the same as above. Determine the optimal number of providers that minimizes the total cost of labor and customer waiting. What is the corresponding minimum total (hourly) cost?

Part III:

Compare your results in parts I and II above.