Seabreeze Furniture in Orlando maintains a large central warehouse where it stores items until they are sold or needed by the company’s many stores in the central Florida area. A four-person crew works at the warehouse to load or unload trucks that arrive at the warehouse at a rate of one per hour (with exponentially distributed interarrival times). The time that it takes the crew to unload each truck follows an exponential distribution with a mean service rate of 4 trucks per hour. Each worker costs the company $21 per hour in wages and benefits. Seabreeze’s management is currently trying to cut costs and is considering reducing the number of workers on this warehouse crew. They believe that three workers could provide a service rate of 3 trucks per hour, two workers a service rate of 2 trucks per hour, and one worker a service rate of 1 truck per hour. The company estimates that it costs $35 for each hour a truck spends at the loading dock (whether it is waiting for service or being loaded or unloaded).
a. Should Seabreeze ever consider having only one worker on the crew? Explain your answer.
b. For each possible crew size, determine the expected queue length, expected total time in the system, the probability that a customer waits, and the total hourly cost.
c. What crew size would you recommend?