The Ikea Furniture Company has a warehouse in Northern Illinois that stores its inventory until it is needed by other local Ikea stores in the region. When a truck arrives at its loading dock, a single crew with four membersis used to unload and/or load its cargo. In an effort to cut costs, the company is downsizing so it needs to determine the future size of its loading dock crew. The following is known about loading and unloading operations:

Trucks arrive randomly at a mean rate of one per hour ( = 1 per hour)

Crew time to load/unload exponential distribution with a mean of this distribution with afour-membercrew size of 15 minutes.

Mean service rate of crew of four ( = 4 customers per hour) is proportion to its size.

Cost of providing each member of the crew is $20 per hour. Cost attributable for not having a truck in use is $30 per hour

a-Identify the servers and customers for this queuing system. How many servers are there?

b. Find the various performance measures (L, Lq, W, Wq and ) for this queuing system based on four members on the crew.

c. Repeat (b) with three members.

d. Repeat part (b) with two members.

e. Should a one-member crew also be considered? Explain.

f. Given the previous results, which crew size do you think management should choose?