Steco has 100 sales representatives in Canada. They call orders into a central office where an office worker using the central inventory control system confirms product availability, price, and delivery date. The representative calls directly from the customer’s office before signing the contract. Calls are held in a queue and served by the first available office worker on a first-come, first-served basis. Calls arrive at the rate of 40 per hour, and the mean service time is 6 minutes. Management estimates that it costs $20 per hour to have a sales representative call in and order, and $12 per hour to employ an office worker. Model this situation as a multiple channel waiting line model with Poisson arrivals and exponential service times with an infinite calling population.
a. Calculate the performance measures of this waiting line system if Steco hires five office workers (namely, L, Lq, Wq, W, Pw, P0 and P1, P2, and P7).
b. Calculate the expected total cost per hour if Steco hires five office workers.
c. Calculate the expected total cost per hour if Steco hires six office workers.
d. Use the solutions to parts (b) and (c) to determine the value of the ratio Cs/Cw for which Steco is indifferent between having five or six office workers.