Reference no: EM132899691

1. Consider an M/M/1 queue with an arrival rate of λ = 3 /hour and a service rate of µ /hour. Assume that it is possible to control the service rate (e.g., vary the manpower in the service facility). Assume that the various service rates may be obtained according to the following schedule of associate costs:

Service rate(µ)/hour Service cost $/hour

4.0 $3.00

4.5 $ 6.00

5.0 $9.00

5.5 $ 12.00

6.0 $15.00

Further assume that the cost per hour for customers waiting is (including service time) is estimated to be $10.00 per hour. Analyze the system over a period of 8 hours. (Note: it will be assumed here that the system is in steady state at the beginning of the 8-hour period of analysis.)

a. Determine the optimum service level (service rate) to employ, and the associated expected total cost.

b. Illustrate the decision analysis graphically, showing service cost, customer waiting cost, and total cost, for the various service rates considered.