Operations Research
Final ( 2009 )
Hiroshi Toyoizumi
7/27/2009
1. What is the queue, waiting time and the number of customers in the system? Explain them, using examples.
2. Suppose, on the average, there are 4 customers in the line at a coffee shop counter and the arrival rate to this shop is 2 customers/min. Estimate the customer’s average sojourn time in the line.
3. Let N (t) be the number of customers in the M/M/1 queue with arrival rate λ = 1 and service rate µ = 2. Set the steady state probability by
pn = lim
t→∞P {N (t) = n}. (1)
Derive the exact value of p0, p1 and p2 and draw the graph of pn. 4. Explain the differences between Produce-to-Order and Produce-to-Stock
systems.
5. Explain how you can use an M/M/1 queue to model Produce-to-Stock systems, using figures and formulas.
6. Explain how to use Linear Programing. 7. You can write anything you want.
Remark 1. Don’t write lengthy answers. Your answers should be concise and focused.
Remark 2. Each problem is 5 point worth.
1