2009final OR toyo_classes

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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. LetN(t) be the number of customers in theM/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 ofpn.

4. Explain the differences between Produce-to-Order and Produce-to-Stock systems.

5. Explain how you can use anM/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.

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