MATH 318: Operations Research

Spring 2023

Assignment 1

Due: Monday, February 20

Reading

Pages l - l7 of Cooper, Bhat and LeBlanc (CBL)

Chapters 1 and 2 of Hillier and Lieberman

"Mathematics and Operations Research in Industry" at http://www.maa.org/mathematics-and-operations-research-in-industry. There is a link from a course website.

Problems

1.         Study carefully the analysis of the gear manufacturing problem (CBL Example 1, pages 3 -7). Carry out all the indicated mathematical steps. In particular, show that the average number of gears in stock during t is y/2. Verify all the details in going from equation (6) to equation (11).

2.         In the discussion of the solution technique of simulation on  page l3, CBL assumes that the only values x can take  on are 0, .1, .2,...,.9. Suppose that x can take on any  value between 0 and .9. Calculate the average value of y in  this case.

Recall that lf y = f(t) is a continuous function on the  closed interval [a,b], then the average  value of f is the  value of the definite integral of f from a to b divided by  (b - a). Make sure that you show all the intermediate steps in finding the antiderivative.

3.         In (a) - (d), draw a decision tree and find an optimal  interviewing policy. State the optimal policy in clear English sentences. Assume all the data as given in class  except for the specific changes indicated below in each  separate part of the exercise.

(a) You are willing to interview at no more than 4 firms. What is the incremental value of interviewing with as many as 3 more employers instead of only 1? What is the incremental value of interviewing with as many as 4 employers instead of a maximum of 3?

(b)       The relative value of a terrific job is 4. What is the incremental value of interviewing as many as 2 more employers instead of 1?

(c)        There is a .2 chance that an employer has a good  job and a .6 chance that it will be a fair one. What is the incremental value of interviewing as many as two more employers instead of one?

(d)       There is a cost of .15 for each interview.

4.         Do one of the problems on page 17 of Cooper, Bhat and LeBlanc. Limit your answer to one page.