IEOR4405, Spring 2019: Homework 4

Assigned: Friday, February 15, 2019
Due: Friday, February 22, 2019

General Instructions

  1. Please review the course information.
  2. You must write down with whom you worked on the assignment. If this changes from problem to problem, then you should write down this information separately with each problem.
  3. Numbered problems are all from the textbook Scheduling: Theory, Algorithms and Systems.

Problems

  1. Problem 3.6 (please show your work for the branch and bound, or write a computer program to solve the problem)
  2. Problem 3.7 (please show your work for the branch and bound, or write a computer program to solve the problem)
  3. Consider the following instance of 1||Σ wjUj in which the jobs have a common deadline of 10.
    j pj wj
    1 1 2
    2 2 3
    3 4 12
    4 3 6
    5 4 5
    Show the execution of the dynamic programming algorithm given in class.
  4. Give a dynamic programming algorithm for 1||Σ wjUj in which the jobs have a common deadline in which you fill in a table f(j,w), where f(j,w) is the minimum deadline d by which you can schedule a subset of jobs 1..j and have that the weight of the jobs finishing by time d is at least w. Be sure to give the recurrence and justify why it is correct.
  5. Problem 3.24. We already discussed the optimal algorithm in class. You need to prove it is optimal via an interchage argument.

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