Maurice Tutor

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    Argosy University/ Phoniex University/
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    Oct-2001 - Nov-2016

Category > Computer Science Posted 17 Sep 2017 My Price 6.00

Scheduling with profits and deadlines

Scheduling with profits and deadlines

 

Suppose you have one machine and a set of n tasks a1, a2,..., an. Each task aj has a processing time tj, a profit pj, and a deadline dj. The machine can process only one task at a time, and task aj must run uninterruptedly for tj consecutive time units. If you complete task aj by its deadline dj, you receive a profit pj, but if you complete it after its deadline, you receive no profit. As an optimization problem, you are given the processing times, profits, and deadlines for a set of n tasks, and you wish to find a schedule that completes all the tasks and returns the greatest amount of profit.

a. State this problem as a decision problem.

b. Show that the decision problem is NP-complete.

c. Give a polynomial-time algorithm for the decision problem, assuming that all processing times are integers from 1 to n. (Hint: Use dynamic programming.)

d. Give a polyomial-time algorithm for the optimization problem, assuming that all processing times are integers from 1 to n.

 

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Maurice Tutor
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Status NEW Posted 17 Sep 2017 09:09 AM My Price 6.00

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