Date of Award

12-2010

Document Type

Thesis

Degree Name

Master of Science (MS)

Legacy Department

Computer Science

Advisor

Dean, Brian C

Committee Member

Hallstrom , Jason O

Committee Member

Jacobs , David P

Abstract

The standard NP-hard knapsack problem can be interpreted as a scheduling problem with n jobs with weights w1 . . .wn and processing times p1 . . . pn, where our goal is to order the jobs on a single machine so as to maximize the weight of all jobs completing prior to a known common deadline d. In this paper, we study the uncertain capacity knapsack problem (UCKP), a generalization of this problem in which the deadline d is not known with certainty, but rather is provided as a probability distribution, and our goal is to order the jobs so as to maximize the expected weight of the set of jobs completing by the deadline. We develop a polynomial-time approximation scheme (PTAS) for this problem. We make no assumptions about probability distributions except that each job, scheduled by itself, completes by the deadline with some constant probability.

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