&&ReWrAp:HEADERFOOTER:0:ReWrAp&&

Author

Jing Wang

Date of Award

2009

Degree Type

Thesis

Degree Name

Master of Applied Science (MASc)

Department

Computational Engineering and Science

Supervisor

George Karakostas

Language

English

Abstract

This thesis provides a Fully Polynomial Time Approximation Scheme (FPTAS) for the minimum total weighted tardiness (TWT) problem with a constant number ofdistinct due dates.

Given a sequence ofjobs on a single machine, each with a weight, processing time, and a due date, the tardiness of a job is the amount of time that its completion time goes beyond its due date. The TWT problem is to find a schedule of the given jobs such that the total weighted tardiness is minimized. This problem is NP-hard even when the number of distinct due dates is fixed. In this thesis, we present a dynamic programming algorithm for the TWT problem with a constant number of distinct due dates first and then adopt a rounding scheme to obtain an FPTAS.

Three major points that we make in this algoritlun are: we observe a series of structural properties of optimal schedules so that we shrink the state space of the DP; we make use of preemption (i.e. allowing the processing of a job to be interrupted and restarted later) for the design of the DP; the rounding scheme that we adopt guarantees that a factor 1+ ℇ of the optimal solution is generated and the algorithm runs within a polynomial time of the problem size.

McMaster University Library