Date of Award
Master of Applied Science (MASc)
Computational Engineering and Science
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.
Wang, Jing, "An FPTAS for the Single Machine Minimum Total Weighted Tardiness Problem With a Fixed Number of Distinct Due Dates" (2009). Open Access Dissertations and Theses. Paper 4617.
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