A dual criteria sequencing problem with earliness and tardiness penalties

Document Type

Article

Publication Date

6-1-2002

Abstract

We consider the problem of sequencing n jobs on a single machine, with each job having a processing time and a common due date. The common due date is assumed to be so large that all jobs can complete by the due date. It is known that there is an O(n log n)-time algorithm for finding a schedule with minimum total earliness and tardiness. In this article, we consider finding a schedule with dual criteria. The primary goal is to minimize the total earliness and tardiness. The secondary goals are to minimize: (1) the maximum earliness and tardiness; (2) the sum of the maximum of the squares of earliness and tardiness; (3) the sum of the squares of earliness and tardiness. For the first two criteria, we Show that the problems are NP-hard and we give a fully polynomial time approximation scheme for both of them. For the last two criteria, we show that the ratio of the worst schedule versus the best schedule is no more than 3/2. © 2002 Wiley Periodicals, Inc. Naval Research Logistics.

Identifier

0036605123 (Scopus)

Publication Title

Naval Research Logistics

External Full Text Location

https://doi.org/10.1002/nav.10020

ISSN

0894069X

First Page

422

Last Page

431

Issue

4

Volume

49

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