A note on due-date assignment and single machine scheduling with a learning/aging effect

Chang, Pei-Chann and Chen, Shih-Hsin and Mani, V (2009) A note on due-date assignment and single machine scheduling with a learning/aging effect. In: International Journal of Production Economics, 117 (1). pp. 142-149.

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Abstract

This paper considers the learning/aging effect in an n job single machine scheduling problem with common due date. The objective is to determine the optimal common due date and the optimal sequence of jobs that minimizes a cost function in the presence of learning/aging effect. The cost function depends on the individual job earliness and tardiness values: i.e., Sigma(n)(j=1) {E-[j] + T-[j]}. This is a well-known problem when the learning/aging effect is not considered and it is shown in earlier studies that there are more than one optimal sequence and optimal common due dates. It is shown in earlier studies that there are 2(r-1) optimal sequences to this problem if n is odd, and 2(r) optimal sequences if n is even. The value of r is (n + 1)/2 if n is odd, and the value of r is n/2 if n is even. In this paper, we derive two bounds B-alpha and B-alpha* for the learning index alpha. We show that when B-alpha < alpha < 0, then the optimal sequence is unique and provide an O(n log n) algorithm to obtain this unique optimal sequence and the optimal common due date. We also show that when alpha <B-alpha*, the optimal sequence is obtained by arranging the longest job in first position and the rest of the jobs in SPT order. Similarly, we derive two bounds A alpha and A(alpha)* for the aging index alpha. We show that when 0<alpha <A(alpha), then the optimal sequence is unique and provide an O(n log n) algorithm to obtain this unique optimal sequence and the optimal common due date. We also show that when alpha > A(alpha)* the optimal sequence is obtained by arranging the jobs in LPT order. We also present a numerical example for ease of understanding. (C) 2008 Elsevier B.V. All rights reserved

Item Type:	Journal Article
Publication:	International Journal of Production Economics
Publisher:	Elsevier Science
Additional Information:	Copyright of this article belongs to Elsevier Science.
Keywords:	Scheduling;Single-machine;Learning effect;Due-date assignment.
Department/Centre:	Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering)
Date Deposited:	05 Nov 2009 08:54
Last Modified:	19 Sep 2010 05:27
URI:	http://eprints.iisc.ac.in/id/eprint/19195

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