A difference of convex functions algorithm for optimal scheduling and real-timeassignment  of   preventive maintenance jobs on parallel processors

Le Thi Hoai An; Tran Duc Quynh; Kondo Hloindo Adjallah

doi:10.3934/jimo.2014.10.243

Article Contents

2014, Volume 10, Issue 1: 243-258. Doi: 10.3934/jimo.2014.10.243

This issue Previous Article A survey of single machine scheduling to minimize weighted number of tardy jobs Next Article Heuristics for parallel machine scheduling with batch delivery consideration

A difference of convex functions algorithm for optimal scheduling and real-time assignment of preventive maintenance jobs on parallel processors

1.
Laboratory of Theoretical and Applied Computer Science (LITA), University of Lorraine, Ile du Saulcy, 57045, Metz
2.
LGIPM, INRIA Costeam, Ecole National d’Ing´enieurs de Metz

Received: January 2012

Revised: July 2013

Published: January 2014

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Abstract

In this paper, we introduce a new approach based on DC (Difference of Convex functions) Programming and DCA (DC Algorithm) for minimizing the maintenance cost involving flow-time and tardiness penalties by optimal scheduling and real-time assignment of preventive maintenance jobs on parallel processors. The main idea is to divide the horizon considered into $H$ intervals. The problem is first formulated as a mixed integer linear problem (MILP) and then reformulated as a DC program. A solution method based on DCA is used to solve the resulting problem. The efficiency of DCA is compared with the algorithm based on the new flow-time and tardiness rule (FTR) given in [1]. The computational results on several test problems show that the solutions provided by DCA are better.

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Mathematics Subject Classification: Primary: 90C11, 68M20; Secondary: 90C30, 90C90.

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