# American Institute of Mathematical Sciences

January  2014, 10(1): 243-258. doi: 10.3934/jimo.2014.10.243

## 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, France, France 2 LGIPM, INRIA Costeam, Ecole National d’Ing´enieurs de Metz, France

Received  January 2012 Revised  July 2013 Published  October 2013

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.
Citation: Le Thi Hoai An, Tran Duc Quynh, Kondo Hloindo Adjallah. A difference of convex functions algorithm for optimal scheduling and real-time assignment of preventive maintenance jobs on parallel processors. Journal of Industrial & Management Optimization, 2014, 10 (1) : 243-258. doi: 10.3934/jimo.2014.10.243
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