Optimizing a multi-stage production/inventory system by DC programming based approaches

Authors:
Hoai An Le Thi;Duc Quynh Tran
Affiliations:
Laboratory of Theoretical and Applied Computer Science LITA EA 3097, University of Lorraine, Metz, France;Laboratory of Theoretical and Applied Computer Science LITA EA 3097, University of Lorraine, Metz, France
Venue:
Computational Optimization and Applications
Year:
2014

Citing 2
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Abstract

This paper deals with optimizing the cost of set up, transportation and inventory of a multi-stage production system in presence of bottleneck. The considered optimization model is a mixed integer nonlinear program. We propose two methods based on DC (Difference of Convex) programming and DCA (DC Algorithm)--an innovative approach in nonconvex programming framework. The mixed integer nonlinear problem is first reformulated as a DC program and then DCA is developed to solve the resulting problem. In order to globally solve the problem, we combine DCA with a Branch and Bound algorithm (BB-DCA). A聽convex minorant of the objective function is introduced. DCA is used to compute upper bounds while lower bounds are calculated from a convex relaxation problem. The numerical results compared with those of COUENNE (http://www.coin-or.org/download/binary/Couenne/), a solver for mixed integer nonconvex programming, show the rapidity and the ∈-globality of DCA in almost cases, as well as the efficiency of the combined DCA-Branch and Bound algorithm. We also propose a simple heuristic algorithm which is proved by experimental results to be better than an existing heuristic in the literature for this problem.