Comput Optim Appl DOI 10.1007/s10589-013-9600-5 Optimizing a multi-stage production/inventory system by DC programming based approaches Hoai An Le Thi · Duc Quynh Tran Received: 20 April 2012 © Springer Science+Business Media New York 2013 Abstract This paper deals with optimizing the cost of set up, transportation and in- ventory 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 non- linear 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 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 ǫ -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. Keywords Mixed integer nonlinear program · DC programming · DCA · Branch and bound · Multistage manufacturing system · Lot size · Unequal batches H.A. Le Thi (B ) · D.Q. Tran Laboratory of Theoretical and Applied Computer Science LITA EA 3097, University of Lorraine, Metz, France e-mail: hoai-an.le-thi@univ-lorraine.fr D.Q. Tran e-mail: tran@univ-metz.fr