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


  • Hoai Le Thi


  • Duc Tran



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 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 ( ), a solver for mixed integer nonconvex programming, show the rapidity and the ϵ-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. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Hoai Le Thi & Duc Tran, 2014. "Optimizing a multi-stage production/inventory system by DC programming based approaches," Computational Optimization and Applications, Springer, vol. 57(2), pages 441-468, March.
  • Handle: RePEc:spr:coopap:v:57:y:2014:i:2:p:441-468
    DOI: 10.1007/s10589-013-9600-5

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    References listed on IDEAS

    1. Bogaschewsky, Ronald W. & Buscher, Udo D. & Lindner, Gerd, 2001. "Optimizing multi-stage production with constant lot size and varying number of unequal sized batches," Omega, Elsevier, vol. 29(2), pages 183-191, April.
    2. Le An & Pham Tao, 2005. "The DC (Difference of Convex Functions) Programming and DCA Revisited with DC Models of Real World Nonconvex Optimization Problems," Annals of Operations Research, Springer, vol. 133(1), pages 23-46, January.
    3. Hsiao, Yu-Cheng, 2008. "Optimal single-cycle policies for the one-warehouse multi-retailer inventory/distribution system," International Journal of Production Economics, Elsevier, vol. 114(1), pages 219-229, July.
    4. Goyal, S. K. & Szendrovits, A. Z., 1986. "A constant lot size model with equal and unequal sized batch shipments between production stages," Engineering Costs and Production Economics, Elsevier, vol. 10(3), pages 203-210, March.
    5. Andrew Z. Szendrovits, 1975. "Manufacturing Cycle Time Determination for a Multi-Stage Economic Production Quantity Model," Management Science, INFORMS, vol. 22(3), pages 298-308, November.
    6. Szendrovits, Andrew Z & Drezner, ZVI, 1980. "Optimizing multi-stage production with constant lot size and varying numbers of batches," Omega, Elsevier, vol. 8(6), pages 623-629.
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