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

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 Al...

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Vydáno v:Computational optimization and applications Ročník 57; číslo 2; s. 441 - 468
Hlavní autoři: Le Thi, Hoai An, Tran, Duc Quynh
Médium: Journal Article
Jazyk:angličtina
Vydáno: Boston Springer US 01.03.2014
Springer Nature B.V
Springer Verlag
Témata:
Algorithms
Computer Science
Convex analysis
Convex and Discrete Geometry
Costs
Decomposition
Direct current
Heuristic
Integer programming
Inventory management
Management Science
Manufacturing
Mathematical models
Mathematics
Mathematics and Statistics
Mixed integer
Nonlinearity
Operations Research
Operations Research/Decision Theory
Optimization
Production management
Programming
Statistics
Stockpiling
Studies
Supply chains
DCA
Branch and bound
Lot size
DC programming
Multistage manufacturing system
Unequal batches
Mixed integer nonlinear program
ISSN:0926-6003, 1573-2894
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Shrnutí: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 ( http://www.coin-or.org/download/binary/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.
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ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-013-9600-5