Journal ArticleDOI
Capacitated lot sizing with setup times
TLDR
In this paper, a Lagrangian relaxation of the capacity constraints of CLSP allows it to be decomposed into a set of uncapacitated single product lot sizing problems, which are solved by dynamic programming.Abstract:
This research focuses on the effect of setup time on lot sizing. The setting is the Capacitated Lot Sizing Problem (the single-machine lot sizing problem) with nonstationary costs, demands, and setup times. A Lagrangian relaxation of the capacity constraints of CLSP allows it to be decomposed into a set of uncapacitated single product lot sizing problems. The Lagrangian dual costs are updated by subgradient optimization, and the single-item problems are solved by dynamic programming. A heuristic smoothing procedure constructs feasible solutions (production plans) which do not require overtime. The algorithm solves problems with setup time or setup cost. Problems with extremely tightly binding capacity constraints were much more difficult to solve than anticipated. Solutions without overtime could not always be found for them. The most significant results are that (1) the tightness of the capacity constraint is a good indicator of problem difficulty for problems with setup time; and (2) the algorithm solve...read more
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Book ChapterDOI
Chapter 7 An overview of production planning
L. Joseph Thomas,John O. McClain +1 more
TL;DR: This chapter discusses practical problems related to the use of OR tools for production planning, in which at least one of the following three items is viewed in an aggregated manner: production facilities, products, or time unit.
Journal ArticleDOI
Combining population-based and exact methods for multi-level capacitated lot-sizing problems
TL;DR: In this article, an ant-based algorithm was proposed to solve multi-level capacitated lot-sizing problems, where the ant system was used to optimize the decomposition of the problem into smaller subproblems.
Journal ArticleDOI
Combining process selection and lot sizing models for production scheduling of electrofused grains
TL;DR: An optimization model to support decisions in the production planning and control of the electrofused grain industry and the results show that the model and the heuristic can produce better solutions than the ones currently used by the company.
Journal ArticleDOI
A subjective evidence model for influence maximization in social networks
TL;DR: In this paper, the authors introduce the notion of subjective evidence, which fuels a new parallel cascade influence propagation model, which sheds light on the phenomena of belief reinforcement and viral spread of innovations, rumors, opinions, etc., in social networks.
Journal ArticleDOI
Local Cuts and Two-Period Convex Hull Closures for Big-Bucket Lot-Sizing Problems
TL;DR: In this paper, the authors proposed a methodology that can approximate the convex hulls of all possible capacitated relaxations by generating violated valid inequalities, which can be used efficiently in a regular branch-and-bound procedure.
References
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Book
Computers and Intractability: A Guide to the Theory of NP-Completeness
TL;DR: The second edition of a quarterly column as discussed by the authors provides a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NP-Completeness,” W. H. Freeman & Co., San Francisco, 1979.
Journal ArticleDOI
Decomposition Principle for Linear Programs
George B. Dantzig,Philip Wolfe +1 more
TL;DR: A technique is presented for the decomposition of a linear program that permits the problem to be solved by alternate solutions of linear sub-programs representing its several parts and a coordinating program that is obtained from the parts by linear transformations.
Journal ArticleDOI
Dynamic Version of the Economic Lot Size Model
Harvey M. Wagner,T. M. Whitin +1 more
TL;DR: Disjoint planning horizons are shown to be possible which eliminate the necessity of having data for the full N periods and desire a minimum total cost inventory management scheme which satisfies known demand in every period.
Journal ArticleDOI
Validation of subgradient optimization
TL;DR: It is concluded that the “relaxation” procedure for approximately solving a large linear programming problem related to the traveling-salesman problem shows promise for large-scale linear programming.
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