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
Citations
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Period Decompositions for the Capacity Constrained Lot Size Problem with Setup Times
TL;DR: In this article, a branch-and-price based heuristic was proposed to solve the capacity constrained lot size problem with setup times (CLST), which is based on two strong reformulations of the problem.
Journal ArticleDOI
A comparison of rules for allocating setup‐reduction investments in a capacitated environment
John P. Leschke,Elliott N. Weiss +1 more
TL;DR: In this article, the authors compare different investment-allocation rules in a multi-item, capacity-constrained, dynamic demand environment under a variety of cost, demand, and investment assumptions.
Proceedings ArticleDOI
Knowledge Evolution Algorithm for Capacitated Lot Sizing Problem
TL;DR: By comparison of the results, it can be found that knowledge evolution algorithm illustrated its higher searching efficiency and better stability than the genetic algorithm and the Annealing penalty hybrid genetic algorithm of other literatures.
Journal ArticleDOI
Lot-sizing problem with several production centers
TL;DR: A case study is carried out concerning the lot-sizing problem involving a single item production planning in several production centers that do not present capacity constraints, and an efficient implementation of a forward dynamic programming algorithm for problems with one single production center is proposed.
Dissertation
Dynamic scheduling of manufacturing systems with setups and random disruptions
TL;DR: In this article, a new heuristic, called the Hedging Zone Policy (HZP), is introduced and developed, which is a dynamic-sequence policy that always produces the current part type at its maximum production rate until a fixed base stock level is reached.
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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Solving multi-item capacitated lot-sizing problems using variable redefinition
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