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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Journal ArticleDOI
A hybrid genetic algorithm for the batch sequencing problem on identical parallel machines
TL;DR: A dispatching rule called the EDD-Greedy heuristic and a pure genetic algorithm (GA) are proposed, and then combined through an insertion method called the Gene Bank Strategy to solve an extension of the batch sequencing problem from single machine case to parallel machine case.
Proceedings ArticleDOI
A model for multi-stage production planning with load dependent lead times
David L. Woodruff,Stefan Voss +1 more
TL;DR: In this paper insights are given into why queuing results in delays and an optimization model is suggested that takes into account load dependent lead times and routing alternatives.
Journal ArticleDOI
Stochastic Lipschitz dynamic programming
TL;DR: In this paper, a nonlinear Lipschitz cuts are constructed to build lower approximations for the non-convex cost-to-go functions, which are derived using augmented Lagrangian duality for MILPs.
Journal Article
Capacitated materials requirements planning and its application in the process industries
TL;DR: In this paper, a two-level, spreadsheet-based procedure developed at Welch's, the largest processor of Concord and Niagara grapes, to perform integrated capacity planning is described, where the logistics of inter-plant transfers, special processing requirements, as well as proprietary product recipes are considered.
Posted Content
The capacitated lot-sizing problem with linked lot-sizes
TL;DR: In this paper, a new mixed integer programming (MIP) model formulation and its incorporation into a time-oriented decomposition heuristic for the capacitated lot-sizing problem with linked lot sizes (CLSPL) is proposed.
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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