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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Book ChapterDOI
Combining Column Generation and Lagrangian Relaxation
TL;DR: This paper focuses on solving the LP relaxation of the Dantzig-Wolfe master problem, and applies Lagrangian relaxation directly to this extended formulation, i.e. no simplex method is used.
Journal ArticleDOI
Classification and literature review of integrated lot-sizing and cutting stock problems
TL;DR: A deterministic mathematical model, that considers multiple dimensions of integration and comprises several aspects found in practice, is proposed and used as a framework to classify the literature related to the integration between the lot-sizing and cutting stock problem.
Journal ArticleDOI
Multi-item production routing problem with backordering: a MILP approach
Nadjib Brahimi,Tarik Aouam +1 more
TL;DR: In this paper, the authors present mixed integer linear programming formulations for the production routing problem with backordering (PRP-B) and a new hybrid heuristic to solve the problem.
Journal ArticleDOI
Ending Inventory Valuation in Multiperiod Production Scheduling
TL;DR: A method to mitigate end-effects in lot sizing by including a valuation term VIT for end-of-horizon inventory IT, in the objective function of the short-Horizon model, which significantly outperforms the other approaches tested, for modest to long model horizons.
Journal ArticleDOI
Solving Lot-Sizing Problems on Parallel Identical Machines Using Symmetry-Breaking Constraints
TL;DR: In this paper, the authors proposed new symmetry-breaking constraints to break the symmetry in the branch-and-bound algorithm for the parallel machine lot-sizing problem, and tested their approach on the problem with setup costs and times, using a network reformulation for this problem.
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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