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
Multi‐item capacitated lot‐sizing problems with setup times and pricing decisions
Mehmet Önal,H. Edwin Romeijn +1 more
TL;DR: In this article, a multi-item capacitated lot-sizing problem with setup times and pricing (CLSTP) over a finite and discrete planning horizon is studied, where the demand for each independent item in each time period is affected by pricing decisions and corresponding demands are then satisfied through production in a single capacitated facility or from inventory.
Production Planning with Load Dependent Lead Times and Sustainability Aspects
TL;DR: In this paper, a discrete dynamic model for aggregate production planning and supply chain management is presented, which takes into account load-dependent lead times and remanufacturing of externally returned items.
Journal ArticleDOI
Grouping in decomposition method for multi-item capacitated lot-sizing problem with immediate lost sales and joint and item-dependent setup cost
TL;DR: This article examines a dynamic and discrete multi-item capacitated lot-sizing problem in a completely deterministic production or procurement environment with limited production/procurement capacity where lost sales (the loss of customer demand) are permitted.
Dissertation
MIP models and exact methods for the Discrete Lot-sizing and Scheduling Problem with sequence-dependent changeover costs and times
TL;DR: In this paper, the authors propose diverses extensions d'une methode disponible dans la litterature for the resolution exacte du problem mono-niveau, mono-ressource.
Journal ArticleDOI
Managing cyclic inventories
James Bradley,Richard W. Conway +1 more
TL;DR: In this paper, the authors show that cyclic inventory is directly proportional to cycle length, which is in turn proportional to total changeover time, and inversely proportional to machine utilization, and demonstrate that both lot-splitting and maximization of utilization are devastatingly counter-productive when changeover times are non-trivial.
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.
Related Papers (5)
Solving multi-item capacitated lot-sizing problems using variable redefinition
Gary D. Eppen,R. Kipp Martin +1 more