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 dynamic lot-sizing-based profit maximization discounted cash flow model considering working capital requirement financing cost with infinite production capacity
Yuan Bian,David Lemoine,Thomas Yeung,Nathalie Bostel,Vincent Hovelaque,Jean-Laurent Viviani,Fabrice Gayraud +6 more
TL;DR: In this article, the authors introduce a link between dynamic lot-sizing and the financial aspects of working capital requirements (WCR), and propose a new generic WCR model which allows evaluating the company's financial situation throughout the planning horizon.
Journal ArticleDOI
Integrating distribution, machine assignment and lot-sizing via Lagrangean relaxation
Francesca Fumero,Carlo Vercellis +1 more
TL;DR: The problem of optimally coordinating and integrating complex decisions at the tactical production planning level is considered and computational evidence on random problem instances, as well as the application to actual production environments, indicates that the proposed approach is practical and effective.
Journal ArticleDOI
Solving the capacitated lot-sizing problem with backorder consideration
TL;DR: This research presents a general model for the lot-sizing problem with backorder options, that can take into consideration various types of production capacities such as regular time, overtime and subcontracting, and develops a heuristic based on the special structure of fixed charge transportation problem.
Journal ArticleDOI
Technical note: New results for the capacitated lot sizing problem with overtime decisions and setup times
TL;DR: In this paper, a genetic algorithm (GATA) integrated with tabu search (TS) and simulated annealing (SA) was used to solve the capacitated lot sizing problem with overtime and setup times (CLSPOS).
Journal ArticleDOI
Lot sizing problem on a paper machine under a cyclic production approach
TL;DR: A new approach is proposed where first the cycle time is computed by assuming constant demand, and then lot sizes are determined for each product within each cycle in order to satisfy demand.
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
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