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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Dissertation
Modèles génériques et méthodes de résolution pour la planification tactique mono-site et multi-site
TL;DR: Les problemes de faisabilite des plans de production ainsi determines au niveau operationnel en utilisant differents couplages entre modeles mathematiques ou modeles de simulation, ce qui permet d'assurer the synchronisation verticale des plans.
Journal ArticleDOI
A comparison of two lot sizing-sequencing heuristics for the process industry
TL;DR: Two heuristics for operational production planning in a chemical processing environment are compared, characterized by a single bottleneck machine, fixed batch sizes, sequence-dependent setup-times, as well as production and storage constraints.
Journal ArticleDOI
Dantzig-Wolfe decomposition for the facility location and production planning problem
TL;DR: It is demonstrated that the pricing subproblems of the item decomposition are related to uncapacitated lot-sizing problems with the Wagner-Whitin property, which can improve lower bounds over other classical lower bounding techniques, such as linear programming relaxation and model reformulation.
Journal ArticleDOI
A novel mixed integer programming formulation and progressively stochastic search for capacitated lot sizing
Tao Wu,Defu Zhang,Yan He +2 more
TL;DR: In this paper, a new mixed integer programming formulation is proposed to solve the capacitated multi-level lot sizing problem, which is able to provide better linear programming relaxation lower bounds than a previously-proposed strong mixed-integer programming formulation.
Journal ArticleDOI
Determining the capacity and its level of utilization in make-to-order manufacturing: A simple deterministic model for single-machine multiple-product case
TL;DR: In this paper, a simple deterministic model is developed to determine the capacity and its level of utilization for a single specific machine producing multiple products in make-to-order manufacturing plants.
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