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 Lagrangean-based heuristic for multi-plant, multi-item, multi-period capacitated lot-sizing problems with inter-plant transfers
Murali Sambasivan,Salleh Yahya +1 more
TL;DR: It has been found that Lagrangean-based approach works quite "efficiently" for this problem and is suitable for multi-plant, capacitated lot-sizing problem.
Journal ArticleDOI
A dual ascent and column generation heuristic for the discrete lotsizing and scheduling problem with setup times
TL;DR: This paper presents a dual ascent and column generation heuristic to solve SPP, the problem of determining the sequence and size of production batches for multiple items on a single machine.
Journal ArticleDOI
Integrated production planning and preventive maintenance in deteriorating production systems
TL;DR: The issue of integrating production planning and preventive maintenance in manufacturing production systems is discussed, and a Lagrangian-based heuristic procedure for the solution of the first planning model is proposed and discussed.
Journal ArticleDOI
A heuristic for dynamic multi-item multi-level capacitated lotsizing for general product structures
Horst Tempelmeier,Stefan Helber +1 more
TL;DR: The proposed procedure uses a modification of the Dixon-Silver heuristic to solve a sequence of single-level capacitated multi-item lotsizing problems (CLSP).
Journal ArticleDOI
Lotsizing and Scheduling on Parallel Machines with Sequence-Dependent Setup Costs
TL;DR: An optimization approach based on a column generation/branch and bound methodology is developed, and heuristically adapted to test problems including five real-world problem instances gathered from industry.
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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