The Capacitated Lot-Sizing Problem with Linked Lot Sizes
TL;DR: Extensive computational tests prove the capability of the new mixed integer programming model formulation and its incorporation into a time-oriented decomposition heuristic for the capacitated lot-sizing problem with linked lot sizes (CLSPL).
Abstract: In this paper a new mixed integer programming (MIP) model formulation and its incorporation into a time-oriented decomposition heuristic for the capacitated lot-sizing problem with linked lot sizes (CLSPL) is proposed. The solution approach is based on an extended model formulation and valid inequalities to yield a tight formulation. Extensive computational tests prove the capability of this approach and show a superior solution quality with respect to other solution algorithms published so far.
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TL;DR: In this paper, the authors extract the essence of SCM and advanced planning in the form of two conceptual frameworks: the house of supply chain management and the supply chain planning matrix.
697 citations
TL;DR: In this article, the authors give an overview of recent developments in the field of modeling deterministic single-level dynamic lot sizing problems, focusing on the modeling of various industrial extensions and not on the solution approaches.
Abstract: In this paper we give an overview of recent developments in the field of modeling deterministic single-level dynamic lot sizing problems. The focus of this paper is on the modeling of various industrial extensions and not on the solution approaches. The timeliness of such a review stems from the growing industry need to solve more realistic and comprehensive production planning problems. First, several different basic lot sizing problems are defined. Many extensions of these problems have been proposed and the research basically expands in two opposite directions. The first line of research focuses on modeling the operational aspects in more detail. The discussion is organized around five aspects: the set ups, the characteristics of the production process, the inventory, demand side and rolling horizon. The second direction is towards more tactical and strategic models in which the lot sizing problem is a core substructure, such as integrated production-distribution planning or supplier selection. Recent advances in both directions are discussed. Finally, we give some concluding remarks and point out interesting areas for future research.
350 citations
TL;DR: A review of four decades of research on dynamic lot-sizing with capacity constraints shows that many practically important problems are still far from being solved in the sense that they could routinely be solved close to optimality in industrial practice.
Abstract: This paper presents a review of four decades of research on dynamic lot-sizing with capacity constraints. We discuss both different modeling approaches to the optimization problems and different algorithmic solution approaches. The focus is on research that separates the lot-sizing problem from the detailed sequencing and scheduling problem. Our conceptional point of reference is the multi-level capacitated lot-sizing problem (MLCLSP). We show how different streams of research emerged over time. One result is that many practically important problems are still far from being solved in the sense that they could routinely be solved close to optimality in industrial practice. Our review also shows that currently mathematical programing and the use of metaheuristics are particularly popular among researchers in a vivid and flourishing field of research.
270 citations
Cites background or methods from "The Capacitated Lot-Sizing Problem ..."
...νmt = 1 indicates that a setup state for one item is carried over from a period t − 1 to the consecutive periods t and t + 1 on resource m. In the case of consecutive carryovers, the additional constraints are ( Surie and Stadtler 2003 ):...
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...It is also applied to the CLSPL in Surie and Stadtler (2003) ....
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...Pochet and Wolsey (1991) I&L LP B&B, VI ML, ST Surie and Stadtler (2003) SPL LP B&C, C&B, VI SL, ML, ST, SC Dillenberger et al. (1993) I&L LP F&R SL, PM, BO, SC...
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... Surie and Stadtler (2003) derived valid inequalities for the CLSPL and the...
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01 Mar 2006
TL;DR: Optimization Modeling starts with an mrp Model and extends to an MRP II Model, a Better Model and Extensions to the Model, and Implementation Examples.
Abstract: Introduction * Optimization Modeling * Starting with an mrp Model * Extending to an MRP II Model * A Better Model * Extensions to the Model * Implementation Examples * Solutions * Some Stochastic Extensions * Research Directions and References.
196 citations
TL;DR: This paper presents an optimization-based solution approach for the dynamic multi-level capacitated lot sizing problem (MLCLSP) with positive lead times and its solution quality outperforms those of the approaches by Tempelmeier/Derstroff and by Stadtler.
168 citations
References
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TL;DR: 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...
444 citations
TL;DR: A useful taxonomy is imposed on production scheduling problems and alternative formulations for a wide variety of problems within the taxonomy are developed and the linear programming relaxation of the new models is very effective in generating bounds.
Abstract: Mixed-integer programming models are typically not used to solve realistic-sized production scheduling problems because they require exorbitant solution times. We impose a useful taxonomy on production scheduling problems and develop alternative formulations for a wide variety of problems within the taxonomy. The linear programming relaxation of the new models is very effective in generating bounds. We show that these bounds are equal to those that could be generated using Lagrangian relaxation or column generation. The linear programming bounds increase in effectiveness as the problems become larger. Perhaps of greatest significance is that practitioners can obtain our results using only standard “off-the-shelf” codes such as LINDO or MPSX/370. We report computational experience in several computing environments (hardware and software) on problems with up to 200 products and 10 time periods (2000 0-1 variables).
412 citations
TL;DR: In this article, a branch-and-bound procedure using Lagrangean relaxation for determining both lower bounds and feasible solutions is presented, and the relaxed problems are solved by dynamic programming.
264 citations
"The Capacitated Lot-Sizing Problem ..." refers background in this paper
...Gopalakrishnan et al. (1995) introduce product independent setup times in the model formulation, which become product dependent in Gopalakrishnan (2000)....
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...The discrete lot sizing and scheduling problem (DLSP) allows at most one product per period, and production must be for the full period or not at all (allor-nothing) (Fleischmann 1990)....
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TL;DR: In this paper, the first heuristics capable of solving multilevel lotsizing problems with capacity constraints on more than one level have been presented, and they can be easily extended to solve a variety of problems.
256 citations
"The Capacitated Lot-Sizing Problem ..." refers methods in this paper
...derived solely from the model data, this step is called preprocessing, which was also used by Maes et al. (1991) for the serial MLCLSP....
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TL;DR: In this paper, a heuristic approach for the dynamic multilevel multiitem lotsizing problem in general product structures with multiple constrained resources and setup times is proposed with the help of Lagrangean relaxation.
Abstract: In this paper a heuristic approach for the dynamic multilevel multiitem lotsizing problem in general product structures with multiple constrained resources and setup times is proposed. With the help of Lagrangean relaxation the capacitated multilevel multiitem lotsizing problem is decomposed into several uncapacitated single-item lotsizing problems. From the solutions of these single-item problems lower bounds on the minimum objective function value are derived. Upper bounds are generated by means of a heuristic finite scheduling procedure. The quality of the approach is tested with reference to various problem groups of differing sizes.
235 citations
"The Capacitated Lot-Sizing Problem ..." refers result in this paper
...This assumption is in line with Tempelmeier and Derstroff (1996), who argue that lot-size decisions in a finite capacity model have to be based on “operations” while the term “item” or “product” are often used for an aggregate of several operations....
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