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The capacitated lot-sizing problem with linked lot-sizes
01 Jan 2003-Research Papers in Economics (Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL))-
TL;DR: 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.
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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Book•
01 Jan 1991
TL;DR: Single Level Lotsizing Problems, Model Survey, The Discrete Lotsizing and Scheduling Problem (DLSP), and the Uncapacitated Problem.
Abstract: Single Level Lotsizing Problems.- Model Survey.- The Discrete Lotsizing and Scheduling Problem (DLSP).- The Single Item DLSP.- The Multi-item DLSP.- Multilevel Lotsizing Problems.- The Uncapacitated Problem.- The Capacitated Problem.
123 citations
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TL;DR: This paper aims at extracting the essence ofSCM and advanced planning in the form of two conceptual frameworks: The house of SCM and the supply chain planning matrix.
Abstract: Literature on supply chain management (SCM) covers several disciplines and is growing rapidly. This paper firstly aims at extracting the essence of SCM and advanced planning in the form of two conceptual frameworks: The house of SCM and the supply chain planning matrix. As an illustration, contributions to this feature issue will then be assigned to the building blocks of the house of SCM or to the modules covering the supply chain planning matrix. Secondly, focusing on software for advanced planning, we outline its main shortcomings and present latest research results for their resolution.
53 citations
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TL;DR: This paper deals with a production planning problem typical for process industries where the production amount of one continuous production run is often constrained by a lower and/or upper bound or such that it has to be in multiples of a predefined batch size.
Abstract: This paper deals with a production planning problem typical for process industries. There the production amount of one continuous production run – referred to as a campaign – is often constrained by a lower and/or upper bound or such that it has to be in multiples of a predefined batch size. For this kind of problem, a new mixed-integer-programming model formulation is proposed that is based on a standard lot-sizing model with uniform time buckets. Thereby the concept of time continuity is integrated into a standard bucket-oriented lot-sizing model formulation. Furthermore, some algorithmic (valid inequalities) and modelling enhancements to the formulation are presented. Extensive computational tests show that this new model formulation clearly outperforms a benchmark model formulation. Moreover, they show the additional computational effort associated with different types of restrictions imposed on campaigns.
24 citations
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TL;DR: A new algorithm for the dynamic Multi-Level Capacitated Lot Sizing Problem with Setup Carry-Overs which is applicable to general bill-of-material structures and which includes minimum lead times of one period and multi-period setup carry-overs is presented.
Abstract: This paper presents a new algorithm for the dynamic Multi-Level Capacitated Lot Sizing Problem with Setup Carry-Overs (MLCLSP-L). The MLCLSP-L is a big-bucket model that allows the production of any number of products within a period, but it incorporates partial sequencing of the production orders in the sense that the first and the last product produced in a period are determined by the model. We solve a model which is applicable to general bill-of-material structures and which includes minimum lead times of one period and multi-period setup carry-overs. Our algorithm solves a series of mixed-integer linear programs in an iterative so-called Fix-and-Optimize approach. In each instance of these mixed-integer linear programs a large number of binary setup variables is fixed whereas only a small subset of these variables is optimized, together with the complete set of the inventory and lot size variables. A numerical study shows that the algorithm provides high-quality results and that the computational effort is moderate.
22 citations
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TL;DR: A new time-oriented decomposition heuristic is proposed to solve the dynamic multi-item multilevel lot-sizing problem in general product structures with single and multiple constrained resources as well as setup times.
Abstract: In this paper a new time-oriented decomposition heuristic is proposed to solve the dynamic multi-item multilevel lot-sizing problem in general product structures with single and multiple constrained resources as well as setup times. While lot-sizing decisions are made sequentially within an internally rolling planning interval (or lot-sizing window), capacities are always considered over the entire planning horizon. For each submodel a model formulation based on the "Simple Plant Location" representation is developed. These mixed-integer linear submodels are solved by standard mathematical programming software even for relatively large test instances. Extensive computational tests show that the heuristic proposed provides a better solution quality than a well-known special purpose heuristic.
16 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, 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
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