A Math-Heuristic for the MultiLevel Capacitated Lot Sizing Problem with Carryover (original) (raw)
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A hybrid heuristic approach to solve the multi level capacitated lot sizing problem
2011 IEEE Congress of Evolutionary Computation (CEC), 2011
This paper presents preliminary results found by a hybrid heuristic applied to solve the Multi-Level Capacitated Lot Sizing Problem (MLCLSP). The proposed method combines a multi-population genetic algorithm and fix-and-optimize heuristic. These methods are also integrated to a mathematical programming approach. For this, a mathematical reformulation of MLCLSP model is proposed to embed the exact solution of the model in the heuristic approaches. The hybrid heuristic is evaluated in two sets of benchmark instances. The solutions found are compared with those reached by other methods from literature. The preliminary results obtained indicate that the hybrid heuristic outperforms other approaches in the majority of problems solved.
An optimization framework for solving capacitated multi-level lot-sizing problems with backlogging
European Journal of Operational Research, 2011
This paper proposes two new mixed integer programming models for capacitated multi-level lot-sizing problems with backlogging, whose linear programming relaxations provide good lower bounds on the optimal solution value. We show that both of these strong formulations yield the same lower bounds. In addition to these theoretical results, we propose a new, effective optimization framework that achieves high quality solutions in reasonable computational time. Computational results show that the proposed optimization framework is superior to other well-known approaches on several important performance dimensions. manuscript no. (Please, provide the mansucript number!) capacitated single level multi-item lot-sizing problem with backlogging. examined the uncapacitated single item lot-sizing problem with backlogging and start-up costs, when Wagner-Whitin costs are assumed. Cheng et al. (2001) formulated single-level lot-sizing problems with provisions for backorders using a fixed-charge transportation model and proposed a heuristic solution method. Ganas and Papachristos (2005) proposed a polynomial-time algorithm for the single-item lot-sizing problem with backlogging. Song and Chan (2005) proposed a dynamic programming algorithm for solving a single-item lot-sizing problem with backlogging on a single machine at a finite production rate. Mathieu (2006) proposed two extended linear programming (LP) reformulations of single-item lot-sizing problems with backlogging and constant capacities. In a recent study, Küçükyavuz and Pochet (2009) provided the full description of the convex hull for the single-level uncapacitated problem with backlogging. Wu and Shi (2009b) proposed a heuristic that combines domain knowledge from the different strategies of relax-and-fix effectively for the capacitated multi-level lot sizing problem with the consideration of backlogging. We refer the interested reader to Pochet and Wolsey (2006) for a detailed general review of different lot-sizing problems. We note that the term backlog is used interchangeably with backorder in the lot-sizing literature, referring to any demand that is not satisfied on time but in a later time period, no matter what type of manufacturing environment. In our context, we consider a model that is flexible enough to apply to both MTO (Make-To-Order) and MTS (Make-To-Stock) environments when production is planned based on fixed demands or forecasts. The past research has also considered other classes of lot sizing problems. For example, Thizy and van Wassenhove (1985) designed a Lagrangian relaxation (LR) approach, in which capacity constraints are relaxed, in an attempt to decompose the problem into N uncapacitated single item lot-sizing subproblems, solvable by the Wagner-Whitin algorithm. Trigeiro (1987) developed a similar approach for solving the deterministic, multi-item, single-operation lot-sizing problem. Trigeiro et al. (1989) also proposed LR based methods for large-scale lot-sizing problems. Kuik and Salomon (1990) evaluated a simulated annealing heuristic for solving multi-level lot-sizing problem. Pochet and Wolsey (1991) applied strong cutting planes
European Journal of Operational Research, 2014
In this study, we improved the variable neighborhood search (VNS) algorithm for solving uncapacitated multilevel lot-sizing (MLLS) problems. The improvement is twofold. First, we developed an effective local search method known as the Ancestors Depth-first Traversal Search (ADTS), which can be embedded in the VNS to significantly improve the solution quality. Second, we proposed a common and efficient approach for the rapid calculation of the cost change for the VNS and other generate-and-test algorithms. The new VNS algorithm was tested against 176 benchmark problems of different scales (small, medium, and large). The experimental results show that the new VNS algorithm outperforms all of the existing algorithms in the literature for solving uncapacitated MLLS problems because it was able to find all optimal solutions (100%) for 96 small-sized problems and new best-known solutions for 5 of 40 medium-sized problems and for 30 of 40 large-sized problems.
Metaheuristics for the multi-item capacitated lot-sizing problem with time Windows and setup times
2011
In this paper, we address to the multi-item capacitated lot-sizing problem with production time windows and setup times under the non-customer specific case. This problem is known to be NP-hard. Two cooperative approaches are proposed for solving this problem by combining mathematical programming and metaheuristics based on a decomposition scheme. The algorithms use simultaneously the mathematical programming and heuristic procedures such that the local Search algorithm and Variable Neighborhood descent algorithm. The computational experiments show the effectiveness of our proposed algorithms according to the approaches already presented in the litterature.
Facets and algorithms for capacitated lot sizing
Mathematical Programming, 1989
The dynamic economic lot sizing model, which lies at the core of numerous production planning applications, is one of the most highly studied models in all of operations research. And yet, capacitated multi-item versions of this problem remain computationally elusive. We study the polyhedral structure of an integer programming formulation of a single-item capacitated version of this problem, and use
Asia-Pacific Journal of Operational Research, 2005
We propose the use of metaheuristics for the resource-capacitated multilevel lot-sizing problem with general product structures, setup costs, setup times, and lead times. Initially, we develop a heuristic which moves production in time in order to obtain feasible solutions with good quality. Strategies for the short-term memory and long-term memory of tabu search are then included to guide the search of the subordinate heuristic for new, feasible, and better solutions. Simulated annealing components are embedded into tabu search in order to improve its performance. For small problems, the solutions provided by tabu search and the hybrid metaheuristic are compared to optimal solutions and for larger problems, the quality of the solutions is evaluated against a lower bound generated by Lagrangean relaxation. 261 Asia Pac. J. Oper. Res. 2005.22:261-286. Downloaded from www.worldscientific.com by UNIVERSIDADE ESTADUAL PAULISTA JULIO DE MESQUITA FILHO (UNESP) on 09/03/13. For personal use only. 262 R. Berretta et al. and uneconomical. The aim of this research is to contribute to the development of more realistic MRP systems.
The capacitated lot sizing problem: a review of models and algorithms
Omega-international Journal of Management Science, 2003
Lot sizing is one of the most important and also one of the most di cult problems in production planning. This subject has been studied extensively in the literature. In this article, we consider single-level lot sizing problems, their variants and solution approaches. After introducing factors a ecting formulation and the complexity of production planning problems, and introducing di erent variants of lot sizing and scheduling problems, we discuss single-level lot sizing problems, together with exact and heuristic approaches for their solution. We conclude with some suggestions for future research. ?
A relax-and-fix with fix-and-optimize heuristic applied to multi-level lot-sizing problems
Journal of Heuristics, 2015
In this paper, we propose a simple but efficient heuristic that combines construction and improvement heuristic ideas to solve multi-level lot-sizing problems. A relax-and-fix heuristic is firstly used to build an initial solution, and this is further improved by applying a fix-and-optimize heuristic. We also introduce a novel way to define the mixed-integer subproblems solved by both heuristics. The efficiency of the approach is evaluated solving two different classes of multi-level lot-sizing problems: the multi-level capacitated lot-sizing problem with backlogging and the two-stage glass container production scheduling problem (TGCPSP). We present extensive computational results including four test sets of the Multi-item Lot-Sizing with Backlogging library, and real-world test problems defined for the TGCPSP, where we benchmark against state-of-the-art methods from the recent literature. The computational results
Combining population-based and exact methods for multi-level capacitated lot-sizing problems
International Journal of Production Research, 2006
We present an ant-based algorithm to solve multi-level capacitated lot sizing problems. We apply a hybrid approach where we use the ant system to optimize the decomposition of the problem into smaller subproblems. These subproblems containing only a few items and periods are solved using CPLEX. Then the overall solution is derived by consolidating the partial solutions. This hybrid approach provides superior results with respect to solution quality in comparison to the existing approaches in the literature.
Metaheuristic for the capacitated lot-sizing problem: a software tool for MPS elaboration
International Journal of Mathematics in Operational Research, 2010
The master production schedule elaboration plays a major part in tactical planning. Among mathematical models which deal with the tactical planning, a particular one is dedicated to it: the capacitated lot-sizing problem. Literature about its resolution is huge, but few metaheuristics have been developed in order to solve it: we propose to use optimisation methods based on a simulated annealing: the data encoding are based on a production planning matrix and the neighbourhood system is maked up of several possible moves. We also proposed a bi-objective function which integrates logistic costs and an evaluation of the degree of the capacities' violation, which allows the neighbourhood system to temporarily leave the set of feasible solutions in order to escape from local minimas. We have tested our optimisation methods on benchmarks from the literature and some best results are outperformed. These methods have been integrated into a software tool.