Lead time considerations for the multi-level capacitated lot-sizing problem

The classical multi-level capacitated lot-sizing problem is often not suitable to correctly capture resource requirements and precedence relations. We tackle this issue by explicitly modeling these two aspects. Two models are presented; one considering batch production and the other one allowing lot-streaming. Comparisons with traditional models demonstrate the capability of the new approach to deliver more realistic and practically feasible results.Large-scale cases are solved by Benders, which has been enhanced in several novel ways

Solving Lotsizing Problems on Parallel Identical Machines Using Symmetry Breaking Constraints

Production planning on multiple parallel machines is an interesting problem, both from a theoretical and practical point of view. The parallel machine lotsizing problem consists of finding the optimal timing and level of production and the best allocation of products to machines. In this paper we look at how to incorporate parallel machines in a Mixed Integer Programming model when using commercial optimization software. More specifically, we look at the issue of symmetry. When multiple identical machines are available, many alternative optimal solutions can be created by renumbering the machines. These alternative solutions lead to difficulties in the branch-and-bound algorithm. We propose new constraints to break this symmetry. We tested our approach on the parallel machine lotsizing problem with setup costs and times, using a network reformulation for this problem. Computational tests indicate that several of the proposed symmetry breaking constraints substantially improve the solution time, except when used for solving the very easy problems. The results highlight the importance of creative modeling in solving Mixed Integer Programming problems.Mixed Integer Programming;Formulations;Symmetry;Lotsizing

Modeling Industrial Lot Sizing Problems: A Review

In this paper we give an overview of recent developments in the field of modeling single-level dynamic lot sizing problems. The focus of this paper is on the modeling 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

An O(Tˆ3) algorithm for the capacitated lot sizing problem with minimum order quantities

This paper explores a single-item capacitated lot sizing problem with minimum order quantity, which plays the role of minor set-up cost. We work out the necessary and suffcient solvability conditions and apply the general dynamic programming technique to develop an O(T³) exact algorithm that is based on the concept of minimal sub-problems. An investigation of the properties of the optimal solution structure allows us to construct explicit solutions to the obtained sub-problems and prove their optimality. In this way, we reduce the complexity of the algorithm considerably and confirm its efficiency in an extensive computational study. --production planning,capacitated lot sizing problem,single item,minimum order quantities,capacity constraints,dynamic programming

Production Lot Sizing Problem with the Lead Time

The issue in lot sizing problem is to plan production processes, so that mean the production quantities must be equal to customer demand quantities such that the inventory cost and setup production cost is minimized. In this work, we use the model Multi Level Capacitated Lot Sizing problem with consideration the Lead times, which means that the problem of finding a feasible solution is complex. For this, we propose a new formula in comparison with the classic model. The efficiency of the new formula is demonstrated and infeasible solutions are solved by a heuristic method that's based on Lagrangian relaxation. Computational tests conducted in 1000 instances with up to 40 components and 16 periods have shown that optimal solutions were obtained on average 96.43% of the large instances. For the improvement of the best solution, the heuristic is able to find the efficiency with 97.62% on average. The solution quality is evaluated through initial iterations, the average solution time provided by Lagrangian relaxation is less than 0.43s

Improvement to an existing multi-level capacitated lot sizing problem considering setup carryover, backlogging, and emission control

This paper presents a multi-level, multi-item, multi-period capacitated lot-sizing problem. The lot-sizing problem studies can obtain production quantities, setup decisions and inventory levels in each period fulfilling the demand requirements with limited capacity resources, considering the Bill of Material (BOM) structure while simultaneously minimizing the production, inventory, and machine setup costs. The paper proposes an exact solution to Chowdhury et al. (2018)\u27s[1] developed model, which considers the backlogging cost, setup carryover & greenhouse gas emission control to its model complexity. The problem contemplates the Dantzig-Wolfe (D.W.) decomposition to decompose the multi-level capacitated problem into a single-item uncapacitated lot-sizing sub-problem. To avoid the infeasibilities of the weighted problem (WP), an artificial variable is introduced, and the Big-M method is employed in the D.W. decomposition to produce an always feasible master problem. In addition, Wagner & Whitin\u27s[2] forward recursion algorithm is also incorporated in the solution approach for both end and component items to provide the minimum cost production plan. Introducing artificial variables in the D.W. decomposition method is a novel approach to solving the MLCLSP model. A better performance was achieved regarding reduced computational time (reduced by 50%) and optimality gap (reduced by 97.3%) in comparison to Chowdhury et al. (2018)\u27s[1] developed model

New Integrated Approach For Solving Multi-level Lot Sizing and Scheduling problems

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Dynamic lot sizing and tool management in automated manufacturing systems

Cataloged from PDF version of article.The overall aim of this study is to show that there is a critical interface between the lot sizing and tool management decisions, and these two problems cannot be viewed in isolation. We propose "ve alternative algorithms to solve lot sizing, tool allocation and machining conditions optimization problems simultaneously. The "rst algorithm is an exact algorithm which "nds the global optimum solution, and the others are heuristics equipped with a look-ahead mechanism to guarantee at least local optimality. The computational results indicate that the amount of improvement is statistically signi"cant for a set of randomly generated problems. The magnitude of cost savings is dependent on the system parameters

Meta-Heuristics for Dynamic Lot Sizing: a review and comparison of solution approaches

Proofs from complexity theory as well as computational experiments indicate that most lot sizing problems are hard to solve. Because these problems are so difficult, various solution techniques have been proposed to solve them. In the past decade, meta-heuristics such as tabu search, genetic algorithms and simulated annealing, have become popular and efficient tools for solving hard combinational optimization problems. We review the various meta-heuristics that have been specifically developed to solve lot sizing problems, discussing their main components such as representation, evaluation neighborhood definition and genetic operators. Further, we briefly review other solution approaches, such as dynamic programming, cutting planes, Dantzig-Wolfe decomposition, Lagrange relaxation and dedicated heuristics. This allows us to compare these techniques. Understanding their respective advantages and disadvantages gives insight into how we can integrate elements from several solution approaches into more powerful hybrid algorithms. Finally, we discuss general guidelines for computational experiments and illustrate these with several examples

A Tabu List-Based Algorithm for Capacitated Multilevel Lot-Sizing with Alternate Bills of Materials and Co-Production Environments

[EN] The definition of lot sizes represents one of the most important decisions in production planning. Lot-sizing turns into an increasingly complex set of decisions that requires efficient solution approaches, in response to the time-consuming exact methods (LP, MIP). This paper aims to propose a Tabu list-based algorithm (TLBA) as an alternative to the Generic Materials and Operations Planning (GMOP) model. The algorithm considers a multi-level, multi-item planning structure. It is initialized using a lot-for-lot (LxL) method and candidate solutions are evaluated through an iterative Material Requirements Planning (MRP) procedure. Three different sizes of test instances are defined and better results are obtained in the large and medium-size problems, with minimum average gaps close to 10.5%.This paper shows the results of the project entitled "Algoritmo heuristico basado en listas tabu para la planificacion de la produccion en sistemas multinivel con listas de materiales alternativas y entornos de coproduccion" supported by Universidad de la Costa and Universitat Politecnica de Valencia.Romero-Conrado, AR.; Coronado-Hernandez, J.; Rius-Sorolla, G.; García Sabater, JP. (2019). A Tabu List-Based Algorithm for Capacitated Multilevel Lot-Sizing with Alternate Bills of Materials and Co-Production Environments. Applied Sciences. 9(7):1-17. https://doi.org/10.3390/app9071464S11797Karimi, B., Fatemi Ghomi, S. M. T., & Wilson, J. M. (2003). The capacitated lot sizing problem: a review of models and algorithms. Omega, 31(5), 365-378. doi:10.1016/s0305-0483(03)00059-8Martí, R., & Reinelt, G. (2010). Heuristic Methods. 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