171 research outputs found

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

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    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

    DYNAMIC LOT-SIZING PROBLEMS: A Review on Model and Efficient Algorithm

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    Due to their importance in industry, dynamic demand lot-sizing problems are frequently studied.This study consider dynamic lot-sizing problems with recent advances in problem and modelformulation, and algorithms that enable large-scale problems to be effectively solved.Comprehensive review is given on model formulation of dynamic lot-sizing problems, especiallyon capacitated lot-sizing (CLS) problem and the coordinated lot-sizing problem. Bothapproaches have their intercorrelated, where CLS can be employed for single or multilevel/stage, item, and some restrictions. When a need for joint setup replenishment exists, thenthe coordinated lot-sizing is the choice. Furthermore, both algorithmics and heuristics solutionin the research of dynamic lot sizing are considered, followed by an illustration to provide anefficient algorithm

    Dynamic lot sizing and tool management in automated manufacturing systems

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    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

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    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 relax-and-fix with fix-and-optimize heuristic applied to multi-level lot-sizing problems

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    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 show that our combined heuristic approach is very efficient and competitive, outperforming benchmark methods for most of the test problems

    Valid inequalities for the single-item capacitated lot sizing problem with step-wise costs

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    This paper presents a new class of valid inequalities for the single-item capacitated lotsizing problem with step-wise production costs (LS-SW). We first provide a survey of different optimization methods proposed to solve LS-SW. Then, flow cover and flow cover inequalities derived from the single node flow set are described in order to generate the new class of valid inequalities. The single node flow set can be seen as a generalization of some valid relaxations of LS-SW. A new class of valid inequalities we call mixed flow cover, is derived from the integer flow cover inequalities by a lifting procedure. The lifting coefficients are sequence independent when the batch sizes (V) and the production capacities (P) are constant and if V divides P. When the restriction of the divisibility is removed, the lifting coefficients are shown to be sequence independent. We identify some cases where the mixed flow cover inequalities are facet defining. A cutting plane algorithmis proposed for these three classes of valid inequalities. The exact separation algorithmproposed for the constant capacitated case runs in polynomial time. Finally, some computational results are given to compare the performance of the different optimization methods including the new class of valid inequalities.single-item capacitated lot sizing problem, flow cover inequalities, cutting plane algorithm

    Polynomial Time Algorithms For Some Multi-Level Lot-Sizing Problems With Production Capacities

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    We consider a model for a serial supply chain in which production, inventory, and transportation decisions are integrated, in the presence of production capacities and for different transportation cost functions. The model we study is a generalization of the traditional single-item economic lot-sizing model, adding stationary production capacities at the manufacturer, as well as multiple intermediate storage levels (including the retailer level), and transportation between these levels. Allowing for general concave production costs and linear holding costs, we provide polynomialtime algorithms for the cases where the transportation costs are either linear, or are concave with a fixed-charge structure. In the latter case, we make the additional common and reasonable assumption that the variable transportation and inventory costs are such that holding inventories at higher levels in the supply chain is more attractive from a variable cost perspective. The running times of the algorithms are remarkably insensitive to the number of levels in the supply chain

    Economic Lot-Sizing Problem with Bounded Inventory and Lost-Sales

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    In this paper we consider an economic lot-sizing problem with bounded inventory and lost-sales. Different structural properties are characterized based on the system parameters such as production and inventory costs, selling prices, and storage capacities. Using these properties and the results on the lot-sizing problems with bounded inventory, we present improved and new algorithms for the problem. Specifically, we provide algorithms for the general lot-sizing problem with bounded inventory and lost-sales, the lot-sizing problem with nonincreasing selling prices and the problem with only lost-sales

    Green Lot-Sizing

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    The lot-sizing problem concerns a manufacturer that needs to solve a production planning problem. The producer must decide at which points in time to set up a production process, and when he/she does, how much to produce. There is a trade-off bet

    Lot Sizing Heuristics Performance

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    Each productive system manager knows that finding the optimal trade‐off between reducing inventory and decreasing the frequency of production/ replenishment orders allows a great cut‐back in operations costs. Several authors have focused their contributions, trying to demonstrate that among the various dynamic lot sizing rules there are big differences in terms of performance, and that these differences are not negligible. In this work, eight of the best known lot sizing algorithms have been described with a unique modelling approach and have then been exhaustively tested on several different scenarios, benchmarking versus Wagner and Whitin’s optimal solution. As distinct from the contributions in the literature, the operational behaviour has been evaluated in order to determine which one is more suitable to the characteristics of each scenario
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