Single Item Lot Sizing Problem for a Warm/Cold Process with Immediate Lost Sales

Cataloged from PDF version of article.We consider the dynamic lot-sizing problem with finite capacity and possible lost sales for a process that could be kept warm at a unit variable cost for the next period t + 1 only if more than a threshold value Qt has been produced and would be cold, otherwise. Production with a cold process incurs a fixed positive setup cost, Kt and setup time, St, which may be positive. Setup costs and times for a warm process are negligible. We develop a dynamic programming formulation of the problem, establish theoretical results on the structure of the optimal production plan in the presence of zero and positive setup times with Wagner–Whitin-type cost structures. We also show that the solution to the dynamic lot-sizing problem with lost sales are generated from the full commitment production series improved via lost sales decisions in the presence of a warm/cold process. 2006 Elsevier B.V. All rights reserved

An optimization framework for solving capacitated multi-level lot-sizing problems with backlogging

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

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

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

Fully Polynomial Approximation Schemes for Single-Item Capacitated Economic Lot-Sizing Problems

NP-hard cases of the single-item capacitated lot-sizing problem have been the topic of extensive research and continue to receive considerable attention. However, surprisingly few theoretical results have been published on approximation methods for these problems. To the best of our knowledge, until now no polynomial approximation method is known which produces solutions with a relative deviation from optimality that is bounded by a constant. In this paper we show that such methods do exist, by presenting an even stronger result: the existence of fully polynomial approximation schemes. The approximation scheme is first developed for a quite general model, which has concave backlogging and production cost functions and arbitrary (monotone) holding cost functions. Subsequently we discuss important special cases of the model and extensions of the approximation scheme to even more general models

Dynamic lot sizing problem for a warm/cold process

We consider a dynamic lot sizing problem with finite capacity for a process that can be kept warm until the next production period at a unit variable cost ωt only if more than a threshold value has been produced and is cold, otherwise. That is, the setup cost in period t is Kt if xt-1 < Qt-1 and kt, otherwise (0 ≤ kt ≤ Kt). We develop a dynamic programming formulation of the problem, establish theoretical results on the structure of the optimal production plan and discuss its computational complexity in the presence of Wagner-Whitin-type cost structures. Based on our stuctural results, we present an optimal polynomial-time solution algorithm for kt = 0, and also show that an optimal linear-time solution algorithm exists for a special case. Our numerical study indicates that utilizing the undertime option (i.e., keeping the process warm via reduced production rates) results in significant cost savings, which has managerial implications for capacity planning and selection

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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European Journal of Operational Research, 99(2), 221-235. doi:10.1016/s0377-2217(97)00030-1Glock, C. H., Grosse, E. H., & Ries, J. M. (2014). The lot sizing problem: A tertiary study. International Journal of Production Economics, 155, 39-51. doi:10.1016/j.ijpe.2013.12.009KUIK, R., SALOMON, M., VAN WASSENHOVE, L. N., & MAES, J. (1993). LINEAR PROGRAMMING, SIMULATED ANNEALING AND TABU SEARCH HEURISTICS FOR LOTSIZING IN BOTTLENECK ASSEMBLY SYSTEMS. IIE Transactions, 25(1), 62-72. doi:10.1080/07408179308964266Standard Price List—AMPLhttps://ampl.com/products/standard-price-list/Seeanner, F., Almada-Lobo, B., & Meyr, H. (2013). Combining the principles of variable neighborhood decomposition search and the fix&optimize heuristic to solve multi-level lot-sizing and scheduling problems. Computers & Operations Research, 40(1), 303-317. doi:10.1016/j.cor.2012.07.002Hung, Y.-F., & Chien, K.-L. (2000). A multi-class multi-level capacitated lot sizing model. Journal of the Operational Research Society, 51(11), 1309-1318. doi:10.1057/palgrave.jors.2601026Kang, Y., Albey, E., & Uzsoy, R. (2018). Rounding heuristics for multiple product dynamic lot-sizing in the presence of queueing behavior. Computers & Operations Research, 100, 54-65. doi:10.1016/j.cor.2018.07.019BERRETTA, R., FRANÇA, P. M., & ARMENTANO, V. A. (2005). METAHEURISTIC APPROACHES FOR THE MULTILEVEL RESOURCE-CONSTRAINED LOT-SIZING PROBLEM WITH SETUP AND LEAD TIMES. Asia-Pacific Journal of Operational Research, 22(02), 261-286. doi:10.1142/s0217595905000510KIMMS, A. (1996). Competitive methods for multi-level lot sizing and scheduling: tabu search and randomized regrets. International Journal of Production Research, 34(8), 2279-2298. doi:10.1080/00207549608905025Sabater, J. P. G., Maheut, J., & Garcia, J. A. M. (2013). A new formulation technique to model materials and operations planning: the generic materials and operations planning (GMOP) problem. European J. of Industrial Engineering, 7(2), 119. doi:10.1504/ejie.2013.052572Maheut, J., & Sabater, J. P. G. (2013). Algorithm for complete enumeration based on a stroke graph to solve the supply network configuration and operations scheduling problem. Journal of Industrial Engineering and Management, 6(3). doi:10.3926/jiem.550Rius-Sorolla, G., Maheut, J., Coronado-Hernandez, J. R., & Garcia-Sabater, J. P. (2018). Lagrangian relaxation of the generic materials and operations planning model. Central European Journal of Operations Research, 28(1), 105-123. doi:10.1007/s10100-018-0593-0Maheut, J., Garcia-Sabater, J. P., & Mula, J. (2012). The Generic Materials and Operations Planning (GMOP) Problem Solved Iteratively: A Case Study in Multi-site Context. IFIP Advances in Information and Communication Technology, 66-73. doi:10.1007/978-3-642-33980-6_8Maheut, J. P. D. (s. f.). Modelos y Algoritmos Basados en el Concepto Stroke para la Planificación y Programación de Operaciones con Alternativas en Redes de Suministro. doi:10.4995/thesis/10251/29290Glover, F. (1989). Tabu Search—Part I. ORSA Journal on Computing, 1(3), 190-206. doi:10.1287/ijoc.1.3.190Glover, F., Taillard, E., & Taillard, E. (1993). A user’s guide to tabu search. Annals of Operations Research, 41(1), 1-28. doi:10.1007/bf02078647Chelouah, R., & Siarry, P. (2000). Tabu Search applied to global optimization. European Journal of Operational Research, 123(2), 256-270. doi:10.1016/s0377-2217(99)00255-6Raza, S. A., Akgunduz, A., & Chen, M. Y. (2006). A tabu search algorithm for solving economic lot scheduling problem. Journal of Heuristics, 12(6), 413-426. doi:10.1007/s10732-006-6017-7Cesaret, B., Oğuz, C., & Sibel Salman, F. (2012). A tabu search algorithm for order acceptance and scheduling. Computers & Operations Research, 39(6), 1197-1205. doi:10.1016/j.cor.2010.09.018Li, X., Baki, F., Tian, P., & Chaouch, B. A. (2014). A robust block-chain based tabu search algorithm for the dynamic lot sizing problem with product returns and remanufacturing. Omega, 42(1), 75-87. doi:10.1016/j.omega.2013.03.003Li, J., & Pan, Q. (2015). Solving the large-scale hybrid flow shop scheduling problem with limited buffers by a hybrid artificial bee colony algorithm. Information Sciences, 316, 487-502. doi:10.1016/j.ins.2014.10.009Hindi, K. S. (1995). Solving the single-item, capacitated dynamic lot-sizing problem with startup and reservation costs by tabu search. Computers & Industrial Engineering, 28(4), 701-707. doi:10.1016/0360-8352(95)00027-xHindi, K. S. (1996). Solving the CLSP by a Tabu Search Heuristic. Journal of the Operational Research Society, 47(1), 151-161. doi:10.1057/jors.1996.13Gopalakrishnan, M., Ding, K., Bourjolly, J.-M., & Mohan, S. (2001). 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Using Geometric Techniques to Improve Dynamic Programming Algorithms for the Economic Lot-Sizing Problem and Extensions

In this paper we discuss two basic geometric techniques that can be used to speed up certain types of dynamic programs. We first present the algorithms in a general form, and then we show how these techniques can be applied to the economic lot-sizing problem and extensions. Furthermore, it is illustrated that the geometric techniques can be used to give elegant and insightful proofs of structural results, like Wagner and Whitin's planning horizon theorem. Finally, we present results of computational experiments in which new algorithms for the economic lot-sizing problem are compared with each other, as well as with other algorithms from the literature

A Strong Cutting Plane Algorithm for Production Scheduling with Changeover Costs

Changeover costs (and times) are central to numerous manufacturing operations. These costs arise whenever work centers capable of processing only one product at a time switch from the manufacture of one product to another. Although many researchers have contributed to the solution of scheduling problems that include changeover costs, due to the problem's combinatorial explosiveness, optimization-based methods have met with limited success. In this paper, we develop and apply polyhedral methods from integer programming for a dynamic version of the problem. Computational tests with problems containing one to five products (and up to 225 integer variables) show that polyhedral methods based upon a set of facet inequalities developed in this paper can effectively reduce the gap between the value of an integer program formulation of the problem and its linear programming relaxation (by a factor of 94 to 100 per cent). These results suggest the use of a combined cutting plane/branch and bound procedure as a solution approach. In a test with a five product problem, this procedure, when compared with a standard linear programming-based branch and bound approach, reduced computation time by a factor of seven

Aplicación de la Búsqueda Tabú en la resolución del problema capacitado de lotificación en sistemas de producción multinivel: Un estado del arte

En este trabajo, se aborda desde la literatura, un estudio de la aplicación de la búsqueda tabú para la resolución del problema de planificación de la producción en sistemas multinivel con restricciones de capacidad. Esta familia de problemas está clasificada dentro de la literatura como Np-Hard. Las estrategias de relajación y búsqueda, especialmente la Búsqueda tabú, han jugado un papel determinante en el desarrollo de alternativas de solución de este tipo de problemas, permitiendo obtener de soluciones cercanas al valor óptimo de mínimo costo, en tiempos operativamente aceptables. El presente artículo tiene por objetivo recopilar, describir y analizar el uso y aplicación de la búsqueda tabú en la solución del problema de lotificación en sistemas de producción multinivel. Contemplando la gran cantidad de variaciones del problema y  haciendo énfasis en la metodología utilizada y la configuración de la búsqueda, se pretende establecer la línea base para el desarrollo de nuevos algoritmos de solución para el problema de lotificación