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

Workforce planning in a lotsizing mail processing problem

The treatment of mail objects in a mail processing centre involves many operations, in particular sorting by destination. Out of the batching problem that we can identify in such a process, there are also staff planning concerns. In this paper, we analyse a treatment area (registered mail) belonging to a mail processing center, where mail objects are treated in a chain production process. The production quantities and the transfer amounts among machines are required to be determined along the daily work period. The objective is to minimize the costs with human resources needed in the process, linked with the lotsizing production plan, by matching staff to work requirements. This leads into a lotsizing and workforce problem, for which we propose an integer programming formulation. A case study of a particular treatment area is also discussed. The formulation is adjusted to the specific constraints of this case study and some computational results are included, considering average, small and high daily amounts of mail arrived to that particular treatment area.http://www.sciencedirect.com/science/article/B6VC5-4CK7RXK-4/1/5986796334d7e593786cb5bf5b7dc4a

Integrated capacitated lot sizing and scheduling problems in a flexible flow line

The lot sizing and scheduling problem in a Flexible Flow Line (FFL) has extensive real-world applications in many industries. An FFL consists of several production stages in series with parallel machines at each stage. The decisions to be taken are the determination of production quantities (lots), machine assignments and production sequences (schedules) on each machine at each stage in an FFL. Lot sizing and scheduling problems are closely interrelated. Solving them separately and then coordinating their interdependencies is often ineffective. However due to their complexity, there is a lack of mathematical modelling and solution procedures in the literature to combine and jointly solve them.Up to now most research has been focused on combining lotsizing and scheduling for the single machine configuration, and research on other configurations like FFL is sparse. This thesis presents several mathematical models with practical assumptions and appropriate algorithms, along with experimental test problems, for simultaneously lotsizing and scheduling in FFL. This problem, called the ‘General Lot sizing and Scheduling Problem in a Flexible Flow Line’ (GLSP-FFL). The objective is to satisfy varying demand over a finite planning horizon with minimal inventory, backorder and production setup costs. The problem is complex as any product can be processed on any machine, but these have different processing rates and sequence-dependent setup times & costs. As a result, even finding a feasible solution of large problems in reasonable time is impossible. Therefore the heuristic solution procedure named Adaptive Simulated Annealing (ASA), with four well-designed initial solutions, is designed to solve GLSP-FFL.A further original contribution of this study is to design linear mixed-integer programming (MILP) formulations for this problem, incorporating all necessary features of setup carryovers, setup overlapping, non-triangular setup while allowing multiple lot production per periods, lot splitting and sequencing through ATSP-adaption based on a variety of subtour elimination

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. Applied Mathematical Sciences, 17-40. doi:10.1007/978-3-642-16729-4_2Barany, I., Van Roy, T. J., & Wolsey, L. A. (1984). Strong Formulations for Multi-Item Capacitated Lot Sizing. Management Science, 30(10), 1255-1261. doi:10.1287/mnsc.30.10.1255Eppen, G. D., & Martin, R. K. (1987). Solving Multi-Item Capacitated Lot-Sizing Problems Using Variable Redefinition. Operations Research, 35(6), 832-848. doi:10.1287/opre.35.6.832Maes, J., McClain, J. O., & Van Wassenhove, L. N. (1991). Multilevel capacitated lotsizing complexity and LP-based heuristics. European Journal of Operational Research, 53(2), 131-148. doi:10.1016/0377-2217(91)90130-nBuschkühl, L., Sahling, F., Helber, S., & Tempelmeier, H. (2008). Dynamic capacitated lot-sizing problems: a classification and review of solution approaches. OR Spectrum, 32(2), 231-261. doi:10.1007/s00291-008-0150-7Drexl, A., & Kimms, A. (1997). Lot sizing and scheduling — Survey and extensions. 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). A Tabu-Search Heuristic for the Capacitated Lot-Sizing Problem with Set-up Carryover. Management Science, 47(6), 851-863. doi:10.1287/mnsc.47.6.851.9813Glover, F. (1990). Tabu Search—Part II. ORSA Journal on Computing, 2(1), 4-32. doi:10.1287/ijoc.2.1.4Overview for Create General Full Factorial Designhttps://support.minitab.com/en-us/minitab/18/help-and-how-to/modeling-statistics/doe/how-to/factorial/create-factorial-design/create-general-full-factorial/before-you-start/overview/Perttunen, J. (1994). On the Significance of the Initial Solution in Travelling Salesman Heuristics. Journal of the Operational Research Society, 45(10), 1131-1140. doi:10.1057/jors.1994.183Elaziz, M. A., & Mirjalili, S. (2019). A hyper-heuristic for improving the initial population of whale optimization algorithm. Knowledge-Based Systems, 172, 42-63. doi:10.1016/j.knosys.2019.02.010Chen, C.-F., Wu, M.-C., & Lin, K.-H. (2013). Effect of solution representations on Tabu search in scheduling applications. Computers & Operations Research, 40(12), 2817-2825. doi:10.1016/j.cor.2013.06.003Tabu List Based Algorithm Datasetshttps://github.com/alfonsoromeroc/tlba-gmo

Production planning in the pulp and paper industry

This paper examines the short term production planning problem encountered in the fine-paper industry. In this industry, different types of pulp are transformed by parallel papermachines into large rolls of paper sheets. The paper sheets are then cut and packaged based oncustomer needs. The paper machines usually represent the bottleneck stage in the productionprocess. At this bottleneck stage, a predetermined production sequence has to be maintained.The paper proposes a tight mixed-integer programming formulation to model this productionprocess. It is showed that real size problem instances can be solved with commercial integerprogramming solvers. Furthermore, we show that by adding some simple valid inequalities tothe proposed formulation, major improvements to the solution time can be achieve

Variable neighborhood search for the multi-level capacitated lotsizing problem

Das dynamische mehrstufige kapazitierte Losgrößenproblem (MLCLSP) behandelt im Rahmen der Produktionsplanung die wichtige Entscheidung über die optimalen Losgrößen, angefangen bei Endprodukten über Komponenten bis hin zu Rohstoffen, bei gleichzeitiger Berücksichtigung beschränkter Kapazitäten der zur Produktion benötigten Ressourcen. Da es sich um ein NP-schweres Problem handelt, stoßen exakte Lösungsverfahren an ihre Grenzen, sobald die Problemdimensionen ein größeres – man könnte durchaus sagen realistisches – Ausmaß erreichen. In der Praxis dominieren deshalb Methoden, die die Losgrößen der einzelnen Produkte sequenziell festlegen und überdies etwaige Kapazitätsbeschränkungen im Nachhinein, falls überhaupt, berücksichtigen. In der Literatur finden sich zahlreiche approximative Ansätze zur Lösung dieses komplexen betriebswirtschaftlichen Problems. Lokale Suche und auf ihr basierende Metaheuristiken stellen vielversprechende Werkzeuge dar, um die Defizite der aktuell eingesetzten Trial-and-Error Ansätze zu beheben und letzten Endes zulässige sowie kostenoptimale Produktionspläne zu erstellen. Die in dieser Diplomarbeit vorgestellte Studie beschäftigt sich mit lokalen Suchverfahren für das MLCLSP. Acht Nachbarschaftsstrukturen, die sich aus einer Veränderung der Rüstvariablen ergeben, werden präsentiert und evaluiert. Grundlegende Optionen bei der Gestaltung eines iterativen Verbesserungsverfahrens, wie beispielsweise unterschiedliche Schrittfunktionen oder die temporäre Berücksichtigung unzulässiger Lösungen, werden getestet und verglichen. Obwohl nur die Switch Nachbarschaft, die durch das Ändern einer einzigen Rüstvariable definiert wird, wirklich überzeugende Resultate liefert, können die übrigen Nachbarschaftsstrukturen durchaus als Perturbationsmechanismen im Rahmen einer Variablen Nachbarschaftssuche (VNS) zum Einsatz kommen. Die Implementierung dieser Metaheuristik, geprägt von den Ergebnissen der einfachen lokalen Suchverfahren, kann allerdings nicht vollkommen überzeugen. Die entwickelte VNS Variante kann die Lösungsgüte anderer zum Vergleich herangezogener Lösungsverfahren nicht erreichen und benötigt relativ lange Laufzeiten. Andererseits sind die Ergebnisse mit einer durchschnittlichen Abweichung zur besten bekannten Lösung von etwa vier Prozent über sämtliche untersuchte Problemklassen weit entfernt von einem Totalversagen. Es überwiegt der Eindruck, dass es sich um eine robuste Methode handelt, die in der Lage ist, Lösungen von hoher, teils sehr hoher Qualität nicht nur in Ausnahmefällen zu liefern. Etwaige Nachjustierungen könnten das Verfahren durchaus zu einem ernstzunehmenden Konkurrenten für bereits existierende Lösungsmethoden für das MLCLSP machen.The Multi-Level Capacitated Lotsizing Problem (MLCLSP) depicts the important decision in production planning of determining adequate lot sizes from final products onward, to subassemblies, parts and raw materials, all the while assuming limited capacities of the resources employed for manufacture. It is an NP-hard problem where exact methods fail in solving larger – one could say realistic – problem instances. Sequential approaches that tackle the problem item by item and postpone capacity considerations dominate current practice; approximate solution methods abound throughout the literature. Local search and metaheuristics based on it constitute a class of approximate methods well-equipped to take on the challenge of eventually replacing the trial-and-error process that impedes manufacturing companies in establishing feasible and cost-minimal production plans. This thesis presents a study of local search based procedures for solving the MLCLSP. Eight different neighborhood structures, resulting from manipulations of the setup variables, are devised and evaluated. Fundamental options when designing an iterative improvement algorithm, such as best-improvement versus first-improvement step functions or the inclusion of infeasible solutions during the search are explored and compared. Although only the Switch move, which alters the value of a single setup value, is convincing as a stand-alone neighborhood structure, the other neighborhoods can in any case be employed for the perturbation of solutions during the shaking step of a Variable Neighborhood Search (VNS). The implementation of this metaheuristic, shaped by the findings from testing the basic local search variants, led to mixed results. The procedure designed to tackle the MLCLSP cannot outperform the compared heuristics. Neither does it produce results that are terribly off – the average gap to the best known solutions settles around four percent over all problem classes tested. Nonetheless, the impression is supported that the VNS procedure is a robust method leading to good, sometimes even very good solutions at a regular basis that is amenable to further adjustments and thus eventually becoming a serious competitor for existing methods dealing with multi-level capacitated lotsizing decisions

Integrated capacitated lot sizing and scheduling problems in a flexible flow line

The lot sizing and scheduling problem in a Flexible Flow Line (FFL) has extensive real-world applications in many industries. An FFL consists of several production stages in series with parallel machines at each stage. The decisions to be taken are the determination of production quantities (lots), machine assignments and production sequences (schedules) on each machine at each stage in an FFL. Lot sizing and scheduling problems are closely interrelated. Solving them separately and then coordinating their interdependencies is often ineffective. However due to their complexity, there is a lack of mathematical modelling and solution procedures in the literature to combine and jointly solve them. Up to now most research has been focused on combining lotsizing and scheduling for the single machine configuration, and research on other configurations like FFL is sparse. This thesis presents several mathematical models with practical assumptions and appropriate algorithms, along with experimental test problems, for simultaneously lotsizing and scheduling in FFL. This problem, called the ‘General Lot sizing and Scheduling Problem in a Flexible Flow Line’ (GLSP-FFL). The objective is to satisfy varying demand over a finite planning horizon with minimal inventory, backorder and production setup costs. The problem is complex as any product can be processed on any machine, but these have different processing rates and sequence-dependent setup times & costs. As a result, even finding a feasible solution of large problems in reasonable time is impossible. Therefore the heuristic solution procedure named Adaptive Simulated Annealing (ASA), with four well-designed initial solutions, is designed to solve GLSP-FFL. A further original contribution of this study is to design linear mixed-integer programming (MILP) formulations for this problem, incorporating all necessary features of setup carryovers, setup overlapping, non-triangular setup while allowing multiple lot production per periods, lot splitting and sequencing through ATSP-adaption based on a variety of subtour elimination.EThOS - Electronic Theses Online ServiceGBUnited Kingdo