Rolling horizon and fix-and-relax heuristcs for the parallel machines lot-sizing and scheduling problem with sequence dependent set-up costs

none4In this paper we develop newrolling-horizon and fix-and-relax heuristics for the identical parallel machine lot-sizing and scheduling problem with sequence-dependent set-up costs. Unlike previous papers, our procedures are based on a compact formulation relying on the hypotheses of identical machines. This feature makes our approach suitable for large-scale applications (with hundreds of machines) arising in the textile and fiberglass industries. Moreover, our procedures are shown to provide a feasible solution for any feasible instance. Comparisons with lower bounds provided by a truncated branch-and-bound show that the gap between the best heuristic solution and the lower bound never exceeds 3%P.BERALDI; G. GHIANI; A. GRIECO; E. GUERRIEROP., Beraldi; Ghiani, Gianpaolo; Grieco, Antonio Domenico; Guerriero, Emanuel

Decomposition Heuristic With Partial Assignment Approach for MLCLSP-M Problem

This research proposes a heuristic method, which decomposes the Multi-level Multi-item Capacitated Lot Sizing Problem with Multi-workstation (MLCLSP-M) into two phases which are an assignment with given lot size and a partial lot size with given assignment. Each iteration, the sub problem mathematical models are solved with AMPL/CPLEX 8.0.0 solver. An example is present for demonstration of the heuristic. The result indicate that the proposed heuristic (Partial Assignment – Lot size: PA-LS) give a satisfactory solution within faster solving time on comparison with the original mathematical model solving

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

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 review of discrete-time optimization models for tactical production planning

This is an Accepted Manuscript of an article published in International Journal of Production Research on 27 Mar 2014, available online: http://doi.org/10.1080/00207543.2014.899721[EN] This study presents a review of optimization models for tactical production planning. The objective of this research is to identify streams and future research directions in this field based on the different classification criteria proposed. The major findings indicate that: (1) the most popular production-planning area is master production scheduling with a big-bucket time-type period; (2) most of the considered limited resources correspond to productive resources and, to a lesser extent, to inventory capacities; (3) the consideration of backlogs, set-up times, parallel machines, overtime capacities and network-type multisite configuration stand out in terms of extensions; (4) the most widely used modelling approach is linear/integer/mixed integer linear programming solved with exact algorithms, such as branch-and-bound, in commercial MIP solvers; (5) CPLEX, C and its variants and Lindo/Lingo are the most popular development tools among solvers, programming languages and modelling languages, respectively; (6) most works perform numerical experiments with random created instances, while a small number of works were validated by real-world data from industrial firms, of which the most popular are sawmills, wood and furniture, automobile and semiconductors and electronic devices.This study has been funded by the Universitat Politècnica de València projects: ‘Material Requirement Planning Fourth Generation (MRPIV)’ (Ref. PAID-05-12) and ‘Quantitative Models for the Design of Socially Responsible Supply Chains under Uncertainty Conditions. Application of Solution Strategies based on Hybrid Metaheuristics’ (PAID-06-12).Díaz-Madroñero Boluda, FM.; Mula, J.; Peidro Payá, D. (2014). A review of discrete-time optimization models for tactical production planning. International Journal of Production Research. 52(17):5171-5205. doi:10.1080/00207543.2014.899721S51715205521

Modelagem de um Sistema de Programação de Produção de uma Indústria de Autopeças utilizando Programação Inteira.

A competitividade entre as empresas vem aumentando com o passar dos anos, isto porque a constante evolução tecnológica vem gerando grandes ganhos de produtividade nas diferentes áreas presentes nos negócios. Para se manter no mercado, portanto, as empresas vêm criando e desenvolvendo métodos e processos cada vez mais produtivos. Uma das áreas mais importantes é a da programação, uma importante parte do planejamento e controle da produção. A programação da produção é responsável por determinar a melhor alocação dos recursos e, se feita com as ferramentas corretas, podem trazer reduções de custos para as empresas. Essas diminuições podem vir do aproveitamento dos setups existentes nas máquinas, a partir de um decréscimo no atraso em peças, do melhor balanceamento das linhas, da diminuição dos custos totais e até estar presente no lead time. Por isso, o objetivo desta dissertação foi modelar um sistema de programação de produção com capacidade finita e com dados obtidos do ERP (Sistema utilizado para gerenciar as demandas existentes em uma operação) de uma empresa de autopeças situada no estado de Minas Gerais, Brasil, visando reduzir o número de atraso em peças e, consequentemente, diminuindo o custo de operação e de fretes extras. Para atingir esse objetivo, foi utilizado como base um modelo do tipo CLSP, do inglês Capacitated Lot Sizing Problem, que possui características específicas como capacidade finita, ser discreto, e possuir setup como parte importante de sua capacidade. O modelo, ainda, foi projetado com transferência de capacidade de um período para o outro, de forma a não perder os minutos restantes, como ocorre em modelos tradicionais de CLSP. Como houve o desenvolvimento matemático e a realização de testes posteriores, foi utilizado o método de pesquisa conhecido como modelagem e simulação, tradicionalmente composta de quatro etapas: Conceituação, modelagem, resolução através do programa e a implantação do sistema. A implantação do sistema a partir dos dados criados apresentou resultados satisfatórios gerando economia para os três tipos de modelos testados, para alta, média e baixa demandas. Para o caso de alta demanda, o modelo gerou uma economia de mais de cem mil reais em um ano, o que pode ser considerado uma grande economia para empresa caso a mesma tente implantar o sistema. Portanto, o modelo apresentou resultados positivos, demostrando ganhos a partir de sua aplicação, e é considerado efetivo para o caso da empresa estudada. Apesar disto, muitos avanços podem ser ainda realizados com o modelo para que ele se torne mais completo. Por fim, o banco de dados obtido com presente estudo fornece informações de uma empresa real, caso seja necessário efetuar novos testes em outros modelos

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

Modelo de un sistema MRP cerrado integrando incertidumbre en los tiempos de entrega, disponibilidad de la capacidad de fabricación e inventarios.

En el proceso de la planeación de la producción existen sistemas muy importantes como los sistemas de planeación de requerimientos de materiales (MRP), los cuales se encargan de traducir necesidades de producción de productos teminados en necesidades netas de producción o compra de cada uno de los componentes de dichos productos. Para que un MRP pueda entregar como resultado una asignación de componentes a fabricar o comprar en determinados periodos y recursos se deben ingresar al sistema varios parámetros, tiempos de entrega, disponibilidad de inventarios, capacidad de fabricación, entre otros, los cuales por su naturaleza tienen una incertidumbre asociada debido a impresiciones, falta de conocimiento y subjetividad en la asignación de valores. Una metodología para tratar la incertidumbre en los sistemas MRP es la lógica difusa, la cual a diferencia de la teoría de la probabilidad permite tener en cuenta el conocimiento y percepción de un tomador de decisiones, quien con base en su experticia puede expresar en modelos matemáticos los valores dentro de los cuales puede variar un parámetro para un sistema MRP, y con qué posibilidad se puede presentar dichos valores. Este tratamiento de la incertidumbre ha permitido que en este trabajo de grado se estudien y analicen modelos de sistemas MRP con incertidumbre expresada a través de la lógica difusa en parámetros tales como la disponibilidad de capacidad de fabricación, tiempos de entrega de materiales y dispobilidad de inventarios. Con base en un problema de producción real se realizan pruebas de los modelos difusos y se contrastan los resultados para determinar cómo varía el costo total de un plan de producción al igual que otras salidas importantes como la complejidad computacional del modelo y el nivel de inventarios.Maestrí