Simultaneous lotsizing and scheduling - extensions and solution approaches

The present thesis focuses on simultaneous lotsizing and scheduling. A comprehensive review of the literature is presented in which the historical development of the subject and the current research gaps are, based on a classification scheme, described. Additionally, a review focusing on so-called secondary resources (e.g., setup operators or raw materials), which are considered alongside the primary production resource, is provided. The insights on different types of secondary resources help to develop a new model formulation generalizing and extending the currently used approaches, which are specific to certain settings. Some illustrative examples demonstrate the functional principle and flexibility of this new formulation which can thus be used in a wide range of applications. Finally, a new heuristic to solve large-scaled simultaneous lotsizing and scheduling problems is presented. The heuristic creates a modified multi-line master problem by aggregating products into groups. The resulting problem is less complex and its solution can be used to define single-line sub problems. These sub problems are solved by heuristics present in the literature and the results are then combined to form a solution to the original problem. Numerical tests show the applicability of the aforementioned approach to solve problems of practical relevance.Die vorliegende Ausarbeitung betrachtet das Thema der simultanen Losgrößen- und Reihenfolgeplanung tiefergehend. Ein ausführlicher Literaturüberblick zeigt unter Zuhilfenahme eines Klassifizierungsschemas den Entwicklungsverlauf und aktuelle Forschungslücken in diesem Bereich auf. Weiterhin wird ein auf zusätzliche Ressourcen (sogenannte secondary resources) fokussierter Literaturüberblick erstellt. Diese Ressourcen (z.B. Personal zur Umrüstung oder Rohmaterial) werden zusätzlich zu der primären Produktionsressource benötigt. Die Erkenntnisse zu den verschiedenen Typen von zusätzlichen Ressourcen werden verwendet, um ein generelles Modell zu entwickeln, welches die bisherigen, auf bestimmte Anwendungsfälle spezialisierten, Formulierungen abbildet und erweitert. Testläufe mit Beispielszenarien demonstrieren die Funktionalität und die Flexibilität der neuen Modellformulierung welche für einen Vielzahl von Anwendungsfällen verwendet werden kann. Abschließend wird eine neue Heuristik zum Lösen von simultanen Losgrößen- und Reihenfolgeplanungsproblemen praxisrelevanter Größen vorgestellt. Innerhalb der Heuristik wird durch Produktaggregation ein modifiziertes Mehrlinien-Masterproblem generiert. Das resultierende Problem ist weniger komplex und die dafür gefundene Lösung kann zum Erstellen von Einlinien-Teilproblemen verwendet werden. Diese Teilprobleme werden mit aus der Literatur bekannten Heuristiken gelöst. Die Ergebnisse werden zu einer Lösung für das ursprüngliche Problem zusammengefasst. Numerische Tests belegen die Tauglichkeit des Verfahrens zum Lösen von praxisrelevanten Problemen

A survey of scheduling problems with setup times or costs

Author name used in this publication: C. T. NgAuthor name used in this publication: T. C. E. Cheng2007-2008 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe

Integrating Capacitated Lot-Sizing and Lot Streaming in Flowshop Schedules with Time Varying Demand

Any reasonable production planning contains three important decisions on lot size, lead time, and capacity. The common approach in the literature is to divide the planning problem into lot sizing, lot sequencing, and lot splitting sub-problems. Very few studies, to the best of our knowledge, have been conducted on the interdependencies and three- way interaction of lead-time, lot size, and actual capacity usage. A particular lot size calculated by the sub-problem method, however, will likely yield an infeasible solution or at least result in schedule instability (nervousness). This is just because in most capacitated lot sizing models, the capacity constraints in the model only take into consideration the available time on each work station, ignoring the sequencing of lots, sublot sizes, and their effect on makespan and lead times. In this thesis we bridge the gap between lot sizing and scheduling in flowshops, and examine the use of the lot splitting and sequencing techniques to reduce schedule instability. A mixed integer programming formulation is presented, which enables us to simultaneously find the optimal lot sizes as well as the corresponding sublot sizes and sequence of jobs. With this model, small size problems can be solved within a reasonable time. The computational results confirm that this model can be advantageous in dampening the scheduling nervousness. For larger size instances, a Genetic algorithm is proposed

The dynamic, resource-constrained shortest path problem on an acyclic graph with application in column generation and literature review on sequence-dependent scheduling

This dissertation discusses two independent topics: a resource-constrained shortest-path problem (RCSP) and a literature review on scheduling problems involving sequence-dependent setup (SDS) times (costs). RCSP is often used as a subproblem in column generation because it can be used to solve many practical problems. This dissertation studies RCSP with multiple resource constraints on an acyclic graph, because many applications involve this configuration, especially in column genetation formulations. In particular, this research focuses on a dynamic RCSP since, as a subproblem in column generation, objective function coefficients are updated using new values of dual variables at each iteration. This dissertation proposes a pseudo-polynomial solution method for solving the dynamic RCSP by exploiting the special structure of an acyclic graph with the goal of effectively reoptimizing RCSP in the context of column generation. This method uses a one-time âÂÂpreliminaryâ phase to transform RCSP into an unconstrained shortest path problem (SPP) and then solves the resulting SPP after new values of dual variables are used to update objective function coefficients (i.e., reduced costs) at each iteration. Network reduction techniques are considered to remove some nodes and/or arcs permanently in the preliminary phase. Specified techniques are explored to reoptimize when only several coefficients change and for dealing with forbidden and prescribed arcs in the context of a column generation/branch-and-bound approach. As a benchmark method, a label-setting algorithm is also proposed. Computational tests are designed to show the effectiveness of the proposed algorithms and procedures. This dissertation also gives a literature review related to the class of scheduling problems that involve SDS times (costs), an important consideration in many practical applications. It focuses on papers published within the last decade, addressing a variety of machine configurations - single machine, parallel machine, flow shop, and job shop - reviewing both optimizing and heuristic solution methods in each category. Since lot-sizing is so intimately related to scheduling, this dissertation reviews work that integrates these issues in relationship to each configuration. This dissertation provides a perspective of this line of research, gives conclusions, and discusses fertile research opportunities posed by this class of scheduling problems. since, as a subproblem in column generation, objective function coefficients are updated using new values of dual variables at each iteration. This dissertation proposes a pseudo-polynomial solution method for solving the dynamic RCSP by exploiting the special structure of an acyclic graph with the goal of effectively reoptimizing RCSP in the context of column generation. This method uses a one-tim

A hybrid genetic approach to solve real make-to-order job shop scheduling problems

Tese (doutorado) - Universidade Federal de Santa Catarina, Centro TecnologicoProcedimentos de busca local (ex. busca tabu) e algoritmos genéticos têm apresentado excelentes resultados em problemas clássicos de programação da produção em ambientes job shop. No entanto, estas abordagens apresentam pobres habilidades de modelamento e poucas aplicações com restrições de ambientes reais de produção têm sido publicadas. Além disto, os espaços de busca considerados nestas aplicações são nomlalmente incompletos e as restrições reais são poucas e dependentes do problema em questão. Este trabalho apresenta uma abordagem genética híbrida para resolver problemas de programação em ambientes job shop com grande número de restrições reais, tais como produtos com vários níveis de submontagem, planos de processamento altemativos para componentes e recursos alternativos para operações, exigência de vários recursos para executar uma operação (ex., máquina, ferramentas, operadores), calendários para todos os recursos, sobreposição de operações, restrições de disponibilidade de matéria-prima e componentes comprados de terceiros, e tempo de setup dependente da sequência de operações. A abordagem também considera funções de avaliação multiobjetivas. O sistema usa algoritmos modificados de geração de programação, que incorporam várias heurísticas de apoio à decisão, para obter um conjunto de soluções iniciais. Cada solução inicial é melhorada por um algoritmo de subida de encosta. Então, um algoritmo genético híbrido com procedimentos de busca local é aplicado ao conjunto inicial de soluções localmente ótimas. Ao utilizar técnicas de programação de alta perfomlance (heurísticas construtivas, procedimentos de busca local e algoritmos genéticos) em problemas reais de programação da produção, este trabalho reduziu o abismo existente entre a teoria e a prática da programação da produção

Unequal individual genetic algorithm with intelligent diversification for the lot-scheduling problem in integrated mills using multiple-paper machines

This paper addresses the lot-sizing and scheduling problem of pulp and paper mills involving multiple paper machines. The underlying multi-stage integrated production process considers the following critical units: continuous digester, intermediate stocks of pulp and liquor, multiple paper machines and a recovery line to treat by-products. This work presents a mixed integer programming (MIP) model to represent the problem, as well as a solution approach based on a customized genetic algorithm (GA) with an embedded residual linear programming model. Some GA tools are explored, including literature and new operators, a novel diversification process and other features. In particular, the diversification process uses a new allele frequency measure to change between diversification and intensification procedures. Computational results show the effectiveness of the method to solve relatively large instances of the single paper machine problem when compared to other single paper machine solution methods found in the literature. For multiple paper machine settings, in most runs the GA solutions are better than those obtained for the MIP model using an optimization software.This paper addresses the lot-sizing and scheduling problem of pulp and paper mills involving multiple paper machines. The underlying multi-stage integrated production process considers the following critical units: continuous digester, intermediate stocks of pulp and liquor, multiple paper machines and a recovery line to treat by-products. This work presents a mixed integer programming (MIP) model to represent the problem, as well as a solution approach based on a customized genetic algorithm (GA) with an embedded residual linear programming model. Some GA tools are explored, including literature and new operators, a novel diversification process and other features. In particular, the diversification process uses a new allele frequency measure to change between diversification and intensification procedures. Computational results show the effectiveness of the method to solve relatively large instances of the single paper machine problem when compared to other single paper machine solution methods found in the literature. For multiple paper machine settings, in most runs the GA solutions are better than those obtained for the MIP model using an optimization software

An investigation of production and transportation policies for multi-item and multi-stage production systems

Die vorliegende kumulative Dissertation besteht aus fünf Artikeln, einem Arbeitspapier und vier Artikeln, die in wissenschaftlichen Zeitschriften veröffentlicht wurden. Alle fünf Artikel beschäftigen sich mit der Losgrößenplanung, jedoch mit unterschiedlichen Schwerpunkten. Artikel 1 bis 4 untersuchen das Economic Lot Scheduling Problem (ELSP), während sich der fünfte Artikel mit einer Variante des Joint Economic Lot Size (JELS) Problems beschäftigt. Die Struktur dieser Dissertation trägt diesen beiden Forschungsrichtungen Rechnung und ordnet die ersten vier Artikel dem Teil A und den fünften Artikel dem Teil B zu

A Digital Twin Framework for Production Planning Optimization: Applications for Make-To-Order Manufacturers

In this dissertation, we develop a Digital Twin framework for manufacturing systems and apply it to various production planning and scheduling problems faced by Make-To-Order (MTO) firms. While this framework can be used to digitally represent a particular manufacturing environment with high fidelity, our focus is in using it to generate realistic settings to test production planning and scheduling algorithms in practice. These algorithms have traditionally been tested by either translating a practical situation into the necessary modeling constructs, without discussion of the assumptions and inaccuracies underlying this translation, or by generating random instances of the modeling constructs, without assessing the limitations in accurately representing production environments. The consequence has been a serious gap between theory advancement and industry practice. The major goal of this dissertation is to develop a framework that allows for practical testing, evaluation, and implementation of new approaches for seamless industry adoption. We develop this framework as a modular software package and emphasize the practicality and configurability of the framework, such that minimal modelling effort is required to apply the framework to a multitude of optimization problems and manufacturing systems. Throughout this dissertation, we emphasize the importance of the underlying scheduling problems which provide the basis for additional operational decision making. We focus on the computational evaluation and comparisons of various modeling choices within the developed frameworks, with the objective of identifying models which are both effective and computationally efficient. In Part 1 of this dissertation, we consider a class of Production Planning and Execution problems faced by job shop manufacturing systems. In Part 2 of this dissertation, we consider a class of scheduling problems faced by manufacturers whose production system is dominated by a single operation