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

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

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 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

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

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

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

Integrated Production and Distribution planning of perishable goods

Tese de doutoramento. Programa Doutoral em Engenharia Industrial e Gestão. Faculdade de Engenharia. Universidade do Porto. 201

Lot-Sizing Problem for a Multi-Item Multi-level Capacitated Batch Production System with Setup Carryover, Emission Control and Backlogging using a Dynamic Program and Decomposition Heuristic

Wagner and Whitin (1958) develop an algorithm to solve the dynamic Economic Lot-Sizing Problem (ELSP), which is widely applied in inventory control, production planning, and capacity planning. The original algorithm runs in O(T^2) time, where T is the number of periods of the problem instance. Afterward few linear-time algorithms have been developed to solve the Wagner-Whitin (WW) lot-sizing problem; examples include the ELSP and equivalent Single Machine Batch-Sizing Problem (SMBSP). This dissertation revisits the algorithms for ELSPs and SMBSPs under WW cost structure, presents a new efficient linear-time algorithm, and compares the developed algorithm against comparable ones in the literature. The developed algorithm employs both lists and stacks data structure, which is completely a different approach than the rest of the algorithms for ELSPs and SMBSPs. Analysis of the developed algorithm shows that it executes fewer number of basic actions throughout the algorithm and hence it improves the CPU time by a maximum of 51.40% for ELSPs and 29.03% for SMBSPs. It can be concluded that the new algorithm is faster than existing algorithms for both ELSPs and SMBSPs. Lot-sizing decisions are crucial because these decisions help the manufacturer determine the quantity and time to produce an item with a minimum cost. The efficiency and productivity of a system is completely dependent upon the right choice of lot-sizes. Therefore, developing and improving solution procedures for lot-sizing problems is key. This dissertation addresses the classical Multi-Level Capacitated Lot-Sizing Problem (MLCLSP) and an extension of the MLCLSP with a Setup Carryover, Backlogging and Emission control. An item Dantzig Wolfe (DW) decomposition technique with an embedded Column Generation (CG) procedure is used to solve the problem. The original problem is decomposed into a master problem and a number of subproblems, which are solved using dynamic programming approach. Since the subproblems are solved independently, the solution of the subproblems often becomes infeasible for the master problem. A multi-step iterative Capacity Allocation (CA) heuristic is used to tackle this infeasibility. A Linear Programming (LP) based improvement procedure is used to refine the solutions obtained from the heuristic method. A comparative study of the proposed heuristic for the first problem (MLCLSP) is conducted and the results demonstrate that the proposed heuristic provide less optimality gap in comparison with that obtained in the literature. The Setup Carryover Assignment Problem (SCAP), which consists of determining the setup carryover plan of multiple items for a given lot-size over a finite planning horizon is modelled as a problem of finding Maximum Weighted Independent Set (MWIS) in a chain of cliques. The SCAP is formulated using a clique constraint and it is proved that the incidence matrix of the SCAP has totally unimodular structure and the LP relaxation of the proposed SCAP formulation always provides integer optimum solution. Moreover, an alternative proof that the relaxed ILP guarantees integer solution is presented in this dissertation. Thus, the SCAP and the special case of the MWIS in a chain of cliques are solvable in polynomial time

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