Using Branch-and-Price to Find High Quality Solutions Quickly

We develop an exact solution approach for integer programs that produces high- quality solutions quickly by solving well-chosen restrictions of the problem. Column generation is used both for generating these problem restrictions and for producing bounds on the value of an optimal solution to the problem. Obtaining primal solutions by solving problem restrictions also provides an easy way to search for improved solutions in the neighborhood of the current best solution. The overall approach is parallelized and computational experiments demonstrate its efficacy. An application to inventory routing is presented

Optimización de la producción y despacho de hormigón para una empresa en Santiago de Chile

En este trabajo proponemos un enfoque basados en modelos de optimización para resolver los problemas de programación de la producción, despacho y transporte en la Región Metropolitana de Santiago (Chile) para una de las mayores empresas en el rubro en país.Sociedad Argentina de Informática e Investigación Operativ

Optimización de la producción y despacho de hormigón para una empresa en Santiago de Chile

En este trabajo proponemos un enfoque basados en modelos de optimización para resolver los problemas de programación de la producción, despacho y transporte en la Región Metropolitana de Santiago (Chile) para una de las mayores empresas en el rubro en país.Sociedad Argentina de Informática e Investigación Operativ

Optimización de la producción y despacho de hormigón para una empresa en Santiago de Chile

En este trabajo proponemos un enfoque basados en modelos de optimización para resolver los problemas de programación de la producción, despacho y transporte en la Región Metropolitana de Santiago (Chile) para una de las mayores empresas en el rubro en país.Sociedad Argentina de Informática e Investigación Operativ

Trucks in movement

Beton erzeugende Unternehmen sehen sich täglich vor die Aufgabe gestellt, für die Belieferung der Baustellen eine möglichst effiziente Tourenplanung - unter Berücksichtigung ihrer heterogenen Fahrzeugflotte - zu erstellen. Da der Betonbedarf einer Baustelle die Kapazität eines einzelnen Fahrzeuges übersteigt, muss in der Regel jede Baustelle mehrmals hintereinander mit Beton beliefert werden. Das Planungsproblem ergibt sich nun insbesondere daraus, dass sich aufeinander folgenden Lieferungen nicht überschneiden dürfen, da nicht mehrere Fahrzeuge gleichzeitig entladen werden können. Eventuell entstehenden Lücken zwischen aufeinanderfolgenden Lieferungen jedoch sollten möglichst kurz gehalten werden. Im Rahmen dieser Dissertation werden mehrere Methoden besprochen, mit Hilfe derer eingangs erwähntes Tourenplanungsproblem gelöst werden kann. Die angewendeten Konzepte basieren auf exakten Verfahren, Heuristiken, Metaheuristiken, sowie hybriden Ansätzen. Ein exaktes Modell, beruhend auf einer Erweiterung des klassischen Vehicle Routing Problems (VRP, Tourenplanungsproblem) wurde entwickelt. Allerdings lässt sich die daraus resultierende Formulierung nur für äußerst kleine Instanzen exakt lösen. In der Praxis hingegen, ist dieser Ansatz aufgrund der zu langen Rechenzeiten und des enormen Rechenaufwandes nicht sinnvoll anwendbar. Daher wurde ein von Local Branching (LB) inspiriertes Verfahren konzipiert. Dieser integrativ hybride Ansatz wendet zusätzlich Nachbarschaftstrukturen, wie sie auch bei Variable Neighborhood Search (VNS) angewendet werden, kombiniert an. Darüber hinaus wurden valid inequalities für eine Verbesserung der unteren Schranken herangezogen. Ein weiterer Ansatz beruht auf einer Formulierung für multi-commodity network flow Problemen (MCNF). Anstatt einer globalen Sicht auf das Problem an sich, werden in diesem Zusammenhang nur ausgewählte Subbereiche näher betrachtet. So genannte Muster werden für alle BestellungenCompanies in the concrete industry are facing the following scheduling problem on a daily basis: concrete produced at several plants has to be delivered at customers' construction sites using a heterogeneous fleet of vehicles in a timely, but cost-effective manner. As the ordered quantity of concrete typically exceeds the capacity of a single vehicle several deliveries need to be scheduled to fulfill an order. The deliveries cannot overlap and the time between consecutive deliveries has to be small. This thesis presents a broad range of different ways on how to solve the problem stated above. Various solution methods based on exact, heuristic, meta-heuristic and hybrid approaches have been developed. Exact methods based on a formulation the so called VRP° (a Split Delivery Multi Depot Heterogeneous Vehicle Routing Problem with Time Windows) have been implemented. The resulting problem formulation can be solved to optimality for very small instances. For real-world-sized instances however, even with a steady increase in computational power, just to ``to MIP'' is not the way to success. Hence an algorithm, which controls the solution process of the embedded MIP-formulation, has been developed in order to tackler larger problem instances. This \emph{integrative hybrid} approach is based on Local Branching (LB) which itself is guided by means of Variable Neighborhood Search (VNS). Attention has also been paid to the development of valid inequalities and cuts in order to improve the quality of lower bounds. Another approach has been developed, which is based on a multi-commodity network flow model (MCNF) formulation. Rather than having a comprehensive view on the problem only subparts are considered and solved to optimality. So called \emph{patterns} (options on how orders could be satisfied) are generated heuristically and serve as an input for the MCNF. Given on a set of input pattern it is possible to solve the problem to optimality. Moreover the entir

Primal Heuristics for Branch-and-Price: the assets of diving methods

International audiencePrimal heuristics have become an essential component in mixed integer programming (MIP) solvers. Extending MIP based heuristics, our study outlines generic procedures to build primal solutions in the context of a branch-and-price approach and reports on their performance. Our heuristic decisions carry on variables of the Dantzig-Wolfe reformulation, the motivation being to take advantage of a tighter linear programming relaxation than that of the original compact formulation and to benefit from the combinatorial structure embedded in these variables. We focus on the so-called diving methods that use re-optimization after each LP rounding. We explore combinations with diversification- intensification paradigms such as limited discrepancy search , sub-MIPing, local branching, and strong branching. The dynamic generation of variables inherent to a column generation approach requires specific adaptation of heuristic paradigms. We manage to use simple strategies to get around these technical issues. Our numerical results on generalized assignment, cutting stock, and vertex coloring problems sets new benchmarks, highlighting the performance of diving heuristics as generic procedures in a column generation context and producing better solutions than state-of-the-art specialized heuristics in some cases

Delivery of ready-mixed concrete in a dynamic environment

Das Thema dieser Magisterarbeit behandelt die Auslieferung von Fertigbeton in einem dynamischen Umfeld. Das Ziel der Arbeit ist mit einem bestehenden Algorithmus eine Laufzeit-Analyse durchzuführen. Die Auslieferung von Fertigbeton stellt eine logistische Herausforderung dar und wird in der Literatur durch ein VRP (Vehicle Routing Problem) beschrieben. Ein VRP, in diesem Fall mit unterschiedlichen Bedingungen, ist eines der schwierigsten Aufgabenstellungen aus dem Bereich der Kombinatorik. Mit Hilfe des Algorithmus kann das VRP jedoch fast optimal gelöst werden, gleichzeitig verbessert sich auch die Lösung über einem längeren Zeitraum. Anhand von drei unterschiedlichen Experimenten soll die Anwendbarkeit und Lösungsgüte des Algorithmus untersucht werden. Dabei werden verschiedene Auftragsszenarien unter statischen, dynamischen bzw. hypothetischen Bedingungen generiert. Der Fokus liegt in der Reaktionsfähigkeit des Algorithmus und den damit verbundenen Auswirkungen auf den Planungsprozess. Die Arbeit besteht aus drei Hauptteilen. Der erste Teil befasst sich mit dem theoretischen Hintergrund. Der zweite Abschnitt beschreibt die spezifischen Eigenschaften und Anforderungen an Fertigbeton. Zum Abschluss der Arbeit werden die drei Experimente genauer beschrieben und die Ergebnisse präsentiert.This thesis deals with the delivery of ready-mixed concrete in a dynamic environment. Its aim is a run time analysis of a certain algorithm which is used for vehicle routing problems, a problem which is in the field of combinatorial optimization problems one of the most challenging ones, which can not only solve this problem to near-optimality, but also improves the given solution over time. For this case the algorithm is applied on three generated experiments set in a static/dynamic environment. The focus lies upon the reaction of the algorithm and on the consequences for the schedulers who have to deal with this matters which often occur on short notice. The thesis consists of three main parts. The first part takes a deeper look at the theory behind this problem. Two combinatorial optimization problems have been explained, and their solutions methods were presented. Then the material itself was presented, its special features and how this inflicts the production system and delivery of ready-mixed concrete. The last part consists of the experiments and the results of the study

Model-Based Heuristics for Combinatorial Optimization

Many problems arising in several and different areas of human knowledge share the characteristic of being intractable in real cases. The relevance of the solution of these problems, linked to their domain of action, has given birth to many frameworks of algorithms for solving them. Traditional solution paradigms are represented by exact and heuristic algorithms. In order to overcome limitations of both approaches and obtain better performances, tailored combinations of exact and heuristic methods have been studied, giving birth to a new paradigm for solving hard combinatorial optimization problems, constituted by model-based metaheuristics. In the present thesis, we deepen the issue of model-based metaheuristics, and present some methods, belonging to this class, applied to the solution of combinatorial optimization problems

A hybrid solution approach for ready-mixed concrete delivery

Companies in the concrete industry are facing the following scheduling problem on a daily basis: concrete produced at several plants has to be delivered at customers’ construction sites using a heterogeneous fleet of vehicles in a timely, but cost-effective manner. As the ordered quantity of concrete typically exceeds the capacity of a single vehicle several deliveries need to be scheduled in order to fulfill an order. The deliveries cannot overlap and the time between consecutive deliveries has to be small. Our solution approach effectively integrates optimization and heuristic techniques. Information is passed back and forth between an integer multicommodity flow optimization component and a variable neighborhood search component in order to find high-quality solutions in a reasonable amount of time. Even though both components are capable of producing feasible solutions, the integrated approach is far more effective. Computational results show that our hybrid approach outperforms an innovative metaheuristic approach by more than 6% on average for large instances