Approximation algorithms for regret minimization in vehicle routing problems

In this thesis, we present new approximation algorithms as well as hardness of approximation results for NP-hard vehicle routing problems related to public transportation. We consider two different problem classes that also occur frequently in areas such as logistics, robotics, or distribution systems. For the first problem class, the goal is to visit as many locations in a network as possible subject to timing or cost constraints. For the second problem class, a given set of locations is to be visited using a minimum-cost set of routes under some constraints. Due to the relevance of both problem classes for public transportation, a secondary objective must be taken into account beyond a low operation cost: namely, it is crucial to design routes that optimize customer satisfaction in order to encourage customers to use the service. Our measure of choice is the regret of a customer, that is the time comparison of the chosen route with the shortest path to a destination. From the first problem class, we investigate variants and extensions of the Orienteering problem that asks to find a short walk maximizing the profit obtained from visiting distinct locations. We give approximation algorithms for variants in which the walk has to respect constraints on the regret of the visited vertices. Additionally, we describe a framework to extend approximation algorithms for Orienteering problems to consider also a second budget constraint, namely node demands, that have to be satisfied in order to collect the profit. We obtain polynomial time approximation schemes for the Capacitated Orienteering problem on trees and Euclidean metrics. Furthermore, we study variants of the School Bus problem (SBP). In SBP, a given set of locations is to be connected to a destination node with both low operation cost and a low maximum regret. We note that the Orienteering problem can be seen as the pricing problem for SBP and it often appears as subroutine in algorithms for SBP. For tree-shaped networks, we describe algorithms with a small constant approximation factor and complement them by showing hardness of approximation results. We give an overview of the known results in arbitrary networks and we prove that a general variant cannot be approximated unless P = NP. Finally, we describe an integer programming approach to solve School Bus problems in practice and present an improved bus schedule for a private school in the lake Geneva region

Prize-Collecting TSP with a Budget Constraint

We consider constrained versions of the prize-collecting traveling salesman and the minimum spanning tree problems. The goal is to maximize the number of vertices in the returned tour/tree subject to a bound on the tour/tree cost. We present a 2-approximation algorithm for these problems based on a primal-dual approach. The algorithm relies on finding a threshold value for the dual variable corresponding to the budget constraint in the primal and then carefully constructing a tour/tree that is just within budget. Thereby, we improve the best-known guarantees from 3+epsilon and 2+epsilon for the tree and the tour version, respectively. Our analysis extends to the setting with weighted vertices, in which we want to maximize the total weight of vertices in the tour/tree subject to the same budget constraint

Applications of biased-randomized algorithms and simheuristics in integrated logistics

Transportation and logistics (T&L) activities play a vital role in the development of many businesses from different industries. With the increasing number of people living in urban areas, the expansion of on-demand economy and e-commerce activities, the number of services from transportation and delivery has considerably increased. Consequently, several urban problems have been potentialized, such as traffic congestion and pollution. Several related problems can be formulated as a combinatorial optimization problem (COP). Since most of them are NP-Hard, the finding of optimal solutions through exact solution methods is often impractical in a reasonable amount of time. In realistic settings, the increasing need for 'instant' decision-making further refutes their use in real life. Under these circumstances, this thesis aims at: (i) identifying realistic COPs from different industries; (ii) developing different classes of approximate solution approaches to solve the identified T&L problems; (iii) conducting a series of computational experiments to validate and measure the performance of the developed approaches. The novel concept of 'agile optimization' is introduced, which refers to the combination of biased-randomized heuristics with parallel computing to deal with real-time decision-making.Las actividades de transporte y logística (T&L) juegan un papel vital en el desarrollo de muchas empresas de diferentes industrias. Con el creciente número de personas que viven en áreas urbanas, la expansión de la economía a lacarta y las actividades de comercio electrónico, el número de servicios de transporte y entrega ha aumentado considerablemente. En consecuencia, se han potencializado varios problemas urbanos, como la congestión del tráfico y la contaminación. Varios problemas relacionados pueden formularse como un problema de optimización combinatoria (COP). Dado que la mayoría de ellos son NP-Hard, la búsqueda de soluciones óptimas a través de métodos de solución exactos a menudo no es práctico en un período de tiempo razonable. En entornos realistas, la creciente necesidad de una toma de decisiones "instantánea" refuta aún más su uso en la vida real. En estas circunstancias, esta tesis tiene como objetivo: (i) identificar COP realistas de diferentes industrias; (ii) desarrollar diferentes clases de enfoques de solución aproximada para resolver los problemas de T&L identificados; (iii) realizar una serie de experimentos computacionales para validar y medir el desempeño de los enfoques desarrollados. Se introduce el nuevo concepto de optimización ágil, que se refiere a la combinación de heurísticas aleatorias sesgadas con computación paralela para hacer frente a la toma de decisiones en tiempo real.Les activitats de transport i logística (T&L) tenen un paper vital en el desenvolupament de moltes empreses de diferents indústries. Amb l'augment del nombre de persones que viuen a les zones urbanes, l'expansió de l'economia a la carta i les activitats de comerç electrònic, el nombre de serveis del transport i el lliurament ha augmentat considerablement. En conseqüència, s'han potencialitzat diversos problemes urbans, com ara la congestió del trànsit i la contaminació. Es poden formular diversos problemes relacionats com a problema d'optimització combinatòria (COP). Com que la majoria són NP-Hard, la recerca de solucions òptimes mitjançant mètodes de solució exactes sovint no és pràctica en un temps raonable. En entorns realistes, la creixent necessitat de prendre decisions "instantànies" refuta encara més el seu ús a la vida real. En aquestes circumstàncies, aquesta tesi té com a objectiu: (i) identificar COP realistes de diferents indústries; (ii) desenvolupar diferents classes d'aproximacions aproximades a la solució per resoldre els problemes identificats de T&L; (iii) la realització d'una sèrie d'experiments computacionals per validar i mesurar el rendiment dels enfocaments desenvolupats. S'introdueix el nou concepte d'optimització àgil, que fa referència a la combinació d'heurístiques esbiaixades i aleatòries amb informàtica paral·lela per fer front a la presa de decisions en temps real.Tecnologies de la informació i de xarxe

Optimization Approaches for Mobility and Service Sharing

Mobility and service sharing is undergoing a fast rise in popularity and industrial growth in recent years. For example, in patient-centered medical home care, services are delivered to patients at home, who share a group of medical staff riding together in a vehicle that also carries shared medical devices; companies such as Amazon and Meijer have been investing tremendous human effort and money in grocery delivery to customers who share the use of delivery vehicles and staff. In such mobility and service sharing systems, decision-makers need to make a wide range of system design and operational decisions, including locating service facilities, matching supplies with demand for shared mobility services, dispatching vehicles and staff, and scheduling appointments. The complexity of the linking decisions and constraints, as well as the dimensionality of the problems in the real world, pose challenges in finding optimal strategies efficiently. In this work, we apply techniques from Operations Research to investigate the optimal and practical solution approaches to improve the quality of service, cost-effectiveness, and operational efficiency of mobility and service sharing in a variety of applications. We deploy stochastic programming, integer programming, and approximation algorithms to address the issues in decision-making for seeking fast and reliable solutions for planning and operations problems. This dissertation contains four main chapters. In Chapter 2, we consider a class of vehicle routing problems (VRPs) where the objective is to minimize the longest route taken by any vehicle as opposed to the total distance of all routes. In such a setting, the traditional decomposition approach fails to solve the problem effectively. We investigate the hardness result of the problem and develop an approximation algorithm that achieves the best approximation ratio. In Chapter 3, we focus on developing an efficient computational algorithm for the elementary shortest path problem with resource constraints, which is solved as the pricing subproblem of the column generation-based approach for many VRP variants. Inspired by the color-coding approach, we develop a randomized algorithm that can be easily implemented in parallel. We also extend the state-of-the-art pulse algorithm for elementary shortest path problem with a new bounding scheme on the load of the route. In Chapter 4, we consider a carsharing fleet location design problem with mixed vehicle types and a restriction on CO2 emission. We use a minimum-cost flow model on a spatial-temporal network and provide insights on fleet location, car-type design, and their environmental impacts. In Chapter 5, we focus on the design and operations of an integrated car-and-ride sharing system for heterogeneous users/travelers with an application of satisfying transportation needs in underserved communities. The system aims to provide self-sustained community-based shared transportation. We address the uncertain travel and service time in operations via a stochastic integer programming model and propose decomposition algorithms to solve it efficiently. Overall, our contributions are threefold: (i) providing mathematical models of various complex mobility and service sharing systems, (ii) deriving efficient solution algorithms to solve the proposed models, (iii) evaluating the solution approaches via extensive numerical experiments. The models and solution algorithms that we develop in this work can be used by practitioners to solve a variety of mobility and service sharing problems in different business contexts, and thus can generate significant societal and economic impacts.PHDIndustrial & Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/155115/1/miaoyu_1.pd

A Study in Three Practical Management Science Problems

This study of practical problems in Management Science (MS) describes novel mathematical models for three different decision settings. It addresses questions of: (a) what optimal route should be taken through a time-windows and topographically complex network; (b) what optimal sequencing of scheduled surgeries best coordinates flow of patients through central recovery; and (c) what prices should be charged and what stock amounts should be produced for two markets or channels to maximize profit explicitly, given various capacity and uncertainty conditions. The first problem is in a sport analytics context, using a novel Integer Programming and big data from Whistler-Blackcomb ski resort. The second is to coordinate dozens of surgeries at London Health Sciences Centre, using a novel Constraint Programming model mapped to and parameterized with hospital data, including a tool for visualizing process and patient flow. The third problem is relevant to almost any business with a secondary market or sales channel, as it helps them identify profit optimal prices based on simple demand estimates and cost information they can easily provide for their own setting. The studies use fundamentally different operational research techniques, in each case uniquely extended to the problem setting. The first two are combinatorial problems, neither one extremely beyond human cognitive ability, and both involving lots of uncertainty, and thus the sort of problem managers tend to dismiss as not efficient or practical to solve analytically. We show in the first study that vastly more skiers could achieve the challenge by following our route recommendation, unintuitive as are some of its elements, initially. In the second study, our scheduling model consistently outperforms currently unstructured-independent approach at the hospital. The final study is mathematical but demonstrates that by considering distinct market costs in pricing a firm can invariably earn more profit

Query processing in complex modern traffic networks

The transport sector generates about one quarter of all greenhouse gas emissions worldwide. In the European Union (EU), passenger cars and light-duty trucks make up for over half of these traffic-related emissions. It is evident that everyday traffic is a serious environmental threat. At the same time, transport is a key factor for the ambitious EU climate goals; among them, for instance, the reduction of greenhouse gas emissions by 85 to 90 percent in the next 35 years. This thesis investigates complex traffic networks and their requirements from a computer science perspective. Modeling of and query processing in modern traffic networks are pivotal topics. Challenging theoretical problems are examined from different perspectives, novel algorithmic solutions are provided. Practical problems are investigated and solved, for instance, employing qualitative crowdsourced information and sensor data of various sources. Modern traffic networks are often modeled as graphs, i.e., defined by sets of nodes and edges. In conventional graphs, the edges are assigned numerical weights, for instance, reflecting cost criteria like distance or travel time. In multicriteria networks, the edges reflect multiple, possibly dynamically changing cost criteria. While these networks allow for diverse queries and meaningful insight, query processing usually is significantly more complex. Novel means for computation are required to keep query processing efficient. The crucial task of computing optimal paths is particularly expensive under multiple criteria. The most established set of optimal paths in multicriteria networks is referred to as path skyline (or set of pareto-optimal paths). Until now, computing the path skyline either required extensive precomputation or networks of minor size or complexity. Neither of these demands can be made on modern traffic networks. This thesis presents a novel method which makes on-the-fly computation of path skylines possible, even in dynamic networks with three or more cost criteria. Another problem examined is the exponentially growth of path skylines. The number of elements in a path skyline is potentially exponential in the number of cost criteria and the number of edges between start and target. This often produces less meaningful results, sometimes hindering usability. These drawbacks emphasize the importance of the linear path skyline which is investigated in this thesis. The linear path skyline is based on a different notion of optimality. By the notion of optimality, the linear path skyline is a subset of the conventional path skyline but in general contains less and more diverse elements. Thus, the linear path skyline facilitates interpretation while in general reducing computational effort. This topic is first studied in networks with two cost criteria and subsequently extended to more cost criteria. These cost criteria are not limited to purely quantitative measures like distance and travel time. This thesis examines the integration of qualitative information into abstractly modeled road networks. It is proposed to mine crowdsourced data for qualitative information and use this information to enrich road network graphs. These enriched networks may in turn be used to produce routing suggestions which reflect an opinion of the crowd. From data processing to knowledge extracting, network enrichment and route computation, the possibilities and challenges of crowdsourced data as a source for information are surveyed. Additionally, this thesis substantiates the practicability of network enrichment in real-world experiments. The description of a demonstration framework which applies some of the presented methods to the use case of tourist route recommendation serves as an example. The methods may also be applied to a novel graph-based routing problem proposed in this thesis. The problem extends the family of Orienteering Problems which find frequent application in tourist routing and other tasks. An approximate solution to this NP-hard problem is presented and evaluated on a large scale, real-world, time-dependent road network. Another central aspect of modern traffic networks is the integration of sensor data, often referred to as telematics. Nowadays, manifold sensors provide a plethora of data. Using this data to optimize traffic is and will continue to be a challenging task for research and industry. Some of the applications which qualify for the integration of modern telematics are surveyed in this thesis. For instance, the abstract problem of consumable and reoccurring resources in road networks is studied. An application of this problem is the search for a vacant parking space. Taking statistical and real-time sensor information into account, a stochastic routing algorithm which maximizes the probability of finding a vacant space is proposed. Furthermore, the thesis presents means for the extraction of driving preferences, helping to better understand user behavior in traffic. The theoretical concepts partially find application in a demonstration framework described in this thesis. This framework provides features which were developed for a real-world pilot project on the topics of electric and shared mobility. Actual sensor car data collected in the project, gives insight to the challenges of managing a fleet of electric vehicles.Verkehrsmittel erzeugen rund ein Viertel aller Treibhausgas-Emissionen weltweit. Für über die Hälfte der verkehrsbedingten Emissionen in der Europäischen Union (EU) zeichnen PKW und Kleinlaster verantwortlich. Die Tragweite ökologischer Konsequenzen durch alltäglichen Verkehr ist enorm. Zugleich ist ein Umdenken im Bezug auf Verkehr entscheidend, um die ehrgeizigen klimapolitischen Ziele der EU zu erfüllen. Dazu gehört unter anderem, Treibhausgas-Emissionen bis 2050 um 85 bis 90 Prozent zu verringern. Die vorliegende Arbeit widmet sich den komplexen Anforderungen an Verkehr und Verkehrsnetzwerke aus der Sicht der Informatik. Dabei spielen sowohl die Modellierung von als auch die Anfragebearbeitung in modernen Verkehrsnetzwerken eine entscheidende Rolle. Theoretische Fragestellungen werden aus unterschiedlichen Persepektiven beleuchtet, neue Algorithmen werden vorgestellt. Ebenso werden praktische Fragestellungen untersucht und gelöst, etwa durch die Einbindung nutzergenerierten Inhalts oder die Verwendung von Sensordaten aus unterschiedlichen Quellen. Moderne Verkehrsnetzwerke werden häufig als Graphen modelliert, d.h., durch Knoten und Kanten dargestellt. Man unterscheidet zwischen konventionellen Graphen und sogenannten Multiattributs-Graphen. Während die Kanten konventioneller Graphen numerische Gewichte tragen, die statische Kostenkriterien wie Distanz oder Reisezeit modellieren, beschreiben die Kantengewichte in Multiattributs-Graphen mehrere, möglicherweise dynamisch veränderliche Kostenkriterien. Das erlaubt einerseits vielseitige Anfragen und aussagekräftige Erkenntnisse, macht die Anfragebearbeitung jedoch ungleich komplexer und verlangt deshalb nach neuen Berechnungsmethoden. Eine besonders aufwendige Anfrage ist die Berechnung optimaler Pfade, zugleich eine der zentralsten Fragestellungen. Die gängigste Menge optimaler Pfade wird als Pfad-Skyline (auch: Menge der pareto-optimalen Pfade) bezeichnet. Die effiziente Berechnung der Pfad-Skyline setzte bisher überschaubare Netzwerke oder beträchtliche Vorberechnungen voraus. Keine der beiden Bedingung kann in modernen Verkehrsnetzwerken erfüllt werden. Diese Arbeit stellt deshalb eine Methode vor, die die Berechnung der Pfad-Skyline erheblich beschleunigt, selbst in dynamischen Netzwerken mit drei oder mehr Kostenkriterien. Außerdem wird das Problem des exponentiellen Wachstums der Pfad-Skyline betrachtet. Die Anzahl der Elemente der Pfad-Skyline wächst im schlechtesten Fall exponentiell in der Anzahl der Kostenkriterien sowie in der Entfernung zwischen Start und Ziel. Dies kann zu unübersichtlichen und wenig aussagekräftigen Resultatmengen führen. Diese Nachteile unterstreichen die Bedeutung der linearen Pfad-Skyline, die auch im Rahmen diese Arbeit untersucht wird. Die lineare Pfad-Skyline folgt einer anderen Definition von Optimalität. Stets ist die lineare Pfad-Skyline eine Teilmenge der konventionellen Pfad-Skyline, meist enthält sie deutlich weniger, unterschiedlichere Resultate. Dadurch lässt sich die lineare Pfad-Skyline im Allgemeinen schneller berechnen und erleichtert die Interpretation der Resultate. Die Berechnung der linearen Pfad-Skyline wird erst für Netzwerke mit zwei Kostenkriterien, anschließend für Netzwerke mit beliebig vielen Kostenkriterien untersucht. Kostenkriterien sind nicht notwendigerweise auf rein quantitative Maße wie Distanz oder Reisezeit beschränkt. Diese Arbeit widmet sich auch der Integration qualitativer Informationen, mit dem Ziel, intuitivere und greifbarere Routingergebnisse zu erzeugen. Dazu wird die Möglichkeit untersucht, abstrakte Straßennetzwerke mit qualitativen Informationen anzureichern, wobei die Informationen aus nutzergenerierten Daten geschöpft werden. Solche sogenannten Enriched Networks ermöglichen die Berechnung von Pfaden, die in gewisser Weise das Wissen der Nutzer reflektieren. Von der Datenverarbeitung, über die Extraktion von Wissen, bis hin zum Network-Enrichment und der Pfadberechnung, gibt diese Arbeit einen überblick zum Thema. Weiterhin wird die Praktikabilität dieses Vorgehens mit Experimenten auf Realdaten untermauert. Die Beschreibung eines Demonstrationstools für den Anwendungsfall der Navigation von Touristen dient als anschauliches Beispiel. Die vorgestellten Methoden sind darüber hinaus auch anwendbar auf ein neues, graphentheoretisches Routingproblem, das in dieser Arbeit vorgestellt wird. Es handelt sich dabei um eine zeitabängige Erweiterung der Familie der Orienteering Probleme, die häufig Anwendung finden, etwa auch im der Bereich der Touristennavigation. Das vorgestellte Problem ist NP-schwer lässt sich jedoch dank eines hier vorgestellten Algorithmus effizient approximieren. Die Evaluation untermauert die Effizienz des vorgestellten Lösungsansatzes und ist zugleich die erste Auswertung eines zeitabhängigen Orienteering Problems auf einem großformatigen Netzwerk. Ein weiterer zentraler Aspekt moderner Verkehrsnetzwerke ist die Integration von Sensordaten, oft unter dem Begriff Telematik zusammengefasst. Heutzutage generiert eine Vielzahl von Sensoren Unmengen an Daten. Diese Daten zur Verkehrsoptimierung einzusetzen ist und bleibt eine wichtige Aufgabe für Wissenschaft und Industrie. Einige der Anwendungen, die sich für den Einsatz von Telematik anbieten, werden in dieser Arbeit untersucht. So wird etwa das abstrakte Problem konsumierbarer und wiederkehrender Ressourcen im Straßennetzwerk untersucht. Ein alltägliches Beispiel für dieses Problem ist die Parkplatzsuche. Der vorgeschlagene Algorithmus, der die Wahrscheinlichkeit maximiert, einen freien Parkplatz zu finden, baut auf die Verwendung statistischer sowie aktueller Sensordaten. Weiterhin werden Methoden zur Ableitung von Fahrerpräferenzen entwickelt. Die theoretischen Fundamente finden zum Teil in einem hier beschriebenen Demonstrationstool Anwendung. Das Tool veranschaulicht Features, die für ein Pilotprojekt zu den Themen Elektromobilität und Fahrzeugflotten entwickelt wurden. Im Rahmen eines Pilotversuchs wurden Sensordaten von Elektrofahrzeugen erhoben, die Einblick in die Herausforderungen beim Management von Elektrofahrzeugflotten geben

Tactical Problems in Vehicle Routing Applications

The class of Vehicle Routing Problems (VRPs) is one the most studied topics in the Operations Research community. The vast majority of the published papers focus on single-period problems, with a few branches of the literature considering multiperiod generalisations. All of these problems though, consider a short horizon and aim at optimising the decisions at an operational level, i.e. that will have to be taken in the near future. One step above are tactical problems, i.e. problems concerning a longer time horizon. Tactical problems are of a fundamental importance as they directly influence the daily operations, and therefore a part of the incurred costs, for a long time. The main focus of this thesis is to study tactical problems arising in routing applications. The first problem considered concerns the design of a fleet of vehicles. Transportation providers often have to design a fleet that will be used for daily operations across a long-time span. Trucks used for transportation are very expensive to purchase, maintain or hire. On the other side, the composition of the fleet strongly influences the daily plans, and therefore costs such as fuel or drivers’ wages. Balancing these two components is challenging, and optimisation models can lead to substantial savings or provide a useful basis for informed decisions. The second problem presented focuses on the use of a split deliveries policy in multi-period routing problems. It is known that the combined optimisation of delivery scheduling and routing can be very beneficial, and lead to significant reductions in costs. However, it also adds complexity to the model. The same is true when split deliveries are introduced. The problem studied considers the possibility of splitting the deliveries over different days. An analysis, both theoretical and numerical, of the impact of this approach on the overall cost is provided. Finally, a districting problem for routing applications is considered. These types of problems typically arise when transportation providers wish to increase their service consistency. There are several reasons a company may wish to do so: to strengthen the customer-driver relationship, to increase drivers’ familiarity with their service area, or, to simplify the management of the service area. A typical approach, considered here, is to divide the area under consideration in sectors that will be subsequently assigned to specific drivers. This type of problem is inherently of a multi-period and tactical nature. A new formulation is proposed, integrating standard routing models into the design of territories. This makes it possible to investigate how operational constraints and other requirements, such as having a fair workload division amongst drivers, influence the effectiveness of the approach. An analysis of the cost of districting, in terms of increased routing cost and decreased routing flexibility, and of several operational constraints, is presented