Comparison of heuristic approaches for the multiple depot vehicle scheduling problem

Given a set of timetabled tasks, the multi-depot vehicle scheduling problemis a well-known problem that consists of determining least-cost schedulesfor vehicles assigned to several depots such that each task is accomplishedexactly once by a vehicle. In this paper, we propose to compare theperformance of five different heuristic approaches for this problem,namely, a heuristic \\mip solver, a Lagrangian heuristic, a columngeneration heuristic, a large neighborhood search heuristic using columngeneration for neighborhood evaluation, and a tabu search heuristic. Thefirst three methods are adaptations of existing methods, while the last twoare novel approaches for this problem. Computational results on randomlygenerated instances show that the column generation heuristic performs thebest when enough computational time is available and stability is required,while the large neighborhood search method is the best alternative whenlooking for a compromise between computational time and solution quality.tabu search;column generation;vehicle scheduling;heuristics;Lagrangian heuristic;large neighborhood search;multiple depot

Electromobility in Public Transport: Scheduling of Electric Vehicles and Location Planning of the Charging Infrastructure

In recent years, considerable efforts have been made to make public transport more environmentally friendly. This should primarily be achieved by reducing greenhouse gas emissions. Electromobility is considered to be a key technology as electric vehicles create a variety of benefits. However, the use of electric vehicles involves a number of challenges. Modern battery electric vehicles have only a fractional part of the ranges of combustion engine vehicles. Thus, a major challenge is charging the vehicles at specific charging stations to compensate for this disadvantage. Technological aspects of electric vehicles are also of importance and have to be considered. Planning tasks of public transport companies are affected by these challanges, especially vehicle scheduling. Vehicle scheduling is a well-studied optimization problem. The objective is to cover a given set of timetabled service trips by a set of vehicles at minimum costs. An issue strongly related to vehicle scheduling is location planning of the charging infrastructure. For an effcient use of electric vehicles, charging stations must be located at suitable locations in order to minimize operational costs. Location planning of charging stations is a long-term planning task whereas vehicle scheduling is a more short-term planning task in public transport. This thesis examines optimization methods for scheduling electric vehicles in public transport and location planning of the charging infrastructure. Electric vehicles' technological aspects are particularly considered. Case studies based on real-world data are used for evaluation of the artifacts developed. An exact optimization method addresses scheduling of mixed vehicles fleets consisting of electric vehicles and vehicles without range limitations. It is examined whether traditional solution methods for vehicle scheduling are able to cope with the challenges imposed by electric vehicles. The results show, that solution methods for vehicle scheduling are able to deal with the additional challenges to a certain degree. However, novel methods are required to fully deal with the requirements of electric vehicles. A heuristic solution method for scheduling electric vehicles and models for the charging process of batteries are developed. The impact of the detail level of electric vehicles' technological aspects on resulting solutions is analyzed. A computational study reveales major discrepancies between model assumptions and real charging behaviours. A metaheuristic solution method for the simultaneous optimization of location planning of charging stations and scheduling electric vehicles is designed to connect the optimization problems and to open up synergy effects. In comparison to a sequential planning, the simultaneous problem solving is necessary because a sequential planning generally leads to either infeasible solutions or to significant increases in costs.In den letzten Jahren wurden erhebliche Anstrengungen unternommen, um den öffentlichen Personennahverkehr (ÖPNV) umweltfreundlicher zu gestalten. Dabei sollen insbesondere Treibhausgasemissionen reduziert werden. Elektromobilität wird dabei auf Grund der zahlreichen Vorteile von Elektrofahrzeugen als Schlüsseltechnologie angesehen. Der Einsatz von Elektrofahrzeugen ist jedoch mit Herausforderungen verbunden, da diese über weitaus geringere Reichweiten im Vergleich zu Fahrzeugen mit Verbrennungsmotoren verfügen, weshalb ein Nachladen der Fahrzeugbatterien während des Betriebs notwendig ist. Zudem müssen technische Aspekte von Elektrofahrzeugen, wie beispielsweise Batteriealterungsprozesse, berücksichtigt werden. Die Fahrzeugeinsatzplanung als Teil des Planungsprozesses von Verkehrsunternehmen im ÖPNV ist besonders von diesen Herausforderungen betroffen. Diese legt den Fahrzeugeinsatz für die Bedienung der angebotenen Fahrplanfahrten bei Minimierung der Gesamtkosten fest. Die Standortplanung der Ladeinfrastruktur ist eng mit dieser Aufgabe verbunden, da für einen effizienten Einsatz der Fahrzeuge Ladestationen an geeigneten Orten errichtet werden müssen, um Betriebskosten zu minimieren. Die Planung der Ladeinfrastruktur ist ein langfristiges Planungsproblem, wohingegen die Fahrzeugeinsatzplanung eine eher kurzfristige Planungsaufgabe darstellt. Diese Dissertation befasst sich mit Optimierungsmethoden für die Fahrzeugeinsatzplanung mit Elektrofahrzeugen und mit der Standortplanung der Ladeinfrastruktur. Technische Aspekte von Elektrofahrzeugen werden dabei berücksichtigt. Die entwickelten Artefakte werden mit Hilfe von realen Datensätzen evaluiert. Durch eine exakte Optimierungsmethode für die Fahrzeugeinsatzplanung mit gemischten Fahrzeugflotten bestehend aus Fahrzeugen mit und ohne Reichweiterestriktionen wird die Anwendbarkeit von Optimierungsmethoden ohne Berücksichtigung von Reichweitebeschränkungen auf die Herausforderungen von Elektrofahrzeugen untersucht. Die Ergebnisse zeigen, dass herkömmliche Optimierungsmethoden für die neuen Herausforderungen bis zu einem gewissen Grad geeignet sind, es jedoch neuartige Lösungsmethoden erfordert, um den Anforderungen von Elektrofahrzeugen vollständig gerecht zu werden. Mit Hilfe einer heuristischen Lösungsmethode für die Fahrzeugeinsatzplanung mit Elektrofahrzeugen und Modellen für den Ladeprozess von Batterien wird untersucht, inwiefern sich der Detailgrad bei der Abbildung von Ladeprozessen auf resultierende Lösungen auswirkt. Erhebliche Unterschiede zwischen Modellannahmen und realen Gegebenheiten von Ladeprozessen werden herausgearbeitet. Durch ein metaheuristisches Lösungsverfahren für die simultane Optimierung der Standortplanung der Ladeinfrastruktur und der Fahrzeugeinsatzplanung werden beide Problemstellungen miteinander verbunden, um Synergieeffekte offenzulegen. Im Vergleich zu einer sequentiellen Planung ist ein simultanes Lösen notwendig, da ein sequentielles Lösen entweder zu unzulässigen Ergebnissen oder zu erheblichen Kostensteigerungen führt

Data-driven optimization of bus schedules under uncertainties

Plusieurs sous-problèmes d’optimisation se posent lors de la planification des transports publics. Le problème d’itinéraires de véhicule (PIV) est l’un d’entre eux et consiste à minimiser les coûts opérationnels tout en assignant exactement un autobus par trajet planifié de sorte que le nombre d’autobus entreposé par dépôt ne dépasse pas la capacité maximale disponible. Bien que les transports publics soient sujets à plusieurs sources d’incertitude (à la fois endogènes et exogènes) pouvant engendrer des variations des temps de trajet et de la consommation d’énergie, le PIV et ses variantes sont la plupart du temps résolus de façon déterministe pour des raisons de résolubilité. Toutefois, cette hypothèse peut compromettre le respect de l’horaire établi lorsque les temps des trajets considérés sont fixes (c.-à-d. déterministes) et peut produire des solutions impliquant des politiques de gestion des batteries inadéquates lorsque la consommation d’énergie est aussi considérée comme fixe. Dans cette thèse, nous proposons une méthodologie pour mesurer la fiabilité (ou le respect de l’horaire établi) d’un service de transport public ainsi que des modèles mathématiques stochastiques et orientés données et des algorithmes de branch-and-price pour deux variantes de ce problème, à savoir le problème d’itinéraires de véhicule avec dépôts multiples (PIVDM) et le problème d’itinéraires de véhicule électrique (PIV-E). Afin d’évaluer la fiabilité, c.-à-d. la tolérance aux délais, de certains itinéraires de véhicule, nous prédisons d’abord la distribution des temps de trajet des autobus. Pour ce faire, nous comparons plusieurs modèles probabilistes selon leur capacité à prédire correctement la fonction de densité des temps de trajet des autobus sur le long terme. Ensuite, nous estimons à l'aide d'une simulation de Monte-Carlo la fiabilité des horaires d’autobus en générant des temps de trajet aléatoires à chaque itération. Nous intégrons alors le modèle probabiliste le plus approprié, celui qui est capable de prédire avec précision à la fois la véritable fonction de densité conditionnelle des temps de trajet et les retards secondaires espérés, dans nos modèles d'optimisation basés sur les données. Deuxièmement, nous introduisons un modèle pour PIVDM fiable avec des temps de trajet stochastiques. Ce problème d’optimisation bi-objectif vise à minimiser les coûts opérationnels et les pénalités associées aux retards. Un algorithme heuristique basé sur la génération de colonnes avec des sous-problèmes stochastiques est proposé pour résoudre ce problème. Cet algorithme calcule de manière dynamique les retards secondaires espérés à mesure que de nouvelles colonnes sont générées. Troisièmement, nous proposons un nouveau programme stochastique à deux étapes avec recours pour le PIVDM électrique avec des temps de trajet et des consommations d’énergie stochastiques. La politique de recours est conçue pour rétablir la faisabilité énergétique lorsque les itinéraires de véhicule produits a priori se révèlent non réalisables. Toutefois, cette flexibilité vient au prix de potentiels retards induits. Une adaptation d’un algorithme de branch-and-price est développé pour évaluer la pertinence de cette approche pour deux types d'autobus électriques à batterie disponibles sur le marché. Enfin, nous présentons un premier modèle stochastique pour le PIV-E avec dégradation de la batterie. Le modèle sous contrainte en probabilité proposé tient compte de l’incertitude de la consommation d’énergie, permettant ainsi un contrôle efficace de la dégradation de la batterie grâce au contrôle effectif de l’état de charge (EdC) moyen et l’écart de EdC. Ce modèle, combiné à l’algorithme de branch-and-price, sert d’outil pour balancer les coûts opérationnels et la dégradation de la batterie.The vehicle scheduling problem (VSP) is one of the sub-problems of public transport planning. It aims to minimize operational costs while assigning exactly one bus per timetabled trip and respecting the capacity of each depot. Even thought public transport planning is subject to various endogenous and exogenous causes of uncertainty, notably affecting travel time and energy consumption, the VSP and its variants are usually solved deterministically to address tractability issues. However, considering deterministic travel time in the VSP can compromise schedule adherence, whereas considering deterministic energy consumption in the electric VSP (E-VSP) may result in solutions with inadequate battery management. In this thesis, we propose a methodology for measuring the reliability (or schedule adherence) of public transport, along with stochastic and data-driven mathematical models and branch-and-price algorithms for two variations of this problem, namely the multi-depot vehicle scheduling problem (MDVSP) and the E-VSP. To assess the reliability of vehicle schedules in terms of their tolerance to delays, we first predict the distribution of bus travel times. We compare numerous probabilistic models for the long-term prediction of bus travel time density. Using a Monte Carlo simulation, we then estimate the reliability of bus schedules by generating random travel times at each iteration. Subsequently, we integrate the most suitable probabilistic model, capable of accurately predicting both the true conditional density function of the travel time and the expected secondary delays, into the data-driven optimization models. Second, we introduce a model for the reliable MDVSP with stochastic travel time minimizing both the operational costs and penalties associated with delays. To effectively tackle this problem, we propose a heuristic column generation-based algorithm, which incorporates stochastic pricing problems. This algorithm dynamically computes the expected secondary delays as new columns are generated. Third, we propose a new two-stage stochastic program with recourse for the electric MDVSP with stochastic travel time and energy consumption. The recourse policy aims to restore energy feasibility when a priori vehicle schedules are unfeasible, which may lead to delays. An adapted algorithm based on column generation is developed to assess the relevance of this approach for two types of commercially available battery electric buses. Finally, we present the first stochastic model for the E-VSP with battery degradation. The proposed chance-constraint model incorporates energy consumption uncertainty, allowing for effective control of battery degradation by regulating the average state-of-charge (SOC) and SoC deviation in each discharging and charging cycle. This model, in combination with a tailored branch-and-price algorithm, serves as a tool to strike a balance between operational costs and battery degradation

Exploring the drive-by sensing power of bus fleet through active scheduling

Vehicle-based mobile sensing (a.k.a drive-by sensing) is an important means of surveying urban environment by leveraging the mobility of public or private transport vehicles. Buses, for their extensive spatial coverage and reliable operations, have received much attention in drive-by sensing. Existing studies have focused on the assignment of sensors to a set of lines or buses with no operational intervention, which is typically formulated as set covering or subset selection problems. This paper aims to boost the sensing power of bus fleets through active scheduling, by allowing instrumented buses to circulate across multiple lines to deliver optimal sensing outcome. We consider a fleet consisting of instrumented and normal buses, and jointly optimize sensor assignment, bus dispatch, and intra- or inter-line relocations, with the objectives of maximizing sensing quality and minimizing operational costs, while serving all timetabled trips. By making general assumptions on the sensing utility function, we formulate the problem as a nonlinear integer program based on a time-expanded network. A batch scheduling algorithm is developed following linearization techniques to solve the problem efficiently, which is tested in a real-world case study in Chengdu, China. The results show that the proposed scheme can improve the sensing objective by 12.0%-20.5% (single-line scheduling) and 16.3%-32.1% (multi-line scheduling), respectively, while managing to save operational costs by 1.0%. Importantly, to achieve the same level of sensing quality, we found that the sensor investment can be reduced by over 33% when considering active bus scheduling. Comprehensive comparative and sensitivity analyses are presented to generate managerial insights and recommendations for practice.Comment: 32 pages, 13 figures, 8 table

A literature overview on scheduling electric vehicles in public transport and location planning of the charging infrastructure

The Vehicle Scheduling Problem (VSP) is a well-studied combinatorial optimization problem arising for bus companies in public transport. The objective is to cover a given set of timetabled trips by a set of buses at minimum costs. The Electric Vehicle Scheduling Problem (E-VSP) complicates traditional bus scheduling by considering electric buses with limited driving ranges. To compensate these limitations, detours to charging stations become necessary for charging the vehicle batteries during operations. To save costs, the charging stations must be located within the road network in such a way that required deadhead trips are as short as possible or even redundant. For solving the traditional VSP, a variety of solution approaches exist capable of solving even real-world instances with large networks and timetables to optimality. In contrast, the problem complexity increases significantly when considering limited ranges and chargings of the batteries. For this reason, there mainly exist solution approaches for the E-VSP which are based von heuristic procedures as exact methods do not provide solutions within a reasonable time. In this paper, we present a literature review of solution approaches for scheduling electric vehicles in public transport and location planning of charging stations. Since existing work differ in addition to the solution methodology also in the mapping of electric vehicles' technical aspects, we pay particular attention to these characteristics. To conclude, we provide a perspective for potential further research