SOLVING MULTI-SCHOOL BUS ROUTING AND SCHEDULING PROBLEM

School bus routing and scheduling is of huge importance in school transportation system operations. It is usually treated as two separated problems and is solved sequentially. But it is shown that such separation will lead to a worse solution than solving them together with respect to the number of buses and travel time. The rationale behind it and the key point connecting routing and scheduling problem – trip compatibility – is thus deeply studied. A Mixed Integer Programming model is proposed along with a School Decomposition Algorithm. The model and algorithm are tested on eight sets of randomly-generated mid-size problems in comparison to the existing models. The results show that the proposed model and algorithm can find a better solution using up to 30% fewer buses than the best traditional models in a reasonable amount of time

Combining Column Generation and Lagrangian Relaxation

Although the possibility to combine column generation and Lagrangian relaxation has been known for quite some time, it has only recently been exploited in algorithms. In this paper, we discuss ways of combining these techniques. We focus on solving the LP relaxation of the Dantzig-Wolfe master problem. In a first approach we apply Lagrangian relaxation directly to this extended formulation, i.e. no simplex method is used. In a second one, we use Lagrangian relaxation to generate new columns, that is Lagrangian relaxation is applied to the compact for-mulation. We will illustrate the ideas behind these algorithms with an application in Lot-sizing. To show the wide applicability of these techniques, we also discuss applications in integrated vehicle and crew scheduling, plant location and cutting stock problems.column generation;Lagrangean relaxation;cutting stock problem;lotsizing;vehicle and crew scheduling

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

Mathematics in the Supply Chain

[no abstract available

Operations research in passenger railway transportation

In this paper, we give an overview of state-of-the-art OperationsResearch models and techniques used in passenger railwaytransportation. For each planning phase (strategic, tactical andoperational), we describe the planning problems arising there anddiscuss some models and algorithms to solve them. We do not onlyconsider classical, well-known topics such as timetabling, rollingstock scheduling and crew scheduling, but we also discuss somerecently developed topics as shunting and reliability oftimetables.Finally, we focus on several practical aspects for each of theseproblems at the largest Dutch railway operator, NS Reizigers.passenger railway transportation;operation research;planning problems

An estimation of distribution algorithm for combinatorial optimization problems

This paper considers solving more than one combinatorial problem considered some of the most difficult to solve in the combinatorial optimization field, such as the job shop scheduling problem (JSSP), the vehicle routing problem with time windows (VRPTW), and the quay crane scheduling problem (QCSP). A hybrid metaheuristic algorithm that integrates the Mallows model and the Moth-flame algorithm solves these problems. Through an exponential function, the Mallows model emulates the solution space distribution for the problems; meanwhile, the Moth-flame algorithm is in charge of determining how to produce the offspring by a geometric function that helps identify the new solutions. The proposed metaheuristic, called HEDAMMF (Hybrid Estimation of Distribution Algorithm with Mallows model and Moth-Flame algorithm), improves the performance of recent algorithms. Although knowing the algebra of permutations is required to understand the proposed metaheuristic, utilizing the HEDAMMF is justified because certain problems are fixed differently under different circumstances. These problems do not share the same objective function (fitness) and/or the same constraints. Therefore, it is not possible to use a single model problem. The aforementioned approach is able to outperform recent algorithms under different metrics for these three combinatorial problems. Finally, it is possible to conclude that the hybrid metaheuristics have a better performance, or equal in effectiveness than recent algorithms

REVISIÓN DE LA LITERATURA DEL PROBLEMA DE RUTEO DE VEHÍCULOS EN UN CONTEXTO DE TRANSPORTE VERDE

In the efficient management of the supply chain the optimal management of transport of consumables and finished products appears. The costs associated with transport have direct impact on the final value consumers must pay, which in addition to requiring competitive products also demand that they are generated in environmentally friendly organizations. Aware of this reality, this document is intended to be a starting point for Master's and Doctoral degree students who want to work in a line of research recently proposed: green routing. The state of the art of the vehicle routing problem is presented in this paper, listing its variants, models and methodologies for solution. Furthermore, the proposed interaction between variants of classical routing problems and environmental effects of its operations, known in the literature as Green-VRP is presented. The goal is to generate a discussion in which mathematical models and solution strategies that can be applied within organizations that consider within their objectives an efficient and sustainable operation are posed. En el gerenciamiento eficiente de la cadena de suministro aparece la gestión óptima del transporte de insumos y productos terminados. Los costos asociados al transporte tienen impacto directo sobre el valor final que deben pagar los consumidores, que además de requerir productos competitivos también exigen que los mismos sean generados en organizaciones amigables con el medioambiente. Consientes de esa realidad este documento pretende ser un punto de partida para estudiantes de maestría y doctorado que quieran trabajar en una línea de investigación propuesta recientemente: el ruteo verde. En este trabajo se muestra un estado del arte del problema de ruteo de vehículos, enumerando sus variantes, modelos y metodologías de solución. Además, se presenta la interacción que se ha propuesto entre variantes clásicas de los problemas de ruteo y los efectos ambientales de su operación, denominados en la literatura como Green-VRP. El objetivo es generar una discusión donde se planteen modelos matemáticos y estrategias de solución que puedan ser aplicadas en organizaciones que consideren dentro de sus objetivos una operación eficiente y sustentable. Document type: Articl

Revisión de la literatura del problema de ruteo de vehículos en un contexto de transporte verde

In the efficient management of the supply chain the optimal management of transport of consumables and finished products appears. The costs associated with transport have direct impact on the final value consumers must pay, which in addition to requiring competitive products also demand that they are generated in environmentally friendly organizations. Aware of this reality, this document is intended to be a starting point for Master’s and Doctoral degree students who want to work in a line of research recently proposed: green routing. The state of the art of the vehicle routing problem is presented in this paper, listing its variants, models and methodologies for solution. Furthermore, the proposed interaction between variants of classical routing problems and environmental effects of its operations, known in the literature as Green- VRP is presented. The goal is to generate a discussion in which mathematical models and solution strategies that can be applied within organizations that consider within their objectives an efficient and sustainable operation are posed.En el gerenciamiento eficiente de la cadena de suministro aparece la gestión óptima del transporte de insumos y productos terminados. Los costos asociados al transporte tienen impacto directo sobre el valor final que deben pagar los consumidores, que además de requerir productos competitivos también exigen que los mismos sean generados en organizaciones amigables con el medioambiente. Consientes de esa realidad este documento pretende ser un punto de partida para estudiantes de maestría y doctorado que quieran trabajar en una línea de investigación propuesta recientemente: el ruteo verde. En este trabajo se muestra un estado del arte del problema de ruteo de vehículos, enumerando sus variantes, modelos y metodologías de solución. Además, se presenta la interacción que se ha propuesto entre variantes clásicas de los problemas de ruteo y los efectos ambientales de su operación, denominados en la literatura como Green-VRP. El objetivo es generar una discusión donde se planteen modelos matemáticos y estrategias de solución que puedan ser aplicadas en organizaciones que consideren dentro de sus objetivos una operación eficiente y sustentable