An Approach to Vehicle Scheduling with Depot Capacity Constraints

Lamatsch, Achim

doi:10.1007/978-3-642-85968-7_13

Cited by 18 publications

(7 citation statements)

References 7 publications

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“…However, due to the fact that the MVSP is NP-hard when D ~ 2 (Bertossi / Carraresi / Gallo (1987» , no polynomial time optimal algorithms are known for this problem. Hence, several heuristics have been proposed for the MVSP (see Bodin / Rosenfield / Kydes (1978), Ceder / Stem (1981), Smith / Wren (1981), EI-Azm (1985), Bertossi / Carraresi / Gallo (1987), Lamatsch (1992), Mesquita / Paixiio (1992». Another solution approach (Daduna / Mojsilovic (1988) is based on a model with a specific structure of the arc costs to solve the MVSP using an assignment algorithm.…”

Section: Br Vehicle Scheduling Problemsmentioning

confidence: 99%

Vehicle Scheduling for Public Mass Transit — An Overview

Daduna

Paixão

1995

Lecture Notes in Economics and Mathematical Systems

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Vehicle scheduling always plays an important role in urban mass transit companies. Efficient schedules of a given timetable have a significant influence on the demand for vehicles and, hence, the demand for personnel. This means that the economic results of a urban mass transit company are closely linked to the planning activities in this area.The objective of the paper is to show the state of the research in vehicle scheduling and its practical application in urban mass transit companies. First a brief outline of the historical developments is given. Subsequently, different retrictions for the vehicle scheduling problem are structured and explained. Some models and their mathematical formulation are described, whereby the questions of incorporating restrictions is an important issue. A depiction of solution possibilities offered by program systems for computer-aided scheduling in operational use and expierences from urban mass transit companies complete the remarks. 1Introduction The vehicle scheduling is an important step in the planning process in public transit companies. This counts both for vehicle operations as for manpower planning. From the maximal number of blocks (during a certain time of the operating day) one gets a lower bound on the needed vehicles, consequently this strongly influences the fleet size. But this number of vehicles and the total duration of all blocks determines also in an important range the need in manpower.In spite of these facts the application of computer technology in public mass transit did not originate with planning vehicle or duty schedules. Initially, during the sixties the use of computer-aided systems was focused only on processing timetable data, especially to produce timetable booklets and wall timetable. Because the timetable data has been available on storage devices, later the idea grew up, to make use of these data flles for other planning problems. In this context the vehicle scheduling problem (VSP) came to the fore.The results were at first not satisfying because the cost-to-performance ratio of available computers and also the the efficiency of the existing implementations of algorithms was not sufficient But step by step, parallel to the extreme development on computer technology and efficient algorithms, computer-aided planning systems got more and more importance in public transit planning. Today there are many public mass transit companies which make

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Section: Br Vehicle Scheduling Problemsmentioning

confidence: 99%

Vehicle Scheduling for Public Mass Transit — An Overview

Daduna

Paixão

1995

Lecture Notes in Economics and Mathematical Systems

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“…In MDVSP [6][7][8][9][10][11][12][13][14][15][16][17][18][19] vehicles are housed at the different depots, but each block of trips starts and ends at the same depot [10]. MDVSP are NP-hard [6].…”

Section: Related Workmentioning

confidence: 99%

“…By including time windows in a VSP, it is allowed to shift scheduled trips within defined interval, in order to introduce flexibility in the departure times of trips [20]. Capacity constraints of depots are also considered [17].…”

Section: Related Workmentioning

confidence: 99%

“…In constraints (16), it is ensured that each task in CT that starts in a PI depot, ends in a PF depot. In constraints (17) and 18 (22) to (24) guarantee that a task that requires a special bus, is performed by a bus with these characteristics. (34) and (35) are the first two terms of the objective function, according to the operators' objectives:…”

Section: Mathematical Programming Formulationmentioning

confidence: 99%

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A model for solving vehicle scheduling problems a case study

Baldoquín

Rengifo-Campo²

2018

Rev. Fac. Ing. Univ. Antioquia

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In this work we formulate a model to solve a type of vehicle scheduling problem, derived from the operation of the mass transit system (MIO) in Cali city, Colombia. Four companies operate the system with 3 types of buses and four depots. Two kinds of tasks should be assigned to operators' buses. A task is a sequence of consecutive travels of a route between two stations: initial and final. Each task should start and should finish in a depot, not necessarily the same. There are two main objectives defined by the operators. One objective is to minimize the total deadhead kilometers between depots and stations where tasks should start or end. The other objective is to minimize the maximum deviation of kilometers (commercial and deadhead) assigned to the operators regarding the ideal quantity of kilometers that they should have, according to the number of their buses in the fleet. We have implemented the proposed model in AMPL using Gurobi solver and we validate it using nine representative instances, generated with real data obtained from the system operation. The results obtained, in all cases, improve the solutions proposed by the company. Model variations are proposed to deal with new desirable constraints for the company. RESUMEN: En este trabajo se formula un modelo para resolver un tipo de problema de programación de vehículos, derivado de la operación del sistema de transporte masivo (MIO) en la ciudad de Cali, Colombia. Cuatro compañías operan el sistema con 3 tipos de buses y cuatro patios. Dos tipos de tareas deben asignarse a los buses de los operadores. Una tarea es una secuencia de viajes consecutivos de una ruta entre dos estaciones: inicial y final. Cada tarea debe comenzar y debe terminar en un patio, no necesariamente el mismo. Hay dos objetivos principales definidos por los operadores. Un objetivo es minimizar el total de kilómetros en vacío entre patios y estaciones donde las tareas deben comenzar o terminar. El otro objetivo es minimizar la desviación máxima de kilómetros (comercial y en vacío) asignada a los operadores con respecto a la cantidad ideal de kilómetros que deberían tener, según el número de sus buses en la flota. El modelo propuesto se implementa con el software Gurobi, utilizando nueve instancias representativas generadas con datos reales obtenidos de la operación del sistema. Todos los resultados obtenidos mejoran las soluciones propuestas por la empresa. Se proponen variaciones del modelo para considerar nuevas restricciones deseables para la empresa.

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“…Their heuristic, based on finding shortest paths that avoid certain arcs in a network, ensures that the minimum possible number of trucks are used. Two heuristics for the MDVSP, based on Lagrangian relaxations, are found in Lamatsch (1992) and Mesquita and Paixão (1992).…”

Section: Introductionmentioning

confidence: 99%

Vehicle Routing and Scheduling with Full Truckloads

Arunapuram¹,

Mathur

Solow

2003

Transportation Science

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T ruckload carriers are constantly faced with the problem of shipping full truckloads of goods at minimum cost between pairs of cities or customers, using a fleet of trucks located at one or more depots. In this paper, a new branch-and-bound algorithm for solving an integer-programming formulation of this vehicle-routing problem (VRP) with full truckloads is developed. The algorithm also takes into consideration the time-window constraints and waiting costs. The resulting efficiency, validated by computational tests on random problems, is due to a column-generation scheme that exploits the special structure of the problem to solve the linear-programming relaxation problems that arise at the nodes.

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An Approach to Vehicle Scheduling with Depot Capacity Constraints

Cited by 18 publications

References 7 publications

Vehicle Scheduling for Public Mass Transit — An Overview

Vehicle Scheduling for Public Mass Transit — An Overview

A model for solving vehicle scheduling problems a case study

Vehicle Routing and Scheduling with Full Truckloads

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