Models and algorithms for Integration of Vehicle and Crew Scheduling

This paper deals with models, relaxations and algorithms for an integrated approach to vehicle and crew scheduling. We discuss potential benefits of integration and provide an overview of the literature, which considers mainly partial integration. Our approach is new in the sense that we can tackle integrated vehicle and crew scheduling problems of practical size.We propose new mathematical formulations for integrated vehicle and crew scheduling problems and we discuss corresponding Langrangian relaxations and Lagrangian heuristics. To solve the Lagrangian relaxations, we use column generation applied to set partitioning type of models. The paper is concluded with a computational study using real life data, which shows the applicability of the proposed techniques to practical problems. Furthermore, we also address the effectiveness of integration in different situations.Lagrangian relaxation;column generation;crew scheduling;integrated planning;vehicle scheduling

Models and algorithms for Integration of Vehicle and Crew Scheduling

This paper deals with models, relaxations and algorithms for an integrated approach to vehicle and crew scheduling. We discuss potential benefits of integration and provide an overview of the literature, which considers mainly partial integration. Our approach is new in the sense that we can tackle integrated vehicle and crew scheduling problems of practical size. We propose new mathematical formulations for integrated vehicle and crew scheduling problems and we discuss corresponding Langrangian relaxations and Lagrangian heuristics. To solve the Lagrangian relaxations, we use column generation applied to set partitioning type of models. The paper is concluded with a computational study using real life data, which shows the applicability of the proposed techniques to practical problems. Furthermore, we also address the effectiveness of integration in different situations

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 solution approach for dynamic vehicle and crew scheduling

In this paper, we discuss the dynamic vehicle and crew schedulingproblem and we propose a solution approach consisting of solving asequence of optimization problems. Furthermore, we explain why itis useful to consider such a dynamic approach and compare it witha static one. Moreover, we perform a sensitivity analysis on ourmain assumption that the travel times of the trips are knownexactly a certain amount of time before actual operation.We provide extensive computational results on some real-world datainstances of a large public transport company in the Netherlands.Due to the complexity of the vehicle and crew scheduling problem,we solve only small and medium-sized instances with such a dynamicapproach. We show that the results are good in the case of asingle depot. However, in the multiple-depot case, the dynamicapproach does not perform so well. We investigate why this is thecase and conclude that the fact that the instance has to be splitin several smaller ones, has a negative effect on the performance.transportation;vehicle and crew scheduling;large-scale optimization;dynamic planning

Multiple-Depot Integrated Vehicle and Crew Scheduling

This paper presents two different models and algorithms for integrated vehicle and crew scheduling in the multiple-depot case. The algorithms are both based on a combination of column generation and Lagrangian relaxation. Furthermore, we compare those integrated approaches with each other and with the traditional sequential one on random generated as well as real-world data instances for a suburban/extra-urban mass transit system. To simulate such a transit system, we propose a new way of generating randomly data instances such that their properties are the same as for our real-world instances

Integrated Dynamic Vehicle and Crew Scheduling Using Multi-Agent System

Vehicle and crew scheduling problem is remarkably difficult to solve because of the large number of resources that need to be allocated, very complex rules for the allocation of crew shifts, high cost of overtime and unpredictability of the urban traffic and crew availability. This article proposes a Multi-Agent System (ll/MS) approach to solve integrated dynamic vehicle and crew scheduling problems. MAS are capable of real-time scheduling and dynamic re-scheduling whenever unpredictable events and change of resources or demands occurs. This paper proposes a conceptual framework for an integrated and dynamic vehicle and crew scheduling by using the concept of MAS

Applying an Integrated Approach to Vehicle and Crew Scheduling in Practice

This paper deals with a practical application of an integrated approach to vehicle and crew scheduling, that we have developed previously. Computational results have shown that our approach can be applied to problems of practical size. However, application of the approach to the actual problems that one encounters in practice, is not always straightforward. This is mainly due to the existence of particular constraints that can be regarded as \\house rules" of the public transport company under consideration. In this paper we apply our approach to problems of individual bus lines of the RET, the Rotterdam public transport company, where particular constraints should be satisfied. Furthermore, we investigate the impact of allowing drivers to change vehicle during a break. Currently, the rule at the RET is that such changeovers are only allowed in split duties; they are never allowed in other type of duties. We show that it is already possible to save crews if for the non-split duties, restricted changeovers are allowed.Lagrangian relaxation;column generation;crew scheduling;integrated planning;vehicle scheduling

A solution approach for dynamic vehicle and crew scheduling

In this paper, we discuss the dynamic vehicle and crew scheduling problem and we propose a solution approach consisting of solving a sequence of optimization problems. Furthermore, we explain why it is useful to consider such a dynamic approach and compare it with a static one. Moreover, we perform a sensitivity analysis on our main assumption that the travel times of the trips are known exactly a certain amount of time before actual operation. We provide extensive computational results on some real-world data instances of a large public transport company in the Netherlands. Due to the complexity of the vehicle and crew scheduling problem, we solve only small and medium-sized instances with such a dynamic approach. We show that the results are good in the case of a single depot. However, in the multiple-depot case, the dynamic approach does not perform so well. We investigate why this is the case and conclude that the fact that the instance has to be split in several smaller ones, has a negative effect on the performance

Solving Public Transit Scheduling Problems

Operational planning within public transit companies has been extensively tackled but still remains a challenging area for operations research models and techniques. This phase of the planning process comprises vehicle scheduling, crew scheduling and rostering problems. In this paper, a new integer mathematical formulation to describe the integrated vehicle-crew-rostering problem is presented. The method proposed to solve this multi-objective problem is a sequential algorithm considered within a preemptive goal programming framework that starts from the solution of an integrated vehicle and crew scheduling problem and ends with the solution of a driver rostering problem. Feasible solutions for the vehicle and crew scheduling problem are obtained by combining a column generation scheme with a branch-and-bound method. These solutions are the input of the rostering problem, which is tackled through a mixed binary linear programming approach. An application to real data of a Portuguese bus company is reported and shows the importance of integrating the three scheduling problems

Solution Approaches for Vehicle and Crew Scheduling with Electric Buses

The use of electric buses is expected to rise due to its environmental benefits. However, electric vehicles are less exible than conventional diesel buses due to their limited driving range and longer recharging times. Therefore, scheduling electric vehicles adds further operational dificulties. Additionally, various labor regulations challenge public transport companies to find a cost-effcient crew schedule. Vehicle and crew scheduling problems essentially define the cost of operations. In practice, these two problems are often solved sequentially. In this paper, we introduce the integrated electric vehicle and crew scheduling problem (E-VCSP). Given a set of timetabled trips and recharging stations, the E-VCSP is concerned with finding vehicle and crew schedules that cover the timetabled trips and satisfy operational constraints, such as limited driving range of electric vehicles and labor regulations for the crew while minimizing total operational cost. An adaptive large neighborhood search that utilizes branch-and-price heuristics is proposed to tackle the E-VCSP. The proposed method is tested on real-life instances from public transport companies in Denmark and Sweden that contain up to 1,109 timetabled trips. The heuristic approach provides evidence of improving efficiency of transport systems when the electric vehicle and crew scheduling aspects are considered simultaneously. By comparing to the traditional sequential approach, the heuristic finds improvements in the range of 1.17-4.37% on average. A sensitivity analysis of the electric bus technology is carried out to indicate its implications for the crew schedule and the total operational cost. The analysis shows that the operational cost decreases with increasing driving range (120 to 250 kilometers) of electric vehicles