Richard Freling

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 for an urban mass transit system with a single depot. 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 Lagrangian 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.

Mathematical Programming for Network Revenue Management Revisited

Mathematical programming models for airline seat inventory control provide booking limits and bid-prices for all itineraries and fare classes. E.L. Williamson [Airline network seat inventory control: methodologies and revenue impacts, Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA, 1992] finds that simple deterministic approximation methods based on average demand often outperform more advanced probabilistic heuristics. We argue that this phenomenon is due to a booking process that includes nesting of the fare classes, which is ignored in the modeling phase. The differences in the performance between these approximations are studied using a stochastic programming model that includes the deterministic model as a special case. Our study carefully examines the trade-off between computation time and the aggregation level of demand uncertainty with examples of a multi-leg flight and a single-hub network.

Models and Algorithms for Single-Depot Vehicle Scheduling

Vehicle scheduling is the process of assigning vehicles to a set of predetermined trips with fixed starting and ending times, while minimizing capital and operating costs. This paper considers modeling, algorithmic, and computational aspects of the polynomially solvable case in which there is a single depot and vehicles are identical. A quasiassignment formulation is reviewed and an alternative asymmetric assignment formulation is given. The main contributions of the paper are a new two-phase approach which is valid in the case of a special cost structure, an auction algorithm for the quasiassignment problem, a core-oriented approach, and an extensive computational study. New algorithms are compared with the most successful algorithms for the vehicle-scheduling problem, using both randomly generated and real-life data. The new algorithms show a significant performance improvement with respect to computation time. Such improvement can, for example, be very important when this particular vehicle-scheduling problem appears as a subproblem in more complex vehicle- and crew-scheduling problems.

A decision support system for crew planning in passenger transportation using a flexible branch-and-price algorithm

This paper discusses a decision support system for airline and railway crew planning. The system is a state-of-the-art branch-and-price solver that is used for crew scheduling and crew rostering. Since it is far from trivial to build such a system from the information provided in the existing literature, technical issues about the system and its implementation are covered in more detail. We also discuss several applications. In particular, we focus on a specific aircrew rostering application. The computational results contain an interesting comparison of results obtained with the approach in which crew scheduling is carried out before crew rostering, and an approach in which these two planning problems are solved in an integrated manner.

An Overview of Models and Techniques for Integrating Vehicle and Crew Scheduling

In this paper, the problem of integrating vehicle and crew scheduling is considered. Traditionally, vehicle and crew scheduling have been dealt with in a sequential manner, where vehicle schedules are determined before the crew schedules. The few papers that have appeared in the literature have in common that no comparison is made between simultaneous and sequential scheduling, so there is no indication of the benefit of a simultaneous approach. In order to get such an indication before even solving the integrated problem, we propose a method to solve crew scheduling independently of vehicle scheduling. We introduce a mathematical formulation for the integrated problem, and briefly outline algorithms. The paper concludes with computational results for an application to bus scheduling at the public transport company RET in Rotterdam, The Netherlands. The results show that the proposed techniques are applicable in practice. Furthermore, we conclude that the effectiveness of integration as compared to a sequential approach is mainly dependent on the flexibility in changing buses during a duty.

A Branch-and-Price Algorithm for the Multiperiod Single-Sourcing Problem

In this paper, we propose a multiperiod single-sourcing problem (MPSSP), which takes both transportation and inventory into consideration, suitable for evaluating the performance of a logistics distribution network in a dynamic environment. We reformulate the MPSSP as a Generalized Assignment Problem (GAP) with a convex objective function. We then extend a branch-and-price algorithm that was developed for the GAP to this problem. The pricing problem is a so-called Penalized Knapsack Problem (PKP), which is a knapsack problem where the objective function includes an additional convex term penalizing the total use of capacity of the knapsack. The optimal solution of the relaxation of the integrality constraints in the PKP shows a similar structure to the optimal solution of the knapsack problem, that allows for an efficient solution procedure for the pricing problem. We perform an extensive numerical study of the branch-and-price algorithm.

Scheduling train crews: a case study for the Dutch Railways

In this paper the problem of scheduling train crew is considered. We discuss a general framework of which the method for solving the train crew scheduling problem is a special case. In particular, our method is a heuristic branch-and-price algorithm suitable for large scale crew scheduling problems. This algorithm is applied to a real life train guard scheduling problem which is provided to us by the Dutch Railways. Computational results show that our algorithm is capable of getting sub-optimal solutions for a large scale instance within reasonable computation time.

Vehicle Scheduling with Time Constraint

We present methods for solving the vehicle scheduling problem with time constraint. Such problem consists of minimizing the costs related to the assignment of vehicles for performing a set of short trips. The vehicles are located at a single depot and one must consider the additional constraint that no vehicle can be away from the depot longer than a maximum time period. For two integer programming models we consider the corresponding Linear Programming and Lagrangean relaxations. The mathematical programming approach as well as a heuristic approach are tested on real-life problems.