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

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. We briefly discuss the mathematical background of the solver, of which most part is covered in the Operations Research literature. Crew scheduling is crew planning for one or a few days that results in crew duties or pairings, and crew rostering is crew planning for at least one week for individual crew members. Technical issues about the system and its implementation are covered in more detail, as well as several applications. In particular, we focus on

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

A dynamic approach to vehicle scheduling

This paper presents a dynamic approach to the vehicle scheduling problem. We discuss the potential benefit of our approach compared to the traditional one, where the vehicle scheduling problem is solved only once for a whole period and the travel times are assumed to be fixed. In our dynamic approach, we solve a sequence of optimization problems, where we take into account different scenarios for future travel times. Because in the multiple-depot case we cannot solve the problem exactly within reasonable computation time, we use a "cluster-reschedule" heuristic where we first assign trips to depots by solving the static problem and then solve dynamic single-depot problems. We use new mathematical formulations of these problems that allow a fast solution by standard optimization software. We report on the results of a computational study with real life data, in which we compare different variants of our approach and perform a sensitivity analysis with respect to deviations of the actual travel times from the estimated ones

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

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

Models and techniques for hotel revenue management using a rolling horizon.

This paper studies decision rules for accepting reservations for stays in a hotel based on deterministic and stochastic mathematical programming techniques. Booking control strategies are constructed that include ideas for nesting, booking limits and bid prices. We allow for multiple day stays. Instead of optimizing a decision period consisting of a fixed set of target booking days, we simultaneously optimize the complete range of target booking dates that are open for booking at the moment of optimization. This yields a rolling horizon of overlapping decision periods, which will conveniently capture the effects of overlapping stays

Stochastic programming for multiple-leg network revenue management

Airline seat inventory control is a very profitable tool in the airline industry. Mathematical programming models provide booking limits or bid-prices for all itineraries and fare classes based on demand forecasts. But the actual revenue generated in the booking process fails to meet expectations. Simple deterministic models based on expected demand generate better revenue than more advanced probabilistic models. Recently suggested models put even more effort into demand forecasting. We will show that the dynamic booking process rather than the demand forecasts needs to be addressed. In particular the nesting strategies applied in booking control will counter-effect the profitability of advanced estimation of booking limits and bid-prices

Shunting of Passenger Train Units in a Railway Station

In this paper we introduce the problem of shunting passenger train units in a railway station. Shunting occurs whenever train units are temporarily not necessary to operate a given timetable. We discuss several aspects of this problem and focus on two subproblems. We propose mathematical models for these subproblems together with a solution method based on column generation. Furthermore, a new efficient and speedy solution technique for pricing problems in column generation algorithms is introduced. Finally, we present computational results based on real life instances from Netherlands Railways

Rostering at a Dutch Security Firm

The roster planning process at the Dutch security firm NVD was traditionally carried out by hand. A few year