An integrated mathematical model of crew scheduling

In conditions of air transport companies, the process of planning flight schedules is one of the most important processes each airline has to deal with. The flight schedule planning process consists of several consecutive plans. The first step of the planning process is defining which air routes will be operated, the decision is based on the business plan of the air transport company. Consequently, suitable airplanes have to be assigned to the individual air routes. And finally, on the basis of the pre-vious steps shifts of pilots can be planned, the shifts are usually planned one month in advance. However, with no respect to the created plan some unexpected disruptions of the flying staff, especially of the pilots, may happen in practice due to many reasons. In such cases the original plan has to be modified in order to react to the disruptions. The modifications can represent an optimisation problem – the air transport company has a set of the pilots and on the basis of their qualification and experience the company has to create new aircrews. The pilots can be found in different localities that are different from the airports of the planned flight departures. That means the newly planned aircrews are assigned to the individual flights with respect to costs associated with transportation of the aircrews to the airports of their departure. The problem can be solved by many approaches. One of the possible approaches is a heuristic approach which is based on sequential solving two linear mathematical models. The first model decides about the aircrews (matches the pilots with respect to their compatibility). The second model solves the assignment problem – the air-crews are matched with the individual flights. The article presents an integrated linear model which deals with both problems at the same time.V podmínkách leteckých dopravců je hlavním výsledkem plánovacího procesu letový řád. Samotná tvorba letového řádu je posloupností několika na sebe navazujících dílčích plánů. Prvním krokem v procesu plánování je naplánování linek podle obchodního záměru dopravce, následně se naplánovaným letům přidělí konkrétní typ letadla. Zpravidla s měsíčním předstihem je nutné vytvořit plán práce pro posádky pilotů, kteří budou letouny obsluhovat. Bez ohledu na vytvořený plán práce posádek však může dojít k neočekávaným výpadkům personálu. Potom je nutné operativně upravit připravený plán a posádky přeplánovat. Jedná se tedy o optimalizační problém, kdy dopravce má k dispozici množinu pilotů, z nichž je nutné na základě jejich kvalifikace a zkušeností vytvořit nové posádky. Piloti se mohou nacházet v různých destinacích, které mohou být různé od letišť odletů. Nově vytvořené posádky jsou potom přidělovány konkrétním letadlům v závislosti na velikosti nákladů spojených s přepravou posádek k letadlům. Uvedený problém lze řešit různými způsoby. První způsob je heuristický založený na postupném řešení dvou lineárních modelů. V prvním modelu se rozhoduje o vytvoření posádek. Druhý model vytvořené posádky přiděluje letadlům. Cílem tohoto příspěvku bude prezentovat integrovaný lineární model řešící oba problémy současně

Solving a robust airline crew pairing problem with column generation

In this study, we solve a robust version of the airline crew pairing problem. Our concept of robustness was partially shaped during our discussions with small local airlines in Turkey which may have to add a set of extra flights into their schedule at short notice during operation. Thus, robustness in this case is related to the ability of accommodating these extra flights at the time of operation by disrupting the original plans as minimally as possible. We focus on the crew pairing aspect of robustness and prescribe that the planned crew pairings incorporate a number of predefined recovery solutions for each potential extra flight. These solutions are implemented only if necessary for recovery purposes and involve either inserting an extra flight into an existing pairing or partially swapping the flights in two existing pairings in order to cover an extra flight. The resulting mathematical programming model follows the conventional set covering formulation of the airline crew pairing problem typically solved by column generation with an additional complication. The model includes constraints that depend on the columns due to the robustness consideration and grows not only column-wise but also row-wise as new columns are generated. To solve this dicult model, we propose a row and column generation approach. This approach requires a set of modifications to the multi-label shortest path problem for pricing out new columns (pairings) and various mechanisms to handle the simultaneous increase in the number of rows and columns in the restricted master problem during column generation. We conduct computational experiments on a set of real instances compiled from a local airline in Turkey

Disruption management in passenger railway transportation.

This paper deals with disruption management in passengerrailway transportation. In the disruption management process, manyactors belonging to different organizations play a role. In this paperwe therefore describe the process itself and the roles of thedifferent actors.Furthermore, we discuss the three main subproblems in railwaydisruption management: timetable adjustment, and rolling stock andcrew re-scheduling. Next to a general description of these problems,we give an overview of the existing literature and we present somedetails of the specific situations at DSB S-tog and NS. These arethe railway operators in the suburban area of Copenhagen, Denmark,and on the main railway lines in the Netherlands, respectively.Since not much research has been carried out yet on OperationsResearch models for disruption management in the railway context,models and techniques that have been developed for related problemsin the airline world are discussed as well.Finally, we address the integration of the re-scheduling processesof the timetable, and the resources rolling stock and crew.

Advanced periodic maintenance scheduling methods for aircraft lifecycle management

This paper reviews existing methods and techniques addressing the problem of maintenance support throughout the life cycle for high value manufacturing products such as aircrafts. As part of this doctorate research the analysis of current methods of maintenance scheduling was conducted. In order to contribute to a more comprehensive solution, an advanced approach (algorithm) of periodic maintenance is presented. The authors believe that this approach will reduce the cost of maintenance of high value manufacturing products. The algorithm based on constraint programming methods is briefly presented and the future research directions are discussed

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