Robust crew pairing for managing extra flights /

The airline industry encounters many optimization problems such as scheduling flights, assigning the fleet, scheduling the crew. Among them, the crew scheduling problem is the most studied one. The main reason is that the crew cost is one of the largest components of the operational cost for an airline company. Therefore, there are many models proposed in the literature to find a cost efficient crew schedule. Most of those models divide the crew scheduling problem into two separate problems, namely the crew pairing and the crew assignment problems. The crew pairing problem that we study here aims at finding the least costly subset of pairings, which cover the scheduled flights. Although there are many approaches to solve the crew pairing problem, most of them assume no disruptions during the operation. However disruptions due to weather conditions, maintenance problems, and so on are common problems leading to higher operational crew cost in practice. These kinds of disruptions result in delaying or canceling some scheduled flights. Another disruption that local airline companies face is adding an extra flight to predetermined (regular) flight schedule. In this study, we propose a model that provides robust crew pairing schedule in the case of adding an extra flight to the regular flight schedule. Two solution approaches are along with the mathematical model are proposed. The objective of the proposed model is to maximize the total number of solutions, while maintaining the increase in the crew cost at an acceptable level. A crew pairing problem is then solved by both the proposed model and the conventional model. Finally, computational experiments are conducted to demonstrate the benefits of the proposed model

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

Column generation approaches to a robust airline crew pairing model for managing extra flights

A typical airline crew pairing problem aims at selecting a set of flight sequences (pairings) for crews such that each flight in the regular schedule is covered by one crew. In this thesis, we consider the management of potential extra flights that can possibly be introduced to the regular flight schedule during operation at a later point in time. Without delaying or canceling any existing flight, we try to handle these extra flights within the regular schedule and refer to the resulting mathematical model as a robust airline crew pairing model. The objective function of the robust model involves not only the regular pairing costs but also the opportunity costs for failing to cover the extra flights. Due to the large number of variables (pairings), a typical crew pairing model is usually solved by column generation methods. Before applying column generation to the proposed robust model, we first discuss several procedures to cover the extra flights by a given set of feasible pairings. However, these procedures introduce extra column-dependent constraints to the model. That is, as new columns are added by column generation to the model, the number of constraints may also increase. Similarly if a column is removed from the model, then some of these extra constraints may be deleted. To handle this dynamic change both in the number of constraints and variables we propose two approaches. The main idea behind these approaches is to generate a set of pairings (column pool) so that the number of constraints can be fixed. To this end, we flag the pairings that can be used for covering the extra flights and keep them in a special pool. We illustrate the proposed column generation approaches on a set of actual data acquired from a local airline