Combining robustness and recovery for airline schedules

In this thesis, we address different aspects of the airline scheduling problem. The main difficulty in this field lies in the combinatorial complexity of the problems. Furthermore, as airline schedules are often faced with perturbations called disruptions (bad weather conditions, technical failures, congestion, crew illness…), planning for better performance under uncertainty is an additional dimension to the complexity of the problem. Our main focus is to develop better schedules that are less sensitive to perturbations and, when severe disruptions occur, are easier to recover. The former property is known as robustness and the latter is called recoverability. We start the thesis by addressing the problem of recovering a disrupted schedule. We present a general model, the constraint-specific recovery network, that encodes all feasible recovery schemes of any unit of the recovery problem. A unit is an aircraft, a crew member or a passenger and its recovery scheme is a new route, pairing or itinerary, respectively. We show how to model the Aircraft Recovery Problem (ARP) and the Passenger Recovery Problem (PRP), and provide computational results for both of them. Next, we present a general framework to solve problems subject to uncertainty: the Uncertainty Feature Optimization (UFO) framework, which implicitly embeds the uncertainty the problem is prone to. We show that UFO is a generalization of existing methods relying on explicit uncertainty models. Furthermore, we show that by implicitly considering uncertainty, we not only save the effort of modeling an explicit uncertainty set: we also protect against possible errors in its modeling. We then show that combining existing methods using explicit uncertainty characterization with UFO leads to more stable solutions with respect to changes in the noise's nature. We illustrate these concepts with extensive simulations on the Multi-Dimensional Knapsack Problem (MDKP). We then apply the UFO to airline scheduling. First, we study how robustness is defined in airline scheduling and then compare robustness of UFO models against existing models in the literature. We observe that the performance of the solutions closely depend on the way the performance is evaluated. UFO solutions seem to perform well globally, but models using explicit uncertainty have a better potential when focusing on a specific metric. Finally, we study the recoverability of UFO solutions with respect to the recovery algorithm we develop. Computational results on a European airline show that UFO solutions are able to significantly reduce recovery costs

Robust scheduling and disruption recovery for airlines

Airline planning include complex and structured operations that must be planned in advance in order to exploit the available resources, provide a reliable and competitive service and forecast system's performances. Decisions regarding operations are based on data which is frequently due to uncertainty. Moreover, unpredicted events may disrupt the current schedule and force managers to take reactive decisions to recover to an operational state. On the other hand, proactive decisions, i.e. decisions which take into account the uncertainty of the data, tend to robust solutions which are able to absorb data deviation and small disruptions. In this talk we address the aircraft routing problem from both reactive and proactive point of view and suggest ways to integrate the two approaches to reach what we call a robust recoverable approach for aircraft routing, i.e. a proactive strategy which accounts for the presence of a disruption recovery strategy. We validate our ideas with a computational study based on real world data provided by a major european airline

Uncertainty Feature Optimization for the Airline Scheduling Problem

Uncertainty Feature Optimization is a framework to cope with optimization problems due to noisy data, using an implicit characterazation of the noise. The Aircraft Scheduling Problem (ASP) is a particular case of such problems, where disruptions randomly perturbate the original flight schedule. This study uses the UFO framework to generate more robust and recoverable schedules, in the sense that more delays are absorbed and when re-optimization is required, the corresponding recovery costs are reduced. We provide computational results for the public data of an European airline provided for the ROADEF Challenge 2009 footnote{\texttt{http://challenge.roadef.or /2009/index.en.htm}}; new schedules are computed with different models, and we compare the a posteriori results obtained by the application of a recovery algorithm

Congestion in a competitive world: a study of the impact of competition on airline operations

Air transport is a fast developing area. Airlines compete for a limited resource, namely airport capacity. The consequence is an increase in airport congestion, which generates huge delays that are enhanced due to delay propagation through the whole network. Currently, in the US, the Federal Aviation Association (FAA) only controls operational capacity allocation when disruptions occur with Ground Delay Programs (GDPs), and airlines are free to schedule their operations. In this paper, we propose a theoretical framework allowing to evaluate different regulations or incentives

Robust and Recoverable Maintenance Routing Schedules

We present a methodology to compute more efficient airline sched-ules that are less sensitive to delay and can be recovered at lower cost in case of severe disruptions. We modify an original schedule by flight re-timing with the intent of improving some structural properties of the schedule. We then apply the new schedules on different disruption scenarios and then recover the disrupted schedule with the same recovery algorithm. We show that solutions with improved structural properties better absorb delays and are more efficiently recoverable than the original schedule. We provide computational evidence using the public data provided by the ROADEF Challenge 20091

A column generation algorithm for disrupted airline schedules

We consider the recovery of an airline schedule after an unforeseen event, called {\em disruption}, that makes the planned schedule unfeasible. In particular we consider the aircraft recovery problem for a heterogeneous fleet of aircrafts, made of regular and reserve planes, where the aircrafts' maintenances are planned in an optimal way in order to satisfy the operational regulations. We propose a column generation scheme, where the pricing problem is modeled as a commodity flow problem on a dedicated network, one for each plane of the fleet. We present a dynamic programming algorithm to build the underlying networks and a dynamic programming algorithm for resource constrained elementary shortest paths to solve the pricing problem. We provide some computational results on real world instances

Optimization of Uncertainty Features for Transportation Problems

In this work we present the concept of Uncertainty Feature Optimization (UFO), an optimization framework to handle problems due to noisy data. We show that UFO is an extension of standard methods as robust optimization and stochastic optimization and we show that the method can be used when no information of the data uncertainty sets is available. We present a proof of concept for the multiple knapsack problem and we show applications to some routing problems: vehicle routing with stochastic demands and airline scheduling

Airline Disruptions: Aircraft Recovery with Maintenance Constraints

In this paper we consider the recovery of an airline schedule after an unforeseen event, commonly called disruption, that makes the planned schedule unfeasible. In particular we consider the aircraft recovery problem for an heterogeneous fleet of aircrafts, made of regular and reserve planes, where the maintenance constraints are explicitly taken into account. We propose a multicommodity network flow model, where each commodity represents a plane, a dynamic programming algorithm to build the underlying network and an heuristic algorithm based on column generation. We provide some computational results on instances obtained from a medium-sized airline