Robust Airline Schedules

Due to economic pressure industries, when planning, tend to focus on optimizing the expected profit or the yield. The consequence of highly optimized solutions is an increased sensitivity to uncertainty. This generates additional "operational" costs, incurred by possible modifications of the original plan to be performed when reality does not reflect what was expected in the planning phase. The modern research trend focuses on "robustness" of solutions instead of yield or profit. Although robust solutions have a lower expected profit, they are less sensitive to noisy data and hence generate less operational costs. In this talk, we focus on the robustness of airline schedules. We compare different existing methods for "robust scheduling" on simulated data in order to analyze their performance. In particular, we analyze the consequences of erroneous prediction models on the performance of robust solutions. Simulations are based on the public data of the ROADEF Challenge 2009 (http://challenge.roadef.org/2009)

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

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

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

A Recovery Algorithm for a Disrupted Airline Schedule

The airline scheduling is a very large and complex problem. Moreover, it is common that only a minority of the initial schedules are carried out as planned because of delays, airport closures or other unforeseen events. Thus, given an actual state of the resources, a so called "disruption" arises when a schedule becomes unrealizable. The problem the scheduler is then faced with is to re-allocate the resources in order to get back to the initial schedule and to define what the priorities are: minimize the recovery time or minimize a given cost function. In this presentation, we will describe briefly a network model and a recovery algorithm based on column generation that solves the minimal cost recovery problem for a given maximal recovery time. We will focus the attention on the recovery network used at the pricing problem level. In particular we will describe some ideas that are useful to speed up the whole algorithm

Constraint-Specific Recovery Networks for Solving Airline Recovery Problems

In this paper, we consider the recovery of an airline schedule after an unforeseen event called disruption, making the planned schedule infeasible. We present a modeling framework that allows the consideration of operational constraints within a Column Generation (CG) scheme. We introduce the general concept of recovery network, generated for each individual unit of the problem, and show how unitspecific constraints are modeled using resources. We fully illustrate the concept by solving the Aircraft Recovery Problem (ARP) with maintenance planning, we give some insights into applying the model to the Passenger Recovery Problem (PRP) and we present computational results on real data. keywords: Airline scheduling, Recovery algorithms, Column generatio

Column Generation Methods for Disrupted Airline Schedules

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 a heterogeneous fleet of aircrafts, made of regular and reserve planes, where the maintenance constraints are explicitly taken into account and different maintenance constraints can be imposed. The aim is to find the optimal combination of routes within a given makespan for each plane in order to recover to the initial schedule, given the initial schedule and the disrupted state of the planes. We propose a column generation scheme based on a multicommodity network flow model, where each commodity represents a plane, a dynamic programming algorithm to build the underlying networks and a dynamic programming algorithm to solve the pricing problem. This project arises from a collaboration between EPFL and APM Technologies, which is a small company selling IT solutions to airlines. We provide some computational results on real world instances obtained from a medium size airline, Thomas Cook Airlines, one of APM main customers

Robust Optimization with Recovery: Application to Shortest Paths and Airline Scheduling

In this exploratory paper we consider a robust approach to decisional problems subject to uncertain data in which we have an additional knowledge on the strategy (algorithm) used to react to an unforeseen event or recover from a disruption. This is a typical situation in scheduling problems where the decision maker has no a priori knowledge on the probabilistic distribution of such events but he only knows rough information on the event, such as its impact on the schedule. We discuss a general framework to address this situation and its links with other existing methods, we present an illustrative example on the Shortest Path Problem with Interval Data (SPPID) and we discuss a more general application to airline scheduling with recovery

An algorithm for the recovery of disrupted airline schedules

We consider the recovery of an airline schedule after an unpredicted event, commonly called 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 maintenance constraints are explicitly taken into account and different maintenance constraints can be imposed. The aim is to find the optimal combination of routes within a given time horizon for each plane in order to recover to the initial schedule, given the initial schedule and the disrupted state of the planes. We present the main methodological ideas and numerical results illustrating the relevance of the method