The Integrated Aircraft Routing and Crew Pairing Problem: ILP Based Formulations

Minimization of cost is very important in airline as great profit is an important objective for any airline system. One way to minimize the costs in airline is by developing an integrated planning process. Airline planning consists of many difficult operational decision problems including aircraft routing and crew pairing problems. These two sub-problems, though interrelated in practice, are usually solved sequentially leading to suboptimal solutions. We propose an integrated aircraft routing and crew pairing problem model, one approach to generate the feasible aircraft routes and crew pairs, followed by three approaches to solve the integrated model. The integrated aircraft routing and crew scheduling problem is to determine a minimum cost aircraft routes and crew schedules while each flight leg is covered by one aircraft and one crew. The first approach is an integer programming solution method, the second formulation is developed in a way to lend itself to be used efficiently by Dantzig Wolfe decomposition whereas the third one is formulated as a Benders decomposition method. Encouraging results are obtained when tested on four types of aircraft based on local flights in Malaysia for one week flight cycle

A decomposition approach to the integrated vehicle-crew-rostering problem

The problem addressed in this paper is the integrated vehicle-crew-rostering problem (VCRP) aiming to define the schedules for the buses and the rosters for the drivers of a public transit company. The VCRP is described by a bi-objective mixed binary linear programming model with one objective function aggregating vehicle and crew scheduling costs and the other the rostering features. The VCRP is solved by a heuristic approach based on Benders decomposition where the master problem is partitioned into daily integrated vehicle-crew scheduling problems and the sub-problem is a rostering problem. Computational experience with data from a bus company in Lisbon shows the ability of the decomposition approach for producing a variety of potentially efficient solutions for the VCRP within low computing times

The Recoverable Robust Tail Assignment Problem

This is the author accepted manuscript. The final version is available from Institute for Operations Research and the Management Sciences (INFORMS) via the DOI in this record Schedule disruptions are commonplace in the airline industry with many flight-delaying events occurring each day. Recently there has been a focus on introducing robustness into airline planning stages to reduce the effect of these disruptions. We propose a recoverable robustness technique as an alternative to robust optimisation to reduce the effect of disruptions and the cost of recovery. We formulate the recoverable robust tail assignment problem (RRTAP) as a stochastic program, solved using column generation in the master and subproblems of the Benders decomposition. We implement a two-phase algorithm for the Benders decomposition incorporating the Magnanti-Wong [21] enhancement techniques. The RRTAP includes costs due to flight delays, cancellation, and passenger rerouting, and the recovery stage includes cancellation, delay, and swapping options. To highlight the benefits of simultaneously solving planning and recovery problems in the RRTAP we compare our tail assignment solution with the tail assignment generated using a connection cost function presented in Gr¨onkvist [15]. Using airline data we demonstrate that by developing a better tail assignment plan via the RRTAP framework, one can reduce recovery costs in the event of a disruption.Australian Research Council Centre of Excellence for MathematicsMASCOS

Large-scale mixed integer optimization approaches for scheduling airline operations under irregularity

Perhaps no single industry has benefited more from advancements in computation, analytics, and optimization than the airline industry. Operations Research (OR) is now ubiquitous in the way airlines develop their schedules, price their itineraries, manage their fleet, route their aircraft, and schedule their crew. These problems, among others, are well-known to industry practitioners and academics alike and arise within the context of the planning environment which takes place well in advance of the date of departure. One salient feature of the planning environment is that decisions are made in a frictionless environment that do not consider perturbations to an existing schedule. Airline operations are rife with disruptions caused by factors such as convective weather, aircraft failure, air traffic control restrictions, network effects, among other irregularities. Substantially less work in the OR community has been examined within the context of the real-time operational environment. While problems in the planning and operational environments are similar from a mathematical perspective, the complexity of the operational environment is exacerbated by two factors. First, decisions need to be made in as close to real-time as possible. Unlike the planning phase, decision-makers do not have hours of time to return a decision. Secondly, there are a host of operational considerations in which complex rules mandated by regulatory agencies like the Federal Administration Association (FAA), airline requirements, or union rules. Such restrictions often make finding even a feasible set of re-scheduling decisions an arduous task, let alone the global optimum. The goals and objectives of this thesis are found in Chapter 1. Chapter 2 provides an overview airline operations and the current practices of disruption management employed at most airlines. Both the causes and the costs associated with irregular operations are surveyed. The role of airline Operations Control Center (OCC) is discussed in which serves as the real-time decision making environment that is important to understand for the body of this work. Chapter 3 introduces an optimization-based approach to solve the Airline Integrated Recovery (AIR) problem that simultaneously solves re-scheduling decisions for the operating schedule, aircraft routings, crew assignments, and passenger itineraries. The methodology is validated by using real-world industrial data from a U.S. hub-and-spoke regional carrier and we show how the incumbent approach can dominate the incumbent sequential approach in way that is amenable to the operational constraints imposed by a decision-making environment. Computational effort is central to the efficacy of any algorithm present in a real-time decision making environment such as an OCC. The latter two chapters illustrate various methods that are shown to expedite more traditional large-scale optimization methods that are applicable a wide family of optimization problems, including the AIR problem. Chapter 4 shows how delayed constraint generation and column generation may be used simultaneously through use of alternate polyhedra that verify whether or not a given cut that has been generated from a subset of variables remains globally valid. While Benders' decomposition is a well-known algorithm to solve problems exhibiting a block structure, one possible drawback is slow convergence. Expediting Benders' decomposition has been explored in the literature through model reformulation, improving bounds, and cut selection strategies, but little has been studied how to strengthen a standard cut. Chapter 5 examines four methods for the convergence may be accelerated through an affine transformation into the interior of the feasible set, generating a split cut induced by a standard Benders' inequality, sequential lifting, and superadditive lifting over a relaxation of a multi-row system. It is shown that the first two methods yield the most promising results within the context of an AIR model.PhDCommittee Co-Chair: Clarke, John-Paul; Committee Co-Chair: Johnson, Ellis; Committee Member: Ahmed, Shabbir; Committee Member: Clarke, Michael; Committee Member: Nemhauser, Georg

Solving the integrated airline recovery problem using column-and-row generation

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this recordAirline recovery presents very large and difficult problems requiring high quality solutions within very short time limits. To improve computational performance, various solution approaches have been employed, including decomposition methods and approximation techniques. There has been increasing interest in the development of efficient and accurate solution techniques to solve an integrated airline recovery problem. In this paper, an integrated airline recovery problem is developed, integrating the schedule, crew and aircraft recovery stages, and is solved using column-and-row generation. A general framework for column-and-row generation is presented as an extension of current generic methods. This extension considers multiple secondary variables and linking constraints and is proposed as an alternative solution approach to Benders’ decomposition. The application of column-and-row generation to the integrated recovery problem demonstrates the improvement in the solution runtimes and quality compared to a standard column generation approach. Columnand-row generation improves solution runtimes by reducing the problem size and thereby achieving faster execution of each LP solve. As a result of this evaluation, a number of general enhancement techniques are identified to further reduce the runtimes of column-and-row generation. This paper also details the integration of the row generation procedure with branch-and-price, which is used to identify integral optimal solutions

Hybrid methods for integrated aircraft routing and crew pairing problem with short flight legs

The aircraft routing and crew pairing problems are two processes that are difficult to be solved in the airline operations planning due to the rules that each flight leg needs to be operated on by one aircraft and one crew pair. These two problems, though interrelated in practice, are usually solved sequentially and often leads to suboptimal solution. Thus, this research contributes to the solution of the integrated aircraft routing and crew pairing problem in order to determine the minimum cost of this integrated problem where each flight leg is covered by one aircraft and one crew pair. This study also considers short connection between two flight legs in order to ensure that the crews do not change the aircraft if the connection time is in between 20 to 59 minutes. Another consideration is the restricted connection that imposes penalty costs when the second flight leg uses the same crew but not the same aircraft. Based on the literature review, most of the existing solutions concentrate on minimizing the planned costs. Although the minimum costs are significantly important in airline operations planning, the efficiency of a solution method in terms of computational time cannot be neglected. It is necessary to solve the integrated problem by using an efficient model that is able to generate a good high quality solution in a short time as requested by the airline industry. In order to solve the problem, a set of feasible aircraft routes and crew pairs are initially generated to be used as the input data in solving the integrated model effectively. There are two heuristic methods which are proposed in generating the set of feasible aircraft routes and crew pairs namely constructive-based heuristic and Genetic Algorithm (GA). The generated feasible aircraft routes and crew pairs are then used in solving the integrated problem by using Integer Linear Programming (ILP) method, Dantzig Wolfe Decomposition method, Benders Decomposition method and Particle Swarm. Computational results obtained from these methods are then compared by testing them on four types of aircraft with different number of flight legs based on Malaysia local flights for one week flight cycle. From the numerical results, it can be concluded that the proposed methods are more efficient compared to the ILP method available in the literature in terms of the computational time where the hybrid algorithm of GA and Benders Decomposition is found to be advantageous compared to the others. The maximum cost deviation of only 4.77% also justifies the strength of this hybrid algorithm. One possible future research that can be extended from this study would be the development of an algorithm that incorporates a parallel GA within the proposed methods for larger instances which are likely to exist in international flights in order to speed up the planning process

Recoverable robust single day aircraft maintenance routing problem

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record Aircraft maintenance planning is of critical importance to the safe and efficient operations of an airline. It is common to solve the aircraft routing and maintenance planning problems many months in advance, with the solution spanning multiple days. An unfortunate consequence of this approach is the possible infeasibility of the maintenance plan due to frequent perturbations occurring in operations. There is an emerging concept that focuses on the generation of aircraft routes for a single day to ensure maintenance coverage that night, alleviating the effects of schedule perturbations from preceding days. In this paper, we present a novel approach to ensure that a sufficient number of aircraft routes are provided each day so maintenance critical aircraft receive maintenance that night. By penalising the under supply of routes terminating at maintenance stations from each overnight airport, we construct a single day routing to provide the best possible maintenance plan. This single day aircraft maintenance routing problem (SDAMRP) is further protected from disruptions by applying the recoverable robustness framework. To efficiently solve the recoverable robust SDAMRP acceleration techniques, such as identifying Pareto-optimal cuts and a trust region approach, have been applied. The SDAMRP is evaluated against a set of flight schedules and the results demonstrate a significantly improved aircraft maintenance plan. Further, the results demonstrate the magnitude of recoverability improvement that is achieved by employing recoverable robustness to the SDAMRP.Australian Research Council Centre of Excellence for Mathematics and Statistics of Complex SystemsNatural Sciences and Engineering Research Council of Canada