Mathematical Problems in Engineering

Volume 2019, Article ID 9523610, 19 pages

https://doi.org/10.1155/2019/9523610

## Considering Passenger Preferences in Integrated Postdisruption Recoveries of Aircraft and Passengers

School of Economics and Management, Harbin Engineering University, Heilongjiang 150001, China

Correspondence should be addressed to Yuzhen Hu; nc.ude.uebrh@uhnehzuy

Received 6 February 2019; Accepted 23 May 2019; Published 2 October 2019

Guest Editor: Danielle Morais

Copyright © 2019 Tianshun Yang and Yuzhen Hu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

After a disruption to its operations, an airline needs to dispatch its aircraft and accommodate affected passengers in order to resume normal operations. When facing a flight delay or cancelation, passengers usually have two options—switching to a different itinerary or receiving ticket refunds. This paper focuses on the integrated recovery of both aircraft and passengers by taking into consideration passengers’ preferences regarding the two options. Objectives include minimizing the financial loss of airlines and minimizing the utility loss of passengers. To solve the optimization problem, we present a loop-based multiobjective genetic algorithm (GA) by leveraging a special characteristic of flight networks. Experiments based on real-world data demonstrate the effectiveness and stability of the algorithm in various situations. The outcome has theoretical and practical implications for disruption management and airline operations.

#### 1. Introduction

According to statistics from the International Air Transport Association (IATA), the global civil aviation industry transported 4.1 billion passengers in 2017, and its growth rate was 7.4%, which is the greatest one in history. However, the total punctuality rate in 2017 was 76.35% and this rate varies significantly among different airlines, which claims that different operational strategies may have great impacts on the punctuality rate. In China, with development of the Chinese economy, civil aviation transportation has unique advantages in convenience and time. With the support of various policies, the number of airline passengers of different countries as well as cities in China has rapidly grown. At the same time, however, complaints from civil aviation passengers have also risen sharply. According to statistics from the China Civil Aviation Administration (CAAC), the total number of complaints received from passengers reached more than twenty thousand in 2017, nearly twice as many as 2016, and flight delay problems accounted for 53% of the complaints. Why did this happen?

One of the most important reasons for the low customer satisfaction with airlines’ handling of disruptions is that airlines often prioritize their own operational convenience and economic impact over passengers’ preferences. Such prioritization of their own margins during flight rescheduling is very common for profit-seeking business like airlines. However, it is extremely unfair and intolerable for their disrupted passengers. The incident of a passenger dragged off a United flight, posted by CNN wire on Apr. 11th 2017, highlighted such ignorance of passengers’ preferences. Meanwhile, the core competitiveness of an airline is its ability to satisfy passengers’ needs. Chang et al. [1] evaluated airline competitiveness and determined that customer service quality is one of the primary considerations of passengers. Thus, during the postdisruption recovery process, airlines should pay more attention to passengers’ preferences when deciding how to accommodate them.

Common methods for airlines flight scheduling recovery from disruptions include flight delays and cancellation, aircraft swapping and ferrying, crew repair, and passenger reassigning; these have been considered in various prior studies, such as Clause et al. [2], Le et al. [3], Castro et al. [4], and Artigues et al. [5]. A topic of concern to an increasing number of researchers is integrated recovery of multiple resources, such as aircraft and crews. In contrast, recovery of passengers’ itineraries, especially their preferences regarding alternate itineraries, has gone unheeded by most studies. However, during the practical recovery process, there is a close connection between passenger recovery and aircraft recovery, and passengers’ satisfaction is paid significant attention by most airlines because of its potential impact on their own reputation and competition level in the aviation market. Therefore, it is critical to integrate interests of an airline and its passengers into a single recovery model, especially with consideration of passengers’ preferences regarding alternate itineraries.

In practice, the cost of recovery for airlines is still an important aspect for the operation of an airline so that a multicriteria model should be built to reflect these two considerations. In the field of integrated of flight, multicriteria model is a common modeling strategy, such as Lee et al. [6], Liu et al. [7], and Khaled [8]. The consideration of different kind of objects for the recovery and using functions separately to describe these objects is the key of this modeling style. After that, well-designed mechanisms are introduced to balance these objects. Although the most common way to handle multiobjective problems is to set weights of different objects so that they can be transferred into one single object, which is relatively easy to solve, we still try to keep two independent objective functions so that both objects can be fully considered. Moreover, the separate consideration of two objects avoid the complexity of how the weight of each object is set during the solving process. Thence, aiming to model the integrated postdisruption recoveries of aircraft and passengers, a multicriteria model is necessary.

The goal of this paper is to define, formulate, and efficiently solve the problem of satisfying passenger preferences in the integrated recovery of both aircraft and passengers. To achieve this goal, it was not only necessary to develop and extend mathematical formulation to consider the disrupted passengers’ preferences in the integrated recovery process but also to design an efficient solution method for the integrated recovery problem with consideration of passengers’ willingness. This paper provides an efficient and computationally manageable method for integrating the aircraft and passenger recovery problems considering passengers’ preferences by establishing a multiobjective optimization model formulation. The objectives of the formulation include clearly describing the airline recovery cost and passengers’ interest loss during disruption recovery. Additionally, a loop-based multiple objective genetic algorithm (GA) that leverages the characteristics of flight networks is also designed to obtain Pareto-optimal solutions for this problem extremely efficiently.

The remainder of the paper is organized as follows: after a review of relevant studies of airlines’ disruption management in Section 1, the problem and model are formally described in Section 2. Section 3 presents a heuristic method for the integrated recovery problem with passenger preferences. Computational experiments that evaluate our approach are presented in Section 4. Section 5 summarizes our work and discusses directions for future work.

#### 2. Literature Review and Contributions

##### 2.1. Postdisruption Recoveries of Aircraft and Passengers

Airline disruption recovery, which is an important guarantee of airline daily operation, includes total aircraft, crew recovery, and passenger recovery such as Clause et al. [2]. Moreover, Hu et al. [9] think passenger itinerary recovery is the most important measure to determine the quality of airline service. The initial research topic focuses on aircraft recovery. Teodorovic et al. [37 performed the first aircraft recovery study using an optimization method. Subsequently, many scholars have primarily focused on the problem of rearranging aircraft after disruptions using minimum–cost network flow theory and corresponding algorithms such as Gershkoff [11], Jarrah et al. [12], Yan et al. [13], and Thengvall et al. [14]. A time-band network was constructed by Bard et al. [15] for the aircraft rerouting optimization problem; it is often combined with the Column Generation algorithm and Bender Decomposition algorithm, to generate feasible aircraft routes in the airline disruption recovery problem by Eggenberg et al. [16]. For the large-scale flight delay recovery problem, metaheuristic algorithms are preferred to obtain near-optimal solutions efficiently, such as Argüello et al. [17] and Løve et al. [18]. However, most studies only focus on single objectives concerning the cost of deviations from original flight schedules. Only a few attempts, such as Liu et al. [19], have employed a hybrid multiobjective GA to find solutions for a daily short-haul aircraft schedule recovery problem.

Besides recovering aircraft, it is also important to recover several resources simultaneously in airline disruption management. Since integrating recovery of the total resources is a difficult task due to the size of the resultant problem, only a few attempts, such as Lettovsky [20], Peterse et al. [21], and Arıkan et al. (2013), have appeared in the literature.

Most studies try to describe the integrated recovery problem of aircraft and passengers in a single model formulation. Bratu et al. [22] were the first to model passenger recovery using a passenger delay metric model (PDM) and a disrupted passenger metric model (DPM). Both models consider the passengers’ disrupted cost and airlines’ operation cost in a single objective. The latter one is validated in three different levels of scenarios and three different degrees of disruption. Jafari et al. [23] presented a single-objective model that simultaneously recovered aircraft and passengers. Their dataset contained 13 aircraft of 2 fleets, and they were able to address disruptions in a small-scale airline.

Bisaillon et al. [24] developed a large neighborhood search heuristic for an airline recovery problem combining aircraft routing and passenger reassignment with one objective of minimizing operating costs and impacts on passengers. Sinclair et al. [25] improved the heuristic by adding some additional steps in each phase for the same problem. Then, Sinclair et al. [26] solved the similar problem with a column generation postoptimization heuristic, which slightly increased the allotted computing time. The heuristic is based on a mixed-integer programming mode and forms various hierarchies of passengers, flights, and other elements to recursively solve the problem. Zhang et al. [27] proposed a three-stage sequential math-heuristic framework to solve the integrated airline service recovery problem. Time-space network flow representations, mixed-integer programming formulations, and algorithms that take advantage of the underlying problem structures were proposed for each of the three stages. However, the computational results of the above studies were employed for the 2009 ROADEF Challenge that was organized by Artigues et al. [5] instead of for real-life situations.

Hu et al. [28] and Hu et al. [9] aimed to find the optimal trade-off between passenger delay costs, passenger reassignment costs, and the cost of refunding tickets in a single-objective model for the integrated recovery problem of both aircraft and passengers. They both consider the airline’s point of view instead of those of the passengers. The former solved the model using CPLEX Solver, and the latter design a meta-heuristic based on GRASP to obtain the near-optimal solutions. In the former research, the average time for solving a real example, including 319 flights and 59 airports, is 49 seconds and the average optimization efficiency is about 10%. Therefore, the computational time and optimization efficiency still have chances to improve.

From the literature review analysis, we observe that most of these papers combine utility losses of passengers with airlines’ financial losses to form a total loss as the single objective of the optimization model. This combined object simplifies the problem-solving process with a certain degree of relevance. However, unlike aircraft or crew members, passengers do not belong to the airline. They are two juxtaposed participants during flight production. Faced with the unforeseen disruption and the following recovery process, an airline cannot cover and compensate for the total loss of disrupted passengers, especially the utility cost and dissatisfaction of the passengers with the airline’s service quality. Therefore, the disruption and recovery costs of the airline and passengers cannot be simply combined. They should be subdivided in order to obtain a recovery solution that is more suitable for both participants in long-term plans.

##### 2.2. Passengers Preferences

In recent years, research on passengers’ travel preferences has gained popularity. Most studies use a logit model to analyze the choice of passengers between flights or railways by Moeckel et al. [29], revealing factors influencing passengers’ flight choices by Algers et al. [30], Yan et al. [31], Hagmann et al. [32], and Fleischer et al. [33], predicting the total number of air travelers [34], or optimizing passenger flows in a flight network, Dou et al. [35] and Yang et al.(2017). The above models are only suitable for normal transportation networks, not analysis of passengers’ preferences in the case of an accident or disruptions. Only a few attempts have discussed the possible behavior of railway passengers during emergency evacuation, and the analysis concluded that gender may result in significant difference in evacuation behavior in the ordered logit model.

However, although an airline’s handling of disruptions is a major source of its passengers’ dissatisfaction, Bratu et al. [22], no study on airline postdisruption recovery has attempted to incorporate passenger preferences. This paper tries to address this gap by quantifying passenger preference via utility losses and considering such losses along with airlines’ financial losses in a multiobjective optimization model. To solve such a multiobjective optimization problem, we choose to use GAs.

##### 2.3. Multiobjective Model and Optimization

In most studies, as stated above, traditional airline recovery problems are only described as single-objective models. Even when faced with multiobjective problems, they often propagate a linear sum on objectives to change them into a single one in the mathematical formulations. However, it is stated that the single-objective solution cannot overall reflect the true interests of both participants, airlines and passengers, Fieldsend et al. [36]. Therefore, a multiobjective model is naturally in-need to describe these two considerations. On one hand, the introduction of multiobjective model is used on the modeling, which means different kinds of object functions are built. Liu et al. [7] used a five-object model to manage a disruption and different weights were set to continue the solving process. On the other hand, the multiobjective idea can be used in the process of solving, such as Burke et al. [37], Chou et al. [38], and Lee et al. [6]. However, there are very few studies that consider the multiobjective optimization problems of integrated recovery of aircraft and passengers. Liu et al. [19] constructed a multiobjective combinational optimization model formulation for daily short-haul recovery problems and developed a hybrid evolutionary algorithm composed of an adaptive evaluated vector and the inequality-based multiobjective GA. A simulated disturbance experiment involving daily domestic airline plans in Taiwan with only 7 aircraft and 39 flights was performed. The efficiency was relatively low. Moreover, the objectives lack formal descriptions of flight cancellation and passenger reassignment, which are common in most airline recovery situations. The short-haul recovery approach is not suitable for general-scale disruptions, especially in larger airlines.

##### 2.4. Genetic Algorithm

GAs represent a widely used method for intricate multiobjective optimization, especially for airlines’ integrated recovery problems. This method, based on a Pareto noninferior solution, is a powerful multiobjective tool, Goldberg [39], that exhibits the superiority and inferiority of each solution. These solutions are then classified to choose the parent individuals during the solution process, leading the whole population to the forefront of Pareto solutions. GAs are especially suitable for problems with large feasible regions and complex constraints.

Especially in the research field of flight rescheduling, the aircraft flow being continuous in time and space increases the difficulty of the integrated recovery problem with multiple objectives, Hu et al. [40]. It is also the reason why few studies have investigated multiobjective optimization for airline recovery. However, the characters of flight loops, especially in the Chinese flight network, can package and protect the aircraft flow as continuous in time and space. Therefore, a loop-based multiple objective GA can be designed by combining an efficient coding strategy and the loop characteristics of the flight networks, in order to obtain near-optimal solutions of the integrated recovery problem.

##### 2.5. Contributions

The main contributions of our research are as follows.

(1) An integer programming model with two objectives constructed in this study reflects the practical interests of two major participants: airline and the disrupted passengers during the disruption recovery process. One objective refers to reducing the financial costs of airlines, and the other one focuses on reducing passengers’ utility losses.

(2) Different from the previous research topic, passengers’ preferences between refunding or endorsing are first considered in the integrated recovery model formulation of aircraft and passengers in order to improve passengers’ satisfaction. It is the first attempt in which passengers’ psychological behaviors are quantified in a probabilistic form in the integrated recovery optimization model.

(3) It is the first time that a recovery solution approach for resolving multiobjective airline rescheduling problems that combines a characteristic flight loop network and a GA is developed. The combination results in distinctly improved efficiency and better solution performance for the integrated airline recovery problem.

#### 3. Problem Description

##### 3.1. Passenger Preferences Analysis

An airline must arrange its aircraft to cover its flights each day. In the case of inclement weather, emergency repairs, and aviation control, the availability of aircraft could change, causing disruptions to the airline’s operations. The airport operation control center (AOCC) will collect all information and start the recovery period. A typical recovery period involves rearranging the assignments of aircraft to flights, mainly with the goal to reduce the financial loss for airlines. However, such a recovery process often ignores the preferences of passengers whose itineraries are affected by the disruption. In other words, it is assumed that passengers will accept the new itinerary provided by the airline.

Figure 1 shows the decision process of a passenger who belongs to a disrupted flight. If the flight is not canceled, which means the flight will land off later, we assume this passenger will still wait for the delayed flight. However, if the flight is canceled, the problem for the passenger of this flight is whether to apply for refund. If so, this passenger will receive a refund from the airline and his/her journey will end. If not, this passenger insists his/her journey and wants to move to another flight. In this paper, a proportion factor is used to illustrate how many passengers want to choose endorsement when the cancellation of flight happened. This factor is external and based on the operation information of the airline. In this situation, the problem waves back to the airline: are there enough available seats for the passenger who wants to endorse? The answer relies on the recovery decision the airline made. If the passenger’s demand can be satisfied, he/she can continue the journey. If not, the passenger will be annoyed about the recovering process so that the utility loss of passenger increases. In conclusion, in the whole recovering process, passengers only need to show their preference to which extend they choose refunding and this is the information they need to give to the airline when adjusted flight schedule is announced.