Airline planning benchmark problems—Part I:

Abstract

This paper is the first of two papers entitled “Airline Planning Benchmark Problems”, aimed at developing benchmark data that can be used to stimulate innovation in airline planning, in particular, in flight schedule design and fleet assignment. While optimisation has made an enormous contribution to airline planning in general, the area suffers from a lack of standardised data and benchmark problems. Current research typically tackles problems unique to a given carrier, with associated specification and data unavailable to the broader research community. This limits direct comparison of alternative approaches, and creates barriers of entry for the research community. Furthermore, flight schedule design has, to date, been under-represented in the optimisation literature, due in part to the difficulty of obtaining data that adequately reflects passenger choice, and hence schedule revenue. This is Part I of two papers taking first steps to address these issues. It does so by providing a framework and methodology for generating realistic airline demand data, controlled by scalable parameters. First, a characterisation of flight network topologies and network capacity distributions is deduced, based on the analysis of airline data. Then a multi-objective optimisation model is proposed to solve the inverse problem of inferring OD-pair demands from passenger loads on arcs. These two elements are combined to yield a methodology for generating realistic flight network topologies and OD-pair demand data, according to specified parameters. This methodology is used to produce 33 benchmark instances exhibiting a range of characteristics. Part II extends this work by partitioning the demand in each market (OD pair) into market segments, each with its own utility function and set of preferences for alternative airline products. The resulting demand data will better reflect recent empirical research on passenger preference, and is expected to facilitate passenger choice modelling in flight schedule optimisation.

Introduction

There has been relatively little work that has addressed the first stage of the airline planning process, namely, flight schedule design. The many algorithms and techniques reported in the literature for later stages of the airline planning process are difficult to compare because they are evaluated on problem instances representative of a particular airline at a particular date. Each airline operates a different network of airports, a different fleet in terms of the size and mix of aircraft, has different passenger quantities and itineraries, and different crew requirements, bases and rules. Furthermore, the data for these instances is considered confidential by most airlines due to its significant commercial implications. Consequently, obtaining real data is difficult and often requires the researcher to establish a good relationship with an airline partner over many years. Such issues create a barrier to entry for many prospective researchers and limits potentially fruitful collaboration between research groups.

Some first steps towards addressing these issues are taken in this paper and its sequel [2] by developing a framework for generating realistic benchmark instances. These instances provide standardised data with which to initiate the airline planning process. Since flight schedule design depends critically on market demand, this initial work has focused on the generation of airline demand benchmark data. The addition of airline resources, such as aircraft and crew, to these benchmarks is planned for the future. By making these instances, and a description of the methodology used to generate them, publicly available it is hoped that research engagement in airline planning will be stimulated in a similar way to what has been so successfully achieved in areas such as vehicle routing, which flourished after the introduction of the Solomon benchmark instances [25]. The DIMACS¹ and ROADEF² challenge instances have had a similar impact.

As a large body of literature attests, optimisation has been a critical part of airline planning for many decades. See, for example, Klabjan [19], Bazargan [7], or Barnhart and Cohn [5]. However, as noted in Klabjan [19], for the most part, airline schedule planning is a manual process with only a few manuscripts on flight schedule design. Notable among these are two papers, Yan and Tseng [30] and Yan et al. [29], on flight scheduling in Taiwan, and that of Lohatepanont and Barnhart [21], combining flight scheduling with fleet assignment. The authors of this paper believe that the dearth of optimisation research on schedule design is in part due to the difficulty of representing passenger choice, and of collecting adequate data to accurately assess schedule revenue. However, there has been a growing body of both empirical and theoretical research seeking to provide insight into airline passenger decision processes and to develop models of passenger utility. See, for example, Coldren et al. [10], Garrow et al. [16], Koppelman et al. [20], Walker [27], and Wojahn [28]. The insights provided in these papers, combined with an empirical analysis of rich data sets from a wide range of airlines worldwide, including all airlines in the Star and oneworld alliances, has led to the development of a new approach to representing airline demand data, and a methodology for generating realistic demand data sets.

The methodology developed in these two papers is a four step framework. Fig. 1 illustrates the four steps in the framework which are:

• Generate the flight network including passenger load on arcs.

• Calculate origin–destination (OD) pair demand.

• Define passenger groups.

• Allocate OD-pair demand to each passenger group.

The flight network connects the set of airports to be served, and the network topology defines arcs indicating airport pairs between which direct non-stop services are to be offered. Passenger load on an arc indicates the total number of passengers expected to travel on the direct non-stop service over some time period, for example, a day.

This paper presents the methodology behind the first two steps in this framework. The first step generates realistic flight networks and passenger loads with specified characteristics that capture the features of a large fraction of existing airline networks. These networks are scalable so that the effect of different scheduling strategies, and different parameters such as network type and size, or fleet mix, on algorithm performance and solution cost can be readily compared. The second step of the framework solves an inverse problem to determine OD-pair based demand that is compatible with the passenger loads on each arc. This data, sometimes called market demand, can be of use in its own right. For example, in performing schedule design, Yan and Tseng [30] work directly from such data collected from airlines in Taiwan.

The second paper [2] presents the methodology behind the third and fourth steps in this framework. The third step partitions the market demand into passenger groups, according to the characteristics that differentiate behaviour in terms of airline product selection. Each passenger group has an origin, a destination, a size (number of passengers), a departure time window, and a departure time utility curve indicating the passengers' willingness to pay for departure in time sub-windows. This data is much richer than simple market demand and can be expected to provide better estimates of schedule revenue in a form that is useful in schedule design optimisation. The integrated airline schedule design and fleet assignment problem studied in a companion paper [3] demonstrates passenger groups to be a potential alternative to the commonly used spill models [12], [18], [6] for estimating passenger flow in an airline network. The fourth step in the framework allocates the previously determined OD-pair demand to each passenger group using a standardised demand profile, a generic percentage-wise allocation of passengers throughout a day.

The design of this methodology readily permits the generation of realistic airline data “from scratch” in a way that supports experimentation with key characteristics of that data, as well as providing an approach that other researchers can still use when they have access to partial data. For example, if an existing flight network is already known, and, perhaps, observed passenger loads are also known for that network.

An airline network consists of a set S of airports to be served, and a set $A\subseteq S\times S$ of directed arcs indicating an ordered pair of airports between which at least one direct non-stop service is offered. An airline's fleet is denoted by the set F of aircraft subtypes, and an aircraft from the fleet $f\in F$ has capacity c_f. The basic time unit used is one day. Let $\mathcal{T}$ denote the length of a day in minutes.

Let $\overline{K}\subset S\times S$ denote the set of ordered potential passenger origin–destination pairs, or OD-pairs. For each OD-pair $(o,d)\in \overline{K}$, the OD-pair demand D_od is the total passenger demand over a day to travel from airport o to airport d. In the case that an OD-pair is not an arc then the only way passengers can complete their travel is to connect to successive arcs by transiting at an intermediate airport. The passenger load n_ij on arc $(i,j)\in A$ is the number of passengers observed traversing the arc over the course of a day.

Section 2 describes methodology to characterise airline networks. This is the first step in the framework for generating sets of realistic airline planning benchmark problems. Section 3 describes methodology to characterise airline demand using limited data. This is the second step in the framework. A description of the generated benchmark instances is provided in Section 4 and an analysis of the instances is given in Section 5. Section 6 presents some conclusions and a brief description of future work.