Airline planning benchmark problems—Part I:: Characterising networks and demand using limited data
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:
- 1.
Generate the flight network including passenger load on arcs.
- 2.
Calculate origin–destination (OD) pair demand.
- 3.
Define passenger groups.
- 4.
Allocate OD-pair demand to each passenger group.
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 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 has capacity cf. The basic time unit used is one day. Let denote the length of a day in minutes.
Let denote the set of ordered potential passenger origin–destination pairs, or OD-pairs. For each OD-pair , the OD-pair demand Dod 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 nij on arc 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.
Section snippets
Characterising airline networks
An airline network's topology depends on factors such as the geographical positions of the airports serviced by the network, the desired operating practices of the airline, the structure of the network of any competitors, and also passenger demand. This paper concentrates on the commonly occurring hub-and-spoke topology. This topology consists of a single hub airport connected by flight legs to a number of spoke airports. The spoke airports are only connected to the hub, that is, no flight legs
Characterising airline demand using limited data
Accurate passenger demand data is vitally important to the design of a good airline schedule and to the subsequent fleet assignment and through assignment problems. There are several dimensions to this demand, starting with the origin and destination of the passengers, moving to their preferred time of flying, and ending with the utility of the various products offered by the different airlines or competing modes of transport.
The existence of demand between an OD pair implies that there is a
Benchmark instances
The benchmark instances consist of 30 single-hub and three two-hub networks. Table 5, Table 6 provide the parameters used to generate the networks. In these tables thee hub name is preceded by either an “s”, “m”, or “l”, indicating whether the instance is considered to be a short-, medium-, or long-haul network, respectively.
To generate a single-hub network having a given number of spokes, the network characteristics identified in Section 2.1 are used. Recall that five possible arc distance
Analysis of instances
Summary statistics are presented for all of the benchmark instances. More detailed results are presented for three selected single-hub instances, one two-hub instance, and a fictitious Australian carrier called Emu Airlines that operates a point-to-point network. For these instances, network and directional capacity diagrams, and CDFs of various network and passenger characteristics.
The arc passenger load CDFs show the fraction of network arcs that have at most the given passenger load as a
Conclusions and future work
This paper is the first of two papers entitled “Airline Planning Benchmark Problems” that present a four step framework for generating realistic airline planning benchmark problem instances. These instances are a result of analysing rich data sets from a wide range of airlines worldwide, including all airlines in the Star and oneworld alliances. The methodology behind the first two steps in the framework, namely, characterising airline networks and OD-pair demand using limited data were
Acknowledgments
The authors are very grateful to Ian Evans and Alan Dormer (CTI Pty Ltd) for their ongoing support and guidance on a variety of practical airline-related issues and for numerous technical suggestions and insightful feedback that improved the content and exposition of this work. The authors would like to thank two anonymous referees for their comments that greatly improved the presentation of the paper. This research is supported by the Australian Research Council, under Linkage Projects
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