Abstract—Both areas, airline planning and railway planning, have attracted a significant interest from the operations research and optimization community during the past decades. Although both areas have significant similarities, i.e. transport of people and goods according to specified schedules, the dissimilarities seem to prevail due to the mostly separate developments of these fields.

In this paper we focus on the main planning fields in railway and airline transport, discuss similarities and differences in these areas and the corresponding modeling and optimization approaches. In some cases, we see that similarities depend on the specific application instance, e.g. the size of a railway network or other aspects of the organizational framework. In other cases there are no good reasons to treat the respective planning problems separately.

I. INTRODUCTION N the first view there are not many aspects which justify completely different planning routines in the two

fields of airline and railway planning. Both have to do with the transport of people and goods along defined lines and according to specified timetables. In both cases scarce and costly resources such as vehicles and stuff have to be considered. In both cases numerous regulations such as working time regulations or with respect to the maintenance of vehicles have to be observed. In both areas the planning has to be flexible enough to cope with unforeseen events such as the unavailability of resources e.g. due to illness or technical problems or because of weather conditions. From a technical point of view the planning problems for railway and airline companies are in many cases "large scale" with respect to the number of services to be planned and the number of resources and other restrictions to be considered.

Nevertheless both areas of application are mostly considered independently. In the subsequent paper we consider this situation in details, point out common aspects and differences in these fields, and discuss approaches for tackling the planning problems. In Section 2, we focus on the aspect of network design in both areas. In Section 3, various scheduling problem in the railway and airline business are discussed. Problem related to revenue

Manuscript received January 31, 2010. T. Hanne is with the Institute for Information Systems at the University

of Applied Sciences Northwestern Switzerland, Riggenbachstr. 16, 4600 Olten, Switzerland; phone: +41 62 2860160; e-mail: thomas.hanne@fhnw.ch.

R. Dornberger is with the Institute for Information Systems at the University of Applied Sciences Northwestern Switzerland, Peter-Merian-Strasse 86, 4002 Basel, Switzerland; (e-mail: rolf.dornberger@fhnw.ch).

management are considered in Section 4. In Section 5 software aspects are discussed briefly. In Section 6 some conclusions are presented.

II. NETWORK DESIGN AND HUB PLACEMENT

Network design is a major strategic issue for many companies in general and for logistic companies in particular. In most cases, companies use a given transportation infrastructure but have to place specific locations such as production plants or warehouses which define the individual network for procuring commodities and for distributing goods to their customers. A forwarding company, for instance, uses a road network provided by the state but has to decide on vehicle depots for efficiently fulfilling transport orders of customers.

In the case of railway companies, this situation is much different. In most countries the provision of a railway network and its utilization with trains is not separated. This means, that railway companies have to plan the construction of new railways, the closure of old ones, the location of train stations and all related infrastructure such as switches. However, in developed countries such networks are mostly well developed (see Fig. 1 for an example) such that the network design problem usually refers to minor changes in the given network, especially extensions of the network or a reduction of the network. The later problem mostly refers to countries with state-owned railway companies which produce losses. Here the main goal is to reduce parts of the network which are not profitable. Also for private railway companies there is often some pressure to operate economically unreasonable lines. On the other hand there are

Optimization Problems in Airline and Railway Planning - A Comparative Survey Thomas Hanne, Rolf Dornberger

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Fig. 1. Example of a railway network (Switzerland)

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Third International Workshop on Advanced Computational Intelligence August 25-27, 2010 - Suzhou, Jiangsu, China

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some options for enlarging an existing network, e.g. by placing simple stations or stopping-points along existing lines, thus leading not to substantial additional investments but to a better fulfillment of customer demands (see, e.g., [21], [22]). An approach of a designing a novel network, e.g. a new suburban train network, is presented in [16].

For airline companies the situation is usually quite

different. On the one hand, there are no substantial investments in the transportation lines themselves. On the other hand, network nodes (i.e. airports) require substantial investments but do usually not belong to the airline companies but are operated by independent companies, some of them being public-owned. In any case the location of a new airport is always a political issue. The airline companies, however, have to pay fees for using the airport infrastructure such that selecting nodes and lines remains an important problem.

Due to the liberation of the air traffic markets since the 1970s, competition grew and costs became more and more an issue in the planning of airline companies. A major impact of this was the reduction of direct connections between served destinations and the emergence of hub-and-spoke networks (see Fig. 2 for an example). These networks are based on the idea that airline companies have one or a few central locations from which a larger number of destinations are served. This means that passengers who do not use the central location of an airline company as starting or destination point have to change the plane, i.e. the total travel consists of two or more flights instead of just one. For the airline company this network structure leads to a reduced number of direct connections, thus to a better utilization of resources such as planes or aircrews, thus to lower costs which are handed over to the customers [11].

Due to the individual nature of network planning problems for any railway company there is no unique approach to solving them. A few publications however can be found concerning problems specific to a country or a railway company [17]. In contrast to that there exists a considerable amount of research on hub and spoke network

planning problems, most of them being related to airline applications (see [28] and [7] for surveys on this topic). In most publications on this topic a rather reduced form of this network design problem is considered for facilitating its mathematical treatment. For instance, capacity constraints are neglected.

Solution algorithms for a capacitated hub location problem are discussed, for instance, in [6]. Typically, these problems are formulated as linear or mixed integer optimization problems and solved by means of mathematical programming. In [8], for instance, refined hub location problems are formulated as mixed integer optimization problems which are solver by two approaches, one is based on a Benders decomposition algorithm, the other one uses a greedy neighborhood search. Another example of metaheuristics such as genetic algorithms applied to a hub locations problem is [30]. In [18] a parallel evolutionary algorithm is applied to hub location problems. A main reason for the recently increased popularity of using evolutionary algorithms and other metaheuristics may be the more complicated formulation of hub locations problems which makes them harder to be treated by exact algorithms.

In railway planning the specific hub location problem usually cannot be applied since nodes are mostly not specifically dedicated as hubs. Instead, many stations serve to changing trains. In railway cargo the situation is different: There are hub-like locations (denoted as classification yards) for routing freight cars by building trains for specific destinations [14]. The selection of classification yards for freight routing can be treated by path models, arborescence models, or multi commodity network flow models and can be solved efficiently, for instance, by column generation approaches (see [13]).

III. SCHEDULING

A. Line Planning and Frequency Assignment Another major planning problem for railway and airline

companies refers to the planning of lines to be served and related decisions on how often these lines are served. This planning problem is mainly located on mid-term operative level to a long-term strategic level.

A detailed description including a literature survey for this type of problem for the airline business is given in [11]. For railway service provider corresponding problem descriptions can be found in ….

For both business areas main considerations for solving the problem are the transportation demand of customers and the available resources and corresponding costs of the service provider. A major difference is that railway companies mostly do not need to take into consideration the behavior of competitors (especially lines, frequencies of services, and prices) since they often operate in monopolistic markets. In contrast to that, airline business is much affected by competition. Therefore the services (served lines and frequency of services) also depend on the services provided

Fig. 2. Example of the hub and spoke network of an airline (US Delta)

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by other companies, by all means if they serve along the same destinations.

For railway companies on the other hand, there are often political regulations concerning lines to be operated and the frequency of operations. For instance, it is often politically desired to provide services along lines with small transportation demand and to operate along these lines with a minimum frequency, e.g. a train each hour.

Methods used in that area are often coming from the area of mathematical programming [11], e.g. by column generation approaches [2] but also metaheuristics such as, for instance, ant colony systems [10] are applied.

B. Service Scheduling The logically subsequent planning problem concerns

the specific scheduling of services, i.e. the determination of the specific starting and arriving times for all destinations.

This problem again refers to the transportation demand, the available resources, such as staff and vehicles. While in the rougher planning of lines and frequency of services these issues have been considered only on a temporally aggregated level, here the specific times of occurring demand and available resources need to be matched. Another important issue to be considered is the adjustment with connecting trains or flights. This is particular important for network structures where the passengers or transport goods have to change the vehicles such as in hub and spoke networks. Whereas railway companies usually have to consider infrastructure resources such as tracks and platforms during the scheduling, airlines have to consider start and landing rights (slots) and airport fees.

For railway services there are usually constant daily schedules (possibly different for Saturdays & Sundays). In many cases these schedules also have a constant structure during (some parts of) the day, e.g. one train per hour. Due to fewer services on some lines, there are typically constant weekly schedules for airline companies (e.g. a flight on Wednesday and Saturdays at a specific time). For busier lines, services might also be provided according to a constant daily scheme.

For airline companies these schedules are usually fixed (when announced) for several months, for railway companies they usually remain fixed for a half or one year.

In a considerable number of companies these schedules are still generated by manual planning, possibly with some semi-automatic software support. Thus, this planning task remains an ambitious and time-consuming activity. However, scheduling problems are well known from many other areas. The application of operations research and optimization techniques for these problems (including applications in the transport sector) has a quite long tradition and led to a significant amount of approaches and corresponding publications (see, e.g., [11], [12]). Thus, there is a certain gap between theory and practice.

A specific problem related to service scheduling is the

delay management. The question when generating schedule here is: How long should one vehicle wait for another delayed one such that passenger can reach a connection? Usually this question is analyzed with respect to trains although it is relevant for airlines as well. Mostly the corresponding problem is formulated as an integer optimization problem and solved by techniques of mathematical programming (see, e.g., [9], [20]). However, other approaches such as, for instance, game-theoretic problem formulations can be found as well [23].

C. Resource Planning Often the detailed planning of resources, i.e. the

assignment of individual resources to services or tasks, is not done in the longer-term service scheduling process. Instead this is accomplished mainly on a shorter-term level. Several of these shorter-term planning levels can be distinguished: On a rather long-term planning horizon, possibly the acquisition of new resources or the replacement or reduction of resources may be considered. The mid-term planning takes place on a weekly and/or monthly basis and is mostly the most important planning level (see Fig. 3 for an example of monthly planning by the railway planning suite RailOpt by Qnamic Inc.). Then, there is the short-term planning and dispatching level which is mainly based on correcting the mid-term plans e.g. because of the break-down or repair of vehicles or the absenteeism of employees.

Resource planning mainly concerns the traffic itself, the preparation of services and duties related to the infrastructure. The resources to be planned are in particular the staff (rail crews and air crews) and the transport vehicles

(locomotives and carriages for railway companies, aircrafts for airlines).

Let us consider the staff planning in some more details: In the case of airlines, staff is often assigned to cover round

Fig. 3. Graphical user interface of a railway staff rostering software. This scheduling is heavily based on a manual planning environment supported by some semi-automatic procedures.

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trips for short distances. Possibly, one crew can handle several services for very short distances during one shift. When there is a flight (with the same aircraft) serving several destinations in sequence, there is usually no crew exchange at stopover locations. For long-distance trips it might be necessary to plan overnight services or hotel accommodation for the crew.

In the case of railway companies, there is often the situation that one service (start location to final destination) is much shorter than a shift. Therefore, such services need to be grouped for building shifts which correspond with the usually daily working hours. Moreover, it is possible to exchange personnel at many intermediate stops during a service. In particular, long services can be split into several shifts (exchange of train crew) such that overnights stays are mostly not required.

The staff planning for railway companies and airlines need to consider a number of constraints: Typically, there are a number of working regulations (governmental, union-based, and company-specific) to be observed, e.g. a maximum number of services (hours) per month, a minimum time between two shifts, rules concerning vacation, rest-times, etc.

The staff skills need to be considered as well, e.g. train driver licenses, pilot licenses. For airlines international aspects or aspects of operating countries are in general more important than for railway companies which often operate in one country only.

Last but not least specific preferences of employees should be considered during the planning process. For railway companies these aspects are often neglected or their consideration requires a lot of manual work. In contrast, many airlines have implemented elaborate approaches for considering the preferences of employees (e.g. approaches for self-rostering, team rostering, bid lines, auctions; see, e.g. [15] and [29]).

Although there may be many differences between the resource planning problems of companies, the general structures of these problems are quite similar for airlines and railway companies. Significant differences between companies may result due to different national laws, regulations, and other specific circumstances (e.g. the size of the network) but are not a result of the mode of transportation.

For these reasons, similar methods have been employed, the most prominent ones being mathematical optimization (e.g. branch and bound), constraint programming, and metaheuristics. Today, there are plenty software tools available for supporting the planning processes in an automatic or semi-automatic way. Some of these tools result from academic projects; others are commercially developed and distributed (see, e.g. [4], [5], [11], [12], and [15]).

D. Maintenance Planning

Besides the provision of regular services, there are a

number of other activities to be planned by transportation service providers. One of the most importance ones is the maintenance of vehicles, infrastructure or other resources. Most consideration in the literature is due to the maintenance planning of vehicles (locomotives, planes).

In the airline business there are various national and international regulations and company-specific rules to be observed. The typical scheme is that there are daily inspections which are carried out as en route-services. Then there are major checks of different categories (A, B, C, and D) which are done according to a time schedule which in particular requires certain maximum intervals between each check of an aircraft. Here it is important to consider that these checks can only be done at specific locations and that dead-head flights to these locations should be avoided if possible. Moreover, the non-availability of the inspected planes needs to be considered in the assignment of resources to services. In general, due to maintenance and the reduced average availability of vehicles additional resources are required.

In the railway business, there are also national regulations and company-specific rules. Since these maintenance rules are less standardized compared with airlines, it is rather necessary to find company-specific formulations of the corresponding optimization problems.

IV. REVENUE MANAGEMENT

A. Basic Ideas, Current Situation, and Impact Revenue management (aka yield management) is

considered as one of the most interesting planning areas for transportation companies (see [19] for a survey).

The basic ideas of revenue management are as follows: For scarce resources, e.g. seats in vehicles and theaters or hotel rooms etc. it is possible to have an individual pricing. For instance, there may be a price differentiation according to target groups or distribution channels. It is also essential to provide services (and the related capacities) according to the demand. Moreover, there may be a service differentiation according to target groups or distribution channels. Apart from the regular revenues, non-fare revenues (e.g. for seat reservations or baggage handling) may be an interesting topic of transportation companies as well.

The objectives in revenue management are as follows: First, of course, the generation of higher overall revenues is a prime objective for the service provider. Secondly, revenue management may lead to a better balancing of demand and workload over time and to an avoidance of idle capacities, thus also to reduce costs.

Since the market liberalization and the increased cost pressure, revenue management became a key area for improving the business situation of airlines. During the 1990s it became extensively used, mainly with a focus on the provision of services according to demand (schedules), the marketing and pricing according to segments (esp. the

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different travel classes and customer groups), the pricing over time (esp. for avoiding idle capacities), and the choice of aircrafts and seat configurations for providing services. Since then a substantial number of OR-related publications including theoretical papers and case studies with airline companies appeared (see, e.g., [25], [26], [27], [31], and [32]). Possibly, the most significant of them is the application honored by the Edelman Prize describing the revenue management systems at American Airlines which contributed $1.4 billion within 3 years.

Until recently revenue management has not been a comparably hot topic for railway service providers. Most companies traditionally do not differentiate prices with respect to the specific demand over time. Instead, transportation prices mostly depend on the travel distance and the travel class, sometimes being fix for some specific type of service (e.g. independent of the travel distance). Occasionally, prices depend on the type of vehicle (e.g. special prices for high-speed trains) or route. Moreover, price setting and differentiation often includes non-economical aspects (e.g. social aspects due to political regulations).

A major problem in applying effective revenue management in railway companies is, however, that tickets are frequently not tied to a specific train or time of service. Thus, it is not sufficiently clear when scarce resources (seats) are actually matched with transportation demand nor is it possible to shift passenger demand and balance resource utilization by price differentiation over time. Since about ten years train companies are increasingly experimenting with dynamic pricing and other means of revenue management, for instance Deutsche Bahn (Germany), NS Hispeed (Netherlands), Thales (France/Belgium), and Indian Railways (India) (see, e.g., [1], [3], [24]).

B. Methods Revenue management is based on a number of methods

from operations research [24]. A main issue concerns the usage of forecasting methods for a sufficiently reliable modeling of the effects of different revenue management strategies. Forecasting is usually based on historic data (daily demand structure, seasonal influences, etc.) and includes assumptions on the temporal shiftability of demand and the price sensitivity of demand (e.g. "What happens when we make the 6:00 to 8:00 a.m. trains 10% more expensive or decrease the train prices for trips between 9:00 and 12:00 a.m.?"). Secondly, in many cases revenue management strategies can be analyzed by simulation models. Especially when the models become quite complex or a large number of variants of revenue management strategies need to be analyzed this may be a feasible alternative to an analytical solutions of the models. Thirdly, optimization techniques are important for finding optimal solutions to revenue models under consideration. Due to the diversity of models, various different optimization techniques may be applicable, e.g. linear programming,

integer programming, nonlinear programming and stochastic variants of these approaches.

Specific approaches in the revenue management for airlines are the seat inventory control and the overbooking and waitlist management. Although not being practices yet, there are, in principle, no reasons why these concepts cannot be applied to railway problems as well.

V. SOFTWARE ASPECTS

Today there is a quite heterogeneous software landscape concerning products which support transportation service providers in their planning tasks.

Many software tools used by the respective companies are custom made, often being developed with academic support. On the other hand, there are a considerable number of small commercial software providers. Often the offered software results from custom-made software solutions. Usually these software solutions do not cover a larger range of the planning problems discussed above but only deal with specific planning tasks (e.g. resource planning or revenue management). In order to provide more attractive tools and to find new customers the software providers try to extend the scope of support. Significant endeavors are also done for providing a software that fits for new customers (e.g. due to specificities of a country, planning constraints, and the company).

A comprehensive and fully integrated planning support is hardly available today although some software providers evoke that their software can do almost everything it's still a long way until there. Due to their difficulty planning problems are mostly decomposed and not solved in an integrated way (see [11] for further discussion and [17] for an example of integrating disperse optimization problems in these fields)

VI. CONCLUSIONS

Our survey has shown that most planning areas in railway and airline business are rather similar. Some differences are due to technical and organizational differences, e.g. different distances in transportation, transportation times, frequency of services, and different network structures. Other differences are due to the degree of regulation and competition. Railway companies are frequently monopolists and are additionally state-owned in many cases. Thus, there is less competitive pressure and less need for reducing costs and improving quality of service in railway industry. This might also be a main reason for a smaller degree of utilizing advanced planning techniques in practice. From a purely theoretical point of view both areas, airline and railway, seem to be equally well covered with respective studies.

The “artificial” differences in using advanced planning techniques may decrease in future. Cost pressure is expected to prevail for railway companies and competition may

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increase. This also a big change for a better dissemination of advanced planning support in both areas.

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