Abstract

In the context of the SESAR (Single European Sky Air traffic management Research) Joint Undertaking, the role that the air navigation service provider (ANSP) could play has been reconsidered. ANSP manages traffic and deals with potential conflict situations and external events, which have led to the reorganization of the air traffic. The modification of traffic inevitably leads to delays for airlines, which is costly. In this study, we suggest that ANSP could provide a costly delay reduction service to airlines. Indeed, if ANSP has several solutions for traffic conflict resolution or reorganization, there is room for a choice between these solutions using additional criteria. Our study thus proposes an original model in which we determine the optimal design of a delay reduction contract signed between welfare- or profit-maximizing ANSPs and a monopoly airline. We give some comparative statics, in particular, the evaluation of the impact of a modification in safety standards on the contract.

1. Introduction

Aviation in Europe is expected to experience rapid growth and more delays in the future. According to STATFOR [1], in the most likely scenario, there will be 14.4 million flights in Europe in 2035; 50% more than in 2012. Moreover, air traffic growth will be limited by the available airport capacity. When the capacity limits are reached, congestion at airports will rapidly increase, leading to even more delays. In addition, in Europe, 15% of the flights are currently delayed due to ATM (Air Traffic management) reasons. To improve and meet the development of the EU air transport sector, in 2004, the European Union and EUROCONTROL founded the SESAR (Single European Sky Air traffic management Research) Joint Undertaking, in which meeting future safety needs and reducing delays are important targets (see [2]; European [3], 2015; [4]). In the context of SESAR, various propositions to reduce delays have been made, such as increasing the quality of air transport services. These propositions are mainly technical; however, a delay reduction service has also been considered. This service corresponds to an evolution in the role of the air navigation service provider (ANSP), which was initially established to be in charge of air traffic management. Under the delay reduction service, when facing potential delays, an airline will contact ANSP to find a solution to limit or to reduce delays well in advance. After receiving an airline’s request, ANSP will determine several solutions that satisfy all regulation constraints. Then, by costly calculation, evaluation, and coordination, ANSP will select the solution to most effectively reduce delays in line with airlines’ demands and then implement it. In the short term, the service can be provided free of charge due to the generous funding of SESAR. In the long term, however, ANSP will face financial constraints. Thus, a contract (hereafter, a “delay reduction contract”) should be signed between ANSP and the airlines, in order to make the service sustainable. This study aims to study the optimal design of the delay reduction contract (in the USA, the Next Generation Air Transportation System is the counterpart of the SESAR program. This program also focuses on the improvement of the performance of ATM. As such, our results can be easily considered).

A delay reduction contract will be set between ANSP and a monopoly airline. This will consist of a degree of reduction in delays to be incurred as a result of the conflict situation to which ANSP commits with a transfer payment made by the airline. We assume that the incentives and motivations of the airline to sign such a contract are unknown by ANSP. This assumption allows us to consider the fact that airlines may vary in their willingness to pay for the same degree of reduction. Indeed, some airlines may greatly value being on time or experiencing as little delay as possible. Incentives from the demand side (reputation and quality of service) and the supply side (network effect and cost of fuel) may explain why airlines particularly value as little delay as possible. We consider that this information is private and that the design of the optimal contract is an adverse selection problem, which results in the well-known trade-off between efficiency and rent extraction.

We analytically derive optimal contracts, considering both the welfare- and profit-maximizing ANSPs. Indeed, we consider that a certain part of the cost of choosing which solution to adopt when delays are to occur has to be taken either by the society (welfare maximization) or by a private firm (profit maximization, only for the delay reduction service). Our results are consistent with the principal-agent literature: under incomplete information, the high-type airline (i.e., a high value of delay reduction) receives an information rent in order to avoid them taking the contract designed for the low-type airline. More interestingly, when the passenger surplus is taken into account, the airline can even be subsidized to participate in the delay reduction service in order to achieve higher welfare.

Furthermore, we conduct comparative static analysis to study the effect of the relevant exogenous parameters on optimal contracts, such as safety standards and flight frequency. This analysis allows us to understand how the delay reduction benefits and the cost of producing the delay reduction service interact. Finally, we use numerical examples to study when a welfare-maximizing ANSP has to use public funds to provide the delay reduction service. The trade-off will be dependent on the impact of the delay reduction on the passenger surplus. Indeed, if passengers greatly value the delay reduction, then it becomes welfare improving to foster the service of delay reduction.

1.1. Related Literature

Our study contributes to the literature on air traffic management in two principal ways. The ATM literature centered on delays mainly focuses on the reduction in global delays in the air transport system. The proposed changes primarily consist of improving the methods, which solve conflicts (new algorithms and speed of computation) or allocate the slots for takeoff and landing (see [5]), and can be found in the operational research literature. However, global efficiency is sought, and several solutions may lead to the same result in terms of global delays. We propose to complete this analysis by allowing for the possibility of selecting particular solutions among those available, in which some airlines could choose the maximum amount by which they will be delayed. Then, we also model the ANSP as a strategic agent and propose to assess the performance of the ATM system while introducing the opportunity to propose a delay reduction service. From this perspective, our study is related to Blondiau et al. [6], in which the relationship between the ANSP and the regulator is modeled. Instead, we consider that ANSP has no personal agenda and faces asymmetric information regarding the airlines. The performance of the ANSP in controlling air traffic has been assessed several times. Economists generally focus on the benchmarking of cost efficiency, as in Bilotkach et al. [7] with EUROCONTROL data from 2002 to 2011, or with the study by Button and Neiva [8], which focuses on the reform of the functional airspace blocks. The performance is, however, measured ex-post, and no economic model explaining where gains or losses can be found is supported by these studies. We propose a simple model to formalize the interaction between ANSP and an airline, thus contributing to formalize how performance could be achieved when making use of the relationship between the stakeholders.

Our second main contribution to the ATM literature concerns the way delays are modeled. Among others, Brueckner [9, 10] models the delay cost as a nondecreasing function of flight frequency during the peak travel period of a day. Brueckner and Van Dender [11] collapse the peak and off-peak travel periods into a single travel period, in which delays always exist. The US Federal Aviation Administration [12] models delays as a convex function of flight frequency and airport capacity. This delay function is estimated from the steady-state queuing theory and has been used by Morrison [13], Zhang and Zhang [14–16], and Basso [17]. Pels and Verhoef [18]; De Borger and Van Dender [19]; Basso and Zhang [20]; Yang and Zhang [21, 22]; and Gillen and Mantin [23] use a linear delay function of flight frequency. In this study, we model the delay function in order to capture the causes of delays. In particular, our delay function consists of the delays due to exceptional events (exceptional events can be, for example, adverse weather conditions, aircraft defects, and airport facility limitations) and the delays induced by other flights, in which the number of exceptional events in a slot follows a Poisson distribution. These assumptions follow the typology of Cook and Tanner [24]. In their study, the cost of the delays of airlines is calculated by strategic delays (those accounted for in advance) and tactical delays (those incurred on the day of operations and not accounted for in advance). Strategic delays are for “adding buffer” to the airline schedule. Tactical delays include “primary” delays, and “secondary” or “reactionary” delays, in which original delays caused by one aircraft (“primary” delays) cause “knock-on” effects to the rest of the network (known as “secondary” or “reactionary” delays). The delays in our model mainly correspond to tactical delays, as in Cook and Tanner [24]. Moreover, the delays due to exceptional events in own slots and the delays induced by other flights in the delay function of this model roughly correspond to primary and reactionary delays, as defined by Cook and Tanner [24], respectively.

Because there is an asymmetric information situation between ANSP and the airline, we need to use incomplete information contract theory. In the incentive theory and regulation literature, Caillaud et al. [25] summarize two types of the regulator’s objective function, that is, distributional objectives and the cost of public funds. Baron and Myerson [26] and Baron and Besanko [27] use the objective function distributional objectives, while Laffont and Tirole [28] use the objective function with the cost of public funds. This study considers the cost of public funds when ANSP acts as a social planner. In particular, because passengers may benefit from the service but do not pay ANSP, it is possible that the service is socially desirable, while the airline’s benefit from the service is not as high as the total cost of providing the service. In this case, ANSP has to use public funds to subsidize the service and thus considers the cost of public funds in the objective function.

The rest of the study is organized as follows. Section 2 introduces the model. Section 3 derives optimal delay reduction contracts. Section 4 studies the adjustment of optimal contracts with respect to the modification of the main exogenous parameters, such as safety (a priority of the ATM) and frequency (a measure of the intensity of the activity consequently producing delays). Section 5 uses numerical examples to study when a welfare-maximizing ANSP has to use public funds to provide the delay reduction service. Section 6 concludes the study.

2. The Model

We consider a monopoly ANSP, a monopoly airline, passengers with a mass , and an air transport system connecting two airports. Indeed, our main objective is to determine under which conditions an airline may want to sign a contract with ANSP, which results in shorter delays, and if so, what form the contract should take.

Conditional on the use of the airline, following Brueckner [29]; Brueckner and Flores-Fillol [30]; and Flores-Fillol [31, 32], the passenger utility is as follows:

In equation (1), is the passengers’ income; is the fare; is the passengers’ travel benefit, which is uniformly distributed on the support ; is the passengers’ utility gain from a safety standard with ; is the passengers’ value of time; and , which is a function of safety standard , is the expected delays per flight (in time units).

With respect to the passenger utility function, there are several points to be noted. First, there is another type of passenger utility function, that is, a quadratic passenger utility, proposed by Dixit [33]. Such utility function can be found in Richard [34]; Fu et al. [35]; Lin [36, 37]; Jiang and Zhang [38]; D’Alfonso et al. [39]; and Wang and Wang [40, 41]. The main purpose of this type of utility function is to include two substitutable air transport services, reflecting horizontal product differentiation. As there is only one type of air transport service in this model, a linear passenger utility function is enough to satisfy the research purpose and helps to simplify the analysis. Second, according to the University of Westminster [42], three types of passenger costs of delay may be considered: (i) “hard” costs (borne by the airline, such as rebooking and compensation); (ii) “soft” costs (borne by the airline, such as the loss of market share due to passenger dissatisfaction); and (iii) “internalized” costs (borne by the passenger and not passed on to the airline, such as the potential loss of business due to the late arrival at meetings). The passengers’ value of time in this model mainly refers to the “internalized” costs in the University of Westminster [42]. Third, a safety standard is introduced to the model in order to take into account the fact that the premier objective of ATM is to ensure a safe flight, no matter the delays induced. Our analysis helps to understand the choices that could be made among the several regulations when conflict occurs, which satisfy the safety standards. This choice could be driven by the fact that some airlines want to buy the delay reduction service. Moreover, the safety standard is exogenous and can vary within .

The specification we build of expected delays per flight is as follows:

In equation (2), the first term in the square brackets is the delays due to exceptional events in own slot. We assume that the number of exceptional events in a slot follows a Poisson distribution with parameter , in which is the exceptional event arriving rate; is the number of available hours; and is the flight frequency. It is assumed that flights are evenly spaced during available hours. Consequently, the duration of a slot is . is the number of exceptional events, is the number of delays caused by an exceptional event, and captures the fact that the higher the safety standard, the longer delays will be (see [2, 4, 43]). The second term in the square brackets is the delays induced by other flights, which decreases with and increases with and . What is more, the parameter is the so-called “delay externality parameter” in this study. A greater implies a more severe effect from other flights. In fact, the second term can be interpreted as the delays caused by airport congestion. The square brackets are two times because we consider two airports.

Passengers also have an outside option, for instance, to travel by train. Conditional on the use of the outside option, the passenger utility is , in which is the net benefit of the outside option.

Hence, a passenger chooses to travel by plane when , which is equivalent to , that is, when the travel benefit exceeds the ticket price minus the passengers utility from safety, plus the impact of delays, parametrized by the safety standard, plus the value of the outside option. The air traffic (air passengers’ demand) then equals the following:

We assume a separable airline cost function, composed of the costs to operate traffic, to launch an activity (and thus this part is fixed), and the cost of being delayed. We assume also that airlines may differ with respect to their value of time (we will further consider only one airline, which can be of the high value of time type or low value of time type. Obviously, the extensions would consider competition between airlines and how it influences the delay reduction contract). Hence, the airline’s cost is as follows:

In equation (4), is the variable cost, in which is the marginal cost per seat; is the fixed cost, in which stands for the frequency of flights, that is, a given number of flights per unit of time; is the fixed operating cost of a flight; and is the supply-side delay cost, in which is the airline’s value of time. may not be observed by ANSP. However, it is common knowledge that belongs to the set , in which and . If is the airline’s private knowledge, the airline can be the one with or with probabilities and , respectively. These probabilities represent ANSP prior to the type of airline (low value of time type or high value of time type).

The airline maximizes profit by choosing the fare (in this model, flight frequency is not an endogenous decision variable of the airline. One reason can be the slot control in Europe. That is, at all major European airports, takeoff and landing slots are allocated through “grandfather rights” and the “use it or lose it” rule. However, in the comparative static analysis, we will study how the change in flight frequency affects optimal contracts), that is,

Letting , the optimal solution of equation (5) is as follows:

The optimal fare increases with the private benefit of traveling for passengers and with the marginal cost to produce the transport service. Note that the optimal fare is increasing with the passengers’ utility gain from a safety standard and decreasing with the delays. Finally, the higher the value of the outside option, the lower the optimal fare.

According to the optimal profit of the airline, delays will play a role both in airline cost and consumer demand. With long delays, the same quantity of transport service (that is, the number of passengers) is to be operated at a lower price. However, costs also increase, and consequently, it may be less and less profitable for the airline to operate traffic. If airlines greatly value delays, they may be interested in buying contracts that enable a fixed and reduced exposure to delays. We thus introduce ANSP, which will maximize the social welfare (or its profit).

We then obtain the passenger utility and surplus as follows:

ANSP makes a take-it-or-leave-it offer (a contract) to the airline, in which contracting variables are and . is the degree of the delay reduction service that ANSP provides to the airline, and is the payment transfer from the airline to ANSP. After signing the contract, the expected delays per flight reduce from to , in which is the fraction of delay reduction and measures the effectiveness of the service. It is assumed that , , and , in which the last two derivatives capture that the marginal value of the service is positive but decreasing with the degree. In order to obtain analytical results, it is assumed that , with . The fare, air traffic, airline profit, passenger utility, and passenger surplus will then be as follows:

, respectively. These results show that the airline can enjoy both demand and supply-side delay reduction benefits and that the passengers can enjoy higher surplus, even though the fare increases.

Finally, ANSP’s cost of providing the service (another feasible setup is the linear benefit and convex cost, which is essentially equivalent to our setting, that is, the concave benefit and linear cost) is as follows:

In equation (9), is the marginal cost of the service, which increases with the safety standard, that is, (see [43]). In fact, when providing the service, the ANSP has to spend more time on evaluation and coordination in order to satisfy a higher safety standard, which will inevitably result in a higher cost.

The timeline of the model is shown in Figure 1.

Figure 1 

Timeline.

3. Optimal Contracts

In this section, we derive optimal contracts by considering both the welfare- and profit-maximizing ANSPs. Note that we focus the following discussions on interior solutions.

3.1. Welfare-Maximizing ANSP

The welfare-maximizing ANSP’s objective is as follows:

Here, is the shadow cost of public funds. Note that when the transfer is not enough to cover the total cost of providing the service and the social values of the service are nonnegative, that is, , public funds should be used to cover the gap between and but at some costs (shadow costs of public funds).

Passengers’ value of time will be a determinant for the existence of an air transport market, as shown in Lemma 1.

Lemma 1. Existence of the air transport market. If passengers place a lot of importance on the event of being delayed, then they will always choose another mode of transportation. Hence, the air transport market exists if .

Proof. In Appendix B.1.
As there might exist a distinction between the benefits of the monopoly airline and the welfare-maximizing ANSP, in the case of welfare-maximizing ANSP, we have to distinguish between two scenarios, that is, the “high airline benefit” and the “low airline benefit.” For a welfare-maximizing ANSP, the sum of the airline profit, passenger surplus, and the cost of providing the delay reduction service are maximized. Therefore, if the social benefit of the airline and passengers derived from a delay reduction service is larger than the social cost of ANSP providing the delay reduction service, the welfare-maximizing ANSP should always provide the delay reduction service.
In fact, both the airline and passengers benefit from the service, but only the airline pays for the service. Hence, if the airline’s benefit from the service is higher than ANSP’s cost of providing the service, the transfer from the airline to ANSP could be enough to cover ANSP’s cost. This is the case in scenario 1 (high airline benefit). However, if the airline’s benefit from the service is lower than ANSP’s cost of providing the service, the airline’s transfer will never be enough to cover ANSP’s cost (note that the highest transfer equals the airline’s benefit from the service), and therefore, ANSP will have to use public funds to provide the delay reduction service at some cost. This is the case in scenario 2 (low-airline benefit).

3.1.1. Scenario 1: High-Airline Benefit

In this scenario, both passengers and the airline benefit from the service and the airline’s benefit are higher than ANSP’s cost of providing the service. Hence, the delay reduction contract could be implemented without using public funds. However, the problem here is to quantify under incomplete information the importance of the information rent. Let us start with a complete information setting.

(1) Complete Information. Under complete information, it is optimal for ANSP to set the transfer at least as the cost of providing the service. Accordingly, the optimization problem of the ANSP is as follows:

Then, by taking the first-order condition of equation (11), we can obtain that the first-best (FB) optimal contracts for the airline with and are and , respectively. In particular, as shown in (12), and are determined by and , respectively. These two implicit functions define the optimal degrees of the delay reduction service in contracts. For both and , the optimal degree is determined by the intersection of a logarithmic and linear function of . According to and in equation (12), because , we also have . A detailed discussion about the second-order condition of equation (11) is in Appendix A. Discussions about other second-order conditions in this study are similar and are, therefore, omitted hereafter. In addition, and are given as follows:

(2) Incomplete Information. Under incomplete information, the first-best optimal degrees of the service can be feasible and induced costs for ANSP are covered (without the need to leverage public funds). Indeed, the benefits of delay reduction together with passengers and the airline are enough to compensate the costs of providing the delay reduction service.

ANSP maximizes the expected social welfare as follows:

For feasible separating contracts, the airline’s incentive compatibility and participation constraints must be satisfied, that is,

The information rent of the airline is denoted with and by and , respectively, in which and . Then, we can write the airline’s incentive compatibility and participation constraints as follows:

In order to solve the ANSP’s problem, first should be made, should be binding, and should be omitted, and then the omitted constraints should be checked after solving the problem. The simplified constraints become and .

In fact, the maximization of equation (13) gives the same optimal degrees of the service as under complete information, that is, and determined by and in equation (12). Furthermore, the second-best (SB) optimal degrees and can satisfy the omitted constraints and . According to and , the second-best optimal transfers are as follows:as long as . Furthermore, as shown in in equation (16), ANSP provides an information rent to the airline with in order to avoid it mimicking the other type.

If , ANSP may still propose separating contracts by using public funds or propose a pooling contract without using public funds. The separating contracts are more effective than the pooling contract in terms of efficiency, while the pooling contract saves the cost of public funds. As the optimality between these two types of contracts depends on parameter values, it will be an issue in practice.

3.1.2. Scenario 2: Low-Airline Benefit

In this scenario, both passengers and the airline can benefit from the service and the airline’s benefit is lower than ANSP’s cost of providing the service. Therefore, as long as the social benefit of the service outweighs the social cost, it is optimal for ANSP to use public funds (even at shadow cost ) to cover the part of the costs, which cannot be covered by the airline’s transfer.

Because the analysis for and under complete information is similar to that in Scenario 1, we will only derive optimal contracts under incomplete information.

(1) Incomplete Information. Under incomplete information, ANSP maximizes the expected social welfare as follows:subject to the airline’s incentive compatibility and participation constraints, as shown in Scenario 1.

Following the same procedure of derivation as in Scenario 1, plugging and into (11) and taking the first-order condition of equation (11), we can obtain the second-best optimal menu of contracts , as shown in equation (12). Again, and are determined by the intersection of a logarithmic and linear function and satisfy the omitted constraints. In addition, the second-order condition is also satisfied.