Evaluation of Strategies to Reduce the Cost Impacts of Flight Delays on Total Network Costs
Evaluation of Strategies to Reduce the Cost Impacts of Flight Delays on Total Network Costs
Rosenow, Judith;Michling, Philipp;Schultz, Michael;Schönberger, Jörn
aerospace Article Evaluation of Strategies to Reduce the Cost Impacts of Flight Delays on Total Network Costs 1, 1 1 2 Judith Rosenow * , Philipp Michling , Michael Schultz and Jörn Schönberger Institute of Logistics and Aviation, Technische Universität Dresden, 01069 Dresden, Germany; email@example.com (M.S.) Institute of Transport and Economics, Technische Universität Dresden, 01069 Dresden, Germany; firstname.lastname@example.org * Correspondence: Judith.Rosenow@tu-dresden.de; Tel.: +49-351-46339446 Received: 26 October 2020; Accepted: 15 November 2020; Published: 18 November 2020 Abstract: Competitive price pressure and economic cost pressure constantly force airlines to improve their optimization strategies. Besides predictable operational costs, delay costs are a signiﬁcant cost driver for airlines. Especially reactionary delay costs can endanger the proﬁtability of such a company. These time-dependent costs depend on the number of sensitive transfer passengers. This cost component is represented by the number of missed ﬂights and the connectivity of onward ﬂights, i.e., the offer of alternative ﬂight connections. The airline has several options to compensate for reactionary delays, for example, by increasing cruising speeds, shortening turnaround times, rebookings and cancellations. The effects of these options on the cost balance of airline total operating costs have been examined in detail, considering a ﬂight-speciﬁc number of transfer passengers. The results have been applied to a 24-h rotation schedule of a large German hub airport. We found, that the fast turnaround and increasing cruise speed are the most effective strategies to compensate for passenger-speciﬁc delay costs. The results could be used in a multi-criteria trajectory optimization to ﬁnd a balance between environmentally-driven and cost-index-driven detours and speed adjustments. Keywords: airline delay costs; delay compensation; connective passengers; multi-criteria trajectory optimization 1. Introduction The International Civil Aviation Organization (ICAO) for the standardization of international air trafﬁc formulated its vision of a global, optimally economical, sustainable, and safe Air Trafﬁc Management (ATM) system in Doc 9854  in 2005. Every six years, ICAO deﬁnes the necessary instruments, procedures, and implementation data in so-called Aviation System Block Upgrades (ASBU) . Therein, together with the Single European Sky ATM Research Programme (SESAR), ICAO plans to implement Trajectory Based Operations (TBO) by 2028, with the prospect of increasing air trafﬁc efﬁciency, increasing the safety level, and increasing the environmental compatibility of air trafﬁc. TBOs describe 4D trajectories with binding-time speciﬁcations to enable airlines to plan and operate ﬂights individually and dynamically. In contrast to today’s long-term and static ﬂight planning along with a ﬁxed route structure, TBOs enable 4D multi-criteria optimized free routes. TBOs are expected to give air trafﬁc control (ATC) access to the separation-related position data of all aircraft [3,4]. With TBO, all air trafﬁc stakeholders (i.e., the ﬂight itself, the airline, the ATM network, and the air trafﬁc service provider (ANSP)) can update individual, sometimes conﬂicting, optimization targets and restrictions on a single trajectory during the ﬂight. Through an efﬁcient exchange of information, Aerospace 2020, 7, 165; doi:10.3390/aerospace7110165 www.mdpi.com/journal/aerospace Aerospace 2020, 7, 165 2 of 22 a revision of the ﬂight path is possible so that during the ﬂight the optimal trajectory is achieved as a compromise between all air trafﬁc participants. This dynamic trajectory optimization carries an important potential to react to operational conditions on a tactical level. For example, TBOs allow us to react to disruptions in the ﬂight plan and therewith to reduce delay costs already during the ﬂight. Those actions may induce additional costs in terms of extra fuel burn. From this follows an optimization problem, wherein costs for delay reducing actions in the air and on the ground have to be balanced with the expected delay costs. The delay costs, however, strongly depend on the number of transfer passengers and are ﬂight-speciﬁc. This paper investigates the success rate and the compensation rate of several actions to reduce delay costs by opposing the costs of these measures to the expected passenger-sensitive delay costs. In this paper, we focus on the estimation of costs of ﬁve different operational strategies to keep delay-induced operation costs in a ﬂight network as low as possible. After we have surveyed the relevant scientiﬁc literature (Section 2), we propose a scheme to estimate the relevant passenger ﬂow from inbound and outbound ﬂight at a major German hub airport (Section 3). We use the resulting passenger ﬂow values to feed a cost calculation scheme that provides a total cost estimation for a given delay situation (Section 4). With the goal to ﬁnd out if we can reduce these costs, we discuss ﬁve different operational strategies to reduce the resulting reactionary costs of a delay of a ﬂight in a network (Section 5). For the evaluation of these strategies, we propose innovative performance indicators (Section 6). Using these indicators, we analyze the ability of the ﬁve operational costs reduction strategies for the given data set (Section 7). 2. State of the Art 2.1. Delays in Airline Operations In 2019, an average of 1328 ﬂights per day in Europe had a delay of more than 15 min . Delay is deﬁned as the difference between the scheduled off-block time (SOBT) and the start time window assigned by the central air trafﬁc ﬂow control unit, the actual off-block time (AOBT) . On average, this also called Air Trafﬁc Flow Management (ATFM) delay caused approximately EUR 100 per minute of delay for airlines . If a ﬂight is delayed, it causes a primary delay at the destination airport. If this disturbance cannot be made up for during the next turnaround, the delay is carried over into the following ﬂight events. Due to these reactionary delays, tactical network delays cannot be excluded. Per minute of primary delay, Europe suffers an average of two thirds of a minute of secondary delay . The reasons for primary and reactionary delays are manifold. For example, technical problems on the aircraft mainly induce primary delay, as long as the aircraft is exchanged. Passenger- or baggage-related delays, cargo or postal-related causes, flight operational disruptions, and aircraft-related malfunctions on the apron, the cause of which is usually queues in the airside infrastructure, are primarily responsible for reactionary delay. If there are technical defects on the aircraft with primary delay, the ﬂight dispatcher must include the replacement or repair of the aircraft in the cost calculation. Both generally lead to unavoidable delays in ﬂight operations. The frequency of a technical defect on an aircraft that causes a delay on the ground of more than 15 min is described as Technical Dispatch Reliability (TDR) and achieves very low failure rates in civil air trafﬁc with values between 2.2% and 1.5% . Airlines send the reasons for their delays as a delay code, deﬁned by the International Air Transport Association (IATA), in AHM 780 (i.e., a standard format for Aircraft Movement Messages) from the departure airport to the destination airport . Among the causes of reactionary delays, passenger-related delays (i.e., waiting for delayed passengers or baggage) are particularly sensitive for airlines as commercial enterprises. If delay costs are to be minimized, it is important to distinguish between primary and reactionary delay. While the primary delay of a single ﬂight is primarily limited to personnel costs and passenger compensation claims, the costs of reactionary delays become almost unpredictable due to the Aerospace 2020, 7, 165 3 of 22 propagation of the primary delay to subsequent ﬂight events and may even have an impact on maintenance costs. Airlines have set up the Airline Operations Control Center (AOCC) to avoid reactionary delays. Here, the ﬂight dispatcher tries to compensate for the reactionary delay costs to the same extent as he tries to maintain passenger comfort. In 2004, passenger rights and conditions were laid down uniformly throughout Europe in EU Regulation (EC) No. 261/2004. In this regulation, compensation claims are dependent on distance and delay. For example, for ﬂights with distances of up to 1500 km, compensation amounting to EUR 250 can be claimed from a delay of two hours (see Section 4.4). Airlines have different possibilities to react to delays. Most of these possibilities may save delay costs, but induce costs themself. Hence, the efﬁciency of each one depends strongly on the duration of the delay, the number of sensitive connective passengers, and possible onward ﬂights. For example, airlines plan time buffers in their ﬂight schedules, which depend on the distance to be ﬂown, the SOBT, and the extent of the delays in the past . The measurement of these time buffers requires a trade-off between opportunity costs (lost revenue due to the longer ground time of an aircraft) and the costs of the delay of an aircraft . Allocating these schedule buffers efﬁciently in daily airline schedules to eliminate critical resource dependencies and therewith to improve the network robustness is still under investigation [12–15]. If delay costs are subject to a multi-criteria trajectory optimization, a rough estimate of the delay costs of EUR 100 per minute cannot be used because reactionary delay costs incurred by an airline are individual cases. For this reason, the individual costs of each strategy must be quantiﬁed and implemented them in a trajectory optimization environment. For example, the Toolchain for Multi-Criteria Aircraft Trajectory Optimization (TOMATO)  enables a comparison of delay costs with the total costs of the whole ﬂight to derive ﬂight-speciﬁc recommendations for action. Only then, environmentally induced detours (e.g., to avoid turbulent areas, trafﬁc congestion, or the formation of contrails) can be offset against the expected delay costs. Today, the avoidance of contrail formation is not an operational target, since contrails are not burdened with costs. However, the radiative impact of contrails on global warming has been proven  and is socially accepted . In line with a greener aviation, contrail costs might be an efﬁcient instrument in the near future. The non-linear relationship between contrail costs and delay costs has already been elaborated . In this study, the detailed cost rates have been applied to each delayed ﬂight individually in a network provided by a representative rotation schedule of an airport, depending on the number of transfer passengers and the airline business model to develop recommendations for actions. 2.2. Quantiﬁcation of Delay Costs In the Airline business, delay costs, especially passenger-related costs, are not published. Airline delay costs are part of the airline business model and often belong to the company secret. The University of Westminster accumulated the delay costs of numerous European airlines and published mean values for three different scenarios . The scenarios reﬂect different passenger sensitivities and are referred to as high, base, and low. This estimation was made aircraft-type speciﬁc for 15 aircraft types and allows a more detailed overview of airline delay costs. Cook and Tanner  provide reference values for the cost of delay to European airlines based on the year 2014. However, not all cost components and aircraft types are considered in this report and the number and connectivity of sensitive transfer passengers of an individual ﬂight are not considered. Usually, intents in optimizing ground operations (e.g., to minimize the turnaround time) have to deal with deﬁning delay costs in the objective function. However, if the turnaround time is to be minimized, costs play an underestimated role. Hence, costs are only approximated in those studies. For example, as part of the Airport-Collaborative Decision Making (A-CDM), several studies deal with an accurate prediction of turnaround target times by incorporating stochastic process time distributions without considering the turnaround costs at all [20–26]. In these studies, delay costs are often linearized and do not consider passenger-related costs. Analytical approaches aiming an optimal allocation Aerospace 2020, 7, 165 4 of 22 of airport resources, such as ground handling equipment [27,28], pushback trucks , de-icing slots  or aircraft stands [31,32] approximate the costs as parameterized boundary conditions in their optimization. All these studies do not couple ground and ﬂight operations and hence do not need to consider detailed ﬂight-speciﬁc monetary delay costs . Beatty et al.  minimize the costs of reactionary delays by allowing the airline to swap landing slots. Ahmadbeygi et al.  and Wu  focus on the advantage of planning slacks in the planned schedule to minimize delay costs. Wu et al.  identiﬁed weak links in an airline network using a Bayesian Network in a delay-tree framework for modeling multiple resource connections for transfer passengers. All these studies do not consider the possibility to reduce the delay costs of individual sensitive passengers. Delay may be reduced by Air Trafﬁc control (ATC) and an intelligent slot assignment. Although this strategic level is out of the scope of this paper, Montlaur and Delgado  analyzed a signiﬁcant regression between minimized total ﬂight delay and minimum passenger delay which motivates the analysis of this paper. They applied other slot allocation priorities than those usually applied in Rotation by Schedule and placed a stronger focus on passenger numbers without considering the number of connective passengers. Manley and Sherry  also considered passenger ﬂows in the slot assignment, but did not distinguish between connective passengers and passengers at their ﬁnal destination. 2.3. Delay Costs in Aircraft Trajectory Optimization Other studies, dealing with monetary delay costs in trajectory optimization often do not consider the environmental part of the trajectory assessment, although it contains the most unpredictable impact factors. The focus of the project Turnaround Integration in Trajectory and Network (TITAN)  was the identiﬁcation of improvement opportunities in the communication between aircraft turnaround stakeholders  to reduce the delay on ground. However, in TITAN the aircraft was still considered stationary. During the turnaround, the trajectory continues to evolve but only in the time dimension . Neither the network level nor environmental issues are developed in detail. Other studies end at the airport slot allocation and are not interested in the effect of trajectory deviations on the delay costs [37–41]. Other authors focus on the absorption of delays, neglecting negative effects as increased costs by gaining speed . The restrictions may result from the necessity to precisely model the individual aircraft trajectory to assess competitive cost factors of the trajectory. To consider different weightings of the cost functions physically reliable modiﬁcations regarding ﬂight path or speed are required. Therefore, an aircraft performance model with optimization potential is essential. Those highly complex and aircraft type-speciﬁc models are rare. Matthes et al.  developed a performance model for the development of environmentally friendly trajectories based on BADA performance tables which is a rough approximation of the aircraft performance . Here, delay costs were not considered. The Air Trafﬁc Optimizer (AirTOp) would be able to couple the trajectory and ground operations, but also relies on BADA performance tables and is restricted to the implementation of a Standard Atmosphere . Commercial products, such as Lido ﬂight 4D by Lufthansa or the Air Trafﬁc Simulator (TAAM) by Jeppesen only consider a Standard Atmosphere without any wind information. Therewith, weather effects cannot be reproduced. The conducted literature scan reveals that the analyzes of reactionary delay costs and its propagation into a flight network has not yet been adequately investigated. This paper aims to contribute to the closure of this research gap. 3. Estimation of the Onward Passenger Flows in the Network 3.1. Data Analysis This evaluation of delay compensating strategies to reduce total network costs is applied to a 24-h rotation schedule on Frankfurt airport (FRA), which is the biggest hub airport in Germany. The data are Aerospace 2020, 7, 165 5 of 22 taken from 22 July 2017 and include 1389 passenger ﬂights, from which 1027 ﬂights were delayed more than ten minutes. Figure 1 provides an overview over the frequency of the analyzed delay categories in the example rotation schedule. As far as our data availability allows a statement, this example represents an operational standard day in summer 2017 at Frankfurt Airport. Figure 1. Frequencies of inbound delay d (minutes) (left) and outbound delay (right) of the example 24-h rotation schedule on Frankfurt airport (FRA) from 22 July 2017. Despite a 75% share of punctual inbound ﬂights, only 50% of outbound ﬂights were on time. 3.2. Aircraft-Type-Speciﬁc Seat Load Factor and Payload Factor In this study, the valuable aircraft-type speciﬁc ﬁndings from Cook and Tanner  are extended by additional aircraft types and delay costs, covering transfer passenger ’s concerns. As pointed out in Section 2.2, the number of connective passengers is highly sensitive to the success rate of a delay compensation strategy. To approximate this number, the overall number of passengers per aircraft type is required and known as seat load factor (SLF). SLF is the quotient of revenue passenger kilometers (RPK) sold and the available seat kilometers (ASK). In the framework of EUROCONTROL’s Programme CARE INO III the University of Westminster  summarized the available number of seats for three different scenarios and 12 aircraft types. For three scenarios (low, base, and high), ratios of passengers depending on the highest number of passengers used in practice have been estimated to 100%, 85% and 75%, respectively. We found a linear relationship between the square root of the maximum take-off weight (MTOW) (t) and the highest number of passengers used in practice with a coefﬁcient of determination R = 0.99 and applied Equation (1) RPK SLF = = 0.8599 MTOW 57.557 (1) ASK to all aircraft types. In contrast to SLF, the payload factor PLF is the ratio of payload and maximum possible payload. It is the ratio of revenue ton-kilometers (RTK) sold to available ton-kilometers (ATK). PLF is required for the estimation of additional fuel burn in the case of a delay. 3.3. Estimation of Primary and Reactionary Delay Since this analysis is based on a rotation schedule of 24-h at Frankfurt Airport, Germany, the primary delay D (min) of each arriving aircraft at Frankfurt is estimated as the difference prim. between SIBT and AIBT and for departing ﬂights as the difference between scheduled off-block time (SOBT) and actual off-block time (AOBT). In contrast to a measurable primary delay, the reactionary delay cannot be estimated using a rotation schedule of an airport. Reactionary delay D (min) strongly depends on the amount of react. primary delay D and on the daytime. Beatty et al.  developed a linear function (Equation (2)) prim. of D depending on D with different parameters for each 30 min between 6 a.m. and 10 p.m. react. prim. These functions have been increased by 1.66% to reﬂect a growth in reactionary delay during 2008 and Aerospace 2020, 7, 165 6 of 22 2014, discovered by . Figure 2 shows the slope a and the of the intersection with the origin b of this linear relationship D = a D + b (2) react. prim. between reactionary delay and primary delay depending on the daytime. 0.030 1.022 0.025 1.020 0.020 1.018 0.015 1.016 0.010 1.014 0.005 1.012 0.000 1.010 6 8 10 12 14 16 18 20 22 24 6 8 10 12 14 16 18 20 22 24 Daytime [h] Daytime [h] Figure 2. Slope a and Intersection with origin b of the linear relationship between reactionary and primary delay depending on daytime. D is limited to 240 min for narrowbodies and 300 min for widebodies as part of an economic react. trade-off between delay costs and cancellation of the ﬂight . Delay costs of D of a subsequent ﬂight do not arise directly from the delay of the delayed ﬂight. react. Therefore, differentiation between rotational and non-rotational delay costs is required. The share of rotatory or non-rotatory delay in the reactionary delay varies depending on the airline. Ref  calculated an average share of 86% rotatory delay of all reactionary delays. The rotatory delay determined in this way is distributed among all further ﬂight movements of the same aircraft on the same day. Narrowbodies are typically used on shorter routes so that these make more ﬂights per day than widebodies. Because the rotation schedule of one airport does not provide the total number of ﬂights per day and aircraft the following assumptions are made . For the low, base and high scenario: four, two, and one ﬂight per day per narrowbody and two, 1.5 and one ﬂight per day per widebody, respectively. 3.4. Estimation of Relevant Transfer Connections and Passenger Flows Since the rotation schedule does not provide information about connecting ﬂights that might be missed by connecting passengers or that might be waiting for the feeder, the ﬁrst three possible connecting ﬂights to a particular destination are considered under the following boundary conditions: Frankfurt Airport is a hub only for airlines within the Lufthansa Group (Lufthansa, Austrian and Swiss). Hence, either feeder or deliverer must be registered with the Lufthansa Group. No direct return to the departure airport. No connection between two ﬂights shorter than 300 km each. Minimum connecting time for travel within the Schengen area: 45 min. Minimum connecting time for journeys starting or ﬁnishing outside the Schengen area: 90 min. Maximum connecting time between ﬂights: 360 min. The number of passengers traveling to a particular destination varies according to the popularity of the destination. The total number of transfer passengers, as well as the share of passengers traveling to certain airports, speciﬁc countries, continents, and regions, are taken from air trafﬁc statistics of Frankfurt Airport . In 2019, 55% of all passengers at FRA were transfer passengers . Because the airline-speciﬁc number of transfer passengers strongly depends on the airline business model, we distribute the total number of transfer passengers with 5% to low-cost carriers, 10% to Linear Slope [a.u.] Intersection with origin [min] Aerospace 2020, 7, 165 7 of 22 leisure carriers, and 40% to network carriers. Note, these shares of passengers do not reﬂect the number of delayed transfer passengers. Based on the assumed distribution of transfer passengers, we deﬁne the share of delayed transfer passengers depending on the business model and scenario at the percentages given in Table 1. Table 1. Assumed number of delayed transfer passengers depending on business model and scenario based on total numbers of transfer passengers provided by Frankfurt Airport . Narrowbody Widebody Airline Low Base High Low Base High Low cost 1.0% 1.5% 2.0% 1.0% 1.5% 2.0% Leisure 1.0% 2.0% 3.0% 2.0% 3.0% 4.0% Network 2.0% 3.0% 4.0% 2.0% 4.0% 6.0% Based on these empirical values, the probability is determined that a passenger would be to a speciﬁc destination airport. If there is more than one daily ﬂight to a destination airport the expected value is calculated based on the proportion of seats available on the ﬂight of the total number of seats available on the day in question. 4. Cost Impacts of Reactionary Delay Since the aim of this paper is the monetization of airline delay costs to be considered in a multi-criteria trajectory optimization, only the tactical delay costs and especially the tactical delay costs at the network level (reactionary delay costs) are relevant. Strategic delay costs are not taken into account because they do not arise in operational business and therefore cannot be inﬂuenced by operational compensation strategies. In this paper, aircraft type-speciﬁc cost components for fuel, maintenance, crew, and passengers developed by Cook et al. [11,47] are extended by carbon dioxide emission costs and missing aircraft types considering improvements in the efﬁciency of recently developed aircraft. 4.1. Fuel Burn and Kerosene In order to determine fuel ﬂow for additional ﬂight time due to delay, we distinguish between ﬂight phases ground (containing auxiliary power unit (APU), idle and taxi), cruise (containing cruise and climb) and descent (containing descent and holding) . For each ﬂight phase and each scenario, a linear function of fuel ﬂow m (kg/min) depending on MTOW (t) has been identiﬁed within the data provided by  with coefﬁcients of determination between 0.96 R 0.99. Again, the scenarios reﬂect different airline business models and different pay load factors (low: PLF = 85%, base: PLF = 65% and high: PLF = 50%). For example, in the high scenario additional fuel during cruise m is calculated by f,cruise m = 14.073 MTOW + 0.0004. (3) f,cruise For each scenario, the functions are used to extend the fuel ﬂow to missing aircraft types. We assume a lower fuel ﬂow of recently developed aircraft types due to technical improvements. For this reason, fuel ﬂow is reduced for A346 by 5%, A20N, A388, and B748 by 10%, and A359, B788, and B789 by 20%. Furthermore, the fuel ﬂow of the old MD82 is increased by 10%. The reduced fuel ﬂow of A20N, A388, and B748 and the increased fuel consumption of MD82 could be approximated with the aircraft performance model COALA . The 5% gain in fuel efﬁciency of the A346 is only an assumption, which must be validated for future analysis. The available, interpolated, and manipulated aircraft types are listed in Table 2. Aerospace 2020, 7, 165 8 of 22 Table 2. Aircraft types considered in this study. Since Cook et al.  do not provide cost components for each aircraft type, some fuel burn values have been interpolated and others additionally manipulated. Provided by Cook et al.  Interpolated Interpolated Interpolated and Manipulated A319 A332 CRJ7 A20N (=A320 20%) A320 A333 CRJ9 A346 (=regression 5%) A321 A343 CRJX A359 (=regression 20%) AT43 B462 DH8D A388 (=regression 10%) AT72 B736 E145 AT75 (=AT72) B733 B737 E190 B748 (=regression 10%) B734 J328 E195 B788 (=regression 20%) B735 B753 E75L B789 (=regression 20%) B738 B764 E75S MD82 (=regression + 10%) B744 B772 F70 B752 B77W B763 BCS1 The price per kilogram kerosene is assumed to be EUR 0.5, EUR 0.6, and EUR 0.7 for the low, base, and high scenario, respectively. In the high scenario, fuel costs per minute delay amount to C = m 0.75. (4) f,cruise 4.2. CO Costs Carbon dioxide emissions constitute a major part of jet engine emissions with contribution to global warming. Depending on the degree of completeness of the combustion of kerosene the emission index E I (kg CO /(kg kerosene)) varies between 3.11 E I 3.32 . In this study, we assume CO 2 CO 2 2 an emission index of E I = 3.11, E I = 3.19 and E I = 3.32 in the low, base and CO ,low CO ,base CO ,high 2 2 2 high scenario, respectively. In the last two years, the price per tonne emitted carbon dioxide EU CO (EUR/t CO ) varied between 18.35 EU 29.46 . Minimum, mean and maximum values are 2 CO transferred to the scenarios. Finally, costs for CO per kilogram kerosene range from EUR 0.057/kg, EUR 0.078/kg and EUR 0.097/kg kerosene for the low, base and high scenario, respectively. Finally, in the high scenario, CO costs yield to C = 3.32 m 0.097. (5) CO ,high f,cruise 4.3. Maintenance Costs (MRT) Cook and Tanner  determined the maintenance costs for twelve different aircraft types (compare Table 2), which are due to the longer stress on an aircraft, e.g., due to the delay in the air or on the ground for the low, base, and high scenario. Costs distinguish between the ﬂight phases gate, taxi, and airborne. Maintenance costs linearly depend on the square root of MTOW ( t). For example, in the high scenario, increased maintenance costs (EUR/min) due to airborne delay can be approximated by C = 1.3088 MTOW + 0.0154. (6) MRT Coefﬁcients of determination between 0.90 R 0.96 give evidence for the linear dependency. Hence, other aircraft types have been interpolated and no manipulation took place. 4.4. Costs for Crew and Passengers Cook and Tanner determined costs for the crew due to extra work during delay C (EUR/min) crew for the base and high scenario as a function of the delay  for twelve different aircraft types (see Table 2). In the low scenario, it is assumed that overtime is not remunerated . Since these numbers reﬂect the analyses of the year 2014, we increased the crew costs by 0.5% and 1% per Aerospace 2020, 7, 165 9 of 22 year for the base and high scenario, respectively. The number of crew members is deﬁned in the prototype certiﬁcation of the aircraft and depends on the number of passengers and the airline business model. The compensation of overtime hours (EUR/min) given by Cook and Tanner  can be linearly approximated as function of MTOW ( t) with coefﬁcients of regression between 0.90 R 0.95. For example, in the high scenario, additional crew costs for the airline are calculated by C = 0.08 MTOW 0.52. (7) crew,high Passenger costs due to delay C (EUR/min) are distinguished between hard costs C pass pass,hard (EUR/min) (for compensation and assistance services which an airline must pay to passengers in the event of delay, regulated by law) and soft costs C (EUR/min) (support for particularly pass,soft time-sensitive ﬁrst-class or business-class passengers, not regulated by law). Compensation payments for hard costs are deﬁned in Regulation (EG) 261/2004. Hard costs for the airline, depending on the number of passengers are provided by Cook and Tanner  and can be approximated as power function of the primary delay D (min) with a regression coefﬁcient of R = 0.99: prim. 0.7702 C = 0.0122 D (8) pass,hard,low prim. 0.7749 C = 0.0195 D (9) pass,hard,base prim. 0.7831 C = 0.0229 D . (10) pass,hard,high prim. The compensation paid for an annulation of the ﬂight in case of a very large delay depends on the travel distance and is deﬁned in Regulation (EG) Nr. 261/2004. Flights with distances shorter than 1500 km, between 1500 and 3500 km and longer than 3500 km are compensated with EUR 250, EUR 400 and EUR 600, respectively. Additionally, a catering/hotel allowance of EUR 86, EUR 107 and EUR 122 are assumed for the low, base, and high scenario, respectively. Passenger soft costs per passenger depending on the primary delay (min) are discretized by  in ﬁve-minute steps. We corrected the ﬁgures for inﬂation of 4.46% between 2014 and 2019, and interpolated linearly between the ﬁve-minute steps. The share of soft costs from the total passenger costs has been assumed to be 10% in the low and base scenario and 20% in the high scenario. Finally, we approximate the amount of total passenger delay costs with the following power functions: 0.7743 C = 0.0125 d (11) pass,low prim. 0.7864 C = 0.0205 d (12) pass,base prim. 0.7915 C = 0.0241 d . (13) pass,high prim. 4.5. Conclusions of Airline Reactionary Delay Costs Finally, the total airline costs per minute reactionary delay can be estimated summarizing Equations (3) to (13) to C = C + C + C + C + C . (14) total m CO MRT crew pass f 2 In the high scenario, the components are quantiﬁed to C = (14.073 MTOW + 0.0004) 0.75 (15) m ,cruise,high C = 3.32 m 0.097 (16) CO ,high f,cruise C = 1.3088 MTOW + 0.0154 (17) MRT C = 0.08 MTOW 0.52 (18) crew,high 0.7915 C = 0.0241 d . (19) pass,high prim. Aerospace 2020, 7, 165 10 of 22 The impact of individual delay cost components on the total delay costs depends on the scenario (low, base, or high), on the aircraft size (narrowbody or widebody), and the total amount of delay. Figure 3 shows the share of cost components as mean values per delay interval. For small amounts of delay (<10 min), the share of crew costs dominates the cost balance. The higher the amount of delay, the more important the share of reactionary passenger costs and the lower the importance of kerosene and crew. Figure 3. Share of reactionary delay costs components for a widebody aircraft in the high scenario, depending on the amount of reactionary delay (D ). react. Note, Figure 3 only shows the result of the analysis done in Section 4. Here, the reactionary delay costs per delayed ﬂight without any compensation strategy is shown. In the following, compensation strategies of reactionary delay are analyzed, formalized, and applied to the ﬂight schedule of FRA. 5. Compensation Strategies of Reactionary Delay In the following, costs for ﬁve compensation strategies to minimize airline delay costs are estimated to ﬁnd the most efﬁcient strategy or combination of strategies for each delayed ﬂight in the example rotation schedule. 5.1. Fast Turnaround (FTA) The total turnaround time (TAT) as the duration of the aircraft on the ground is hard to predict, especially in case of an arrival delay [21,25,26]. The reasons for that are manifold: First: the actual gate position may vary from the scheduled one, second: resources of the ground operations may be limited, third: the ATC clearance for take-off may be retarded because of a missed take-off slot, and fourth: the network management operations center (NMOC) may retard the clearance because of a missed airway slot. This often results in a delay increase of an already delayed aircraft due to an unexpectedly long stand on ground . The analyzed rotation plan of Frankfurt Airport showed that 81% of the delayed ﬂights exceeded their scheduled TAT. Nevertheless, reducing the TAT to a minimum TAT is an acknowledged compensatory strategy . Aircraft-type speciﬁc minimum TATs are deﬁned in the airplane characteristics for airport planning, e.g., . It is assumed, that minimum TAT can be reached by using increased personnel and planning resources for the ground manager. Salaries of personal resources are deﬁned in the staff hourly rates of each airport . For the ground manager, an additional EUR 50 are assumed in the low and base scenario, and EUR 100 are allocated for the high scenario. Furthermore, a standard processing fee for a fast turnaround of EUR 100 is allocated. In the low scenario, one additional cleaning and one loading staff member and one loadmaster are assumed for narrowbodies, two cleaning and loading staff members, and one loadmaster for widebodies are allocated. In the base scenario, the cleaning staff members are doubled and in the high scenario cleaning and loading staff members are doubled. Aerospace 2020, 7, 165 11 of 22 In summary, the costs for FTA depend on the scenario (low, base, high), the aircraft size (widebody, narrowbody) and on the salary of the cleaning and catering staff. The number of delay minutes that can be reduced is limited depending on the aircraft. Note, the success of this strategy depend neither on the number of connective passengers nor on the amount of reactionary delay. This compensation strategy cannot be applied to aircraft with overnight stays at the airport and to aircraft with an increased TAT of more than 45 min, because those aircraft are assumed to have a different problem than personnel shortages (e.g., unexpected maintenance). The reduction to a minimum TAT reduces the reactionary delay costs but causes higher personnel costs. 5.2. Increasing Aircraft Cruising Speed (I ACS) Usually, with the ﬁrst notice to airmen (NOTAM) after take-off, the crew receives information about the latest time on position to guarantee that each passenger onboard will reach the booked connection ﬂight. This NOTAM contains a priority list (in terms of passenger soft costs) of passengers and their connecting ﬂight and provides the opportunity to adjust the aircraft speed (more precisely, the cost index as ratio of time costs and fuel costs ((USD/minute) (USD/kg fuel) ) for Airbus and ((USD/min) (USD/lb fuel) ) for Boeing) in case of very sensitive passenger connections. Although the aircraft performance envelopes during the cruise are limited, on long-haul ﬂights the aircraft can save up to 50 min of ﬂight time . With a regression coefﬁcient of R = 0.94, ﬂight time savings S (min) depending on the great circle distance d (km) between departure and destination, provided by , can be linearly approximated by S = 0.0043 d + 0.39. (20) The increased fuel ﬂow m per jet engine (kg) due to the increased cruising speed can be f,add approximated as a function of S m = 0.583 S + 47.64 S 37.92. (21) f,add Equation (21) has been derived from values provided by  with a regression coefﬁcient of R = 0.93. Because of expected technological improvements, we decreased the additional fuel ﬂow for the aircraft types A359, B788, and B789 by 10%. Additionally, to the amount of increased fuel costs (Section 4.1), we calculated increased CO costs (compare Section 4.2) for the additionally burned fuel. These additional costs must be weighed against the reduced reactionary delay costs. Note, we ignore that the increased amount of fuel must have been tanked before take-off. From this follows, that in operations the cruising speed may not be increased during the whole cruising phase. Furthermore, the performance limits of modern aircraft severely limit the speed of cruising ﬂight between the stall speed for lift generation and the maximum Mach number . Often, the recommended cruising speed is already close to the upper limit of the maximum Mach number. Increased fuel costs and engine loads are cost-driving negative effects that make this measure only recommendable for extremely sensitive transfer passengers. In summary, the costs for I ACS depend on the aircraft type and on the fuel price which is a function of the scenario. The number of delay minutes that can be reduced depends on the distance between departure and destination and on the potential of the aircraft to increase cruising speed. Note, the success of this strategy depend neither on the number of connective passengers nor on the amount of reactionary delay. 5.3. Rebooking of Passengers (REBP) Passenger compensation claims will be reduced by rebooking the transfer passengers if an alternative connection to the destination is available. In this context, co-operations, especially strategic alliances with other airlines, represent an enormous competitive advantage. Table 3 lists preferences (with increasing costs) when determining the substitute transport to be booked. Aerospace 2020, 7, 165 12 of 22 Table 3. Cooperation partners for rebooking passengers to other ﬂights and multiplier M to consider different co-operations in the new ticket price. Cooperation Multiplier M Own airline 1.00 Same aviation group 1.02 Same alliance 1.20 Airlines within a strategic partnership (e.g., code sharing) 2.00 Other airlines 2.00 Other modes of transport 2.00 Compensation costs for rebooking passengers are deﬁned as the difference between the original ticket price and the expected price of the passenger ’s new ticket on the one hand, and a ﬂat rate per passenger on the other. To determine the expected additional ticket costs, the average ticket price for ﬂights from a German airport is used  and this is deﬁned as the price for the base scenario. We distinguish between destinations in Germany, Europe, and other continents than Europe. For the low and high-cost scenario, this ticket price is reduced (low scenario) and increased (high scenario) by 50%, respectively. A multiplier M on the ticket price is used to consider the cooperation between the airline and the new provider (see Table 3 for details). Based on the calculated seat load factor (Equation (1)) of the selected connecting ﬂight and the calculated number of connecting passengers (see Section 3.4) it is assumed that the connecting ﬂight can be fully loaded with connecting passengers. The resulting ticket prices for rebooking passengers are listed in Table 4. Table 4. Assumed ticket prices for rebooking passengers from Frankfurt Airport. Additionally, the prices are multiplied with M to consider different cooperation levels (see Table 3). Destination Low Base High Germany EUR 80.00 EUR 160.00 EUR 240.00 Europe EUR 72.50 EUR 145.00 EUR 217.50 Intercontinental EUR 262.50 EUR 525.00 EUR 787.50 In summary, the costs for REBP depend on the scenario (low, base, high), the number and destinations of delayed passengers (i.e., the aircraft size), the number and connectivity of alternative connections and on the cooperation of the airline with other airlines. Therewith, the number of delay minutes cannot be reduced and the success of this strategy depends signiﬁcantly on the number of connective passengers and on the amount of reactionary delay. For example, for a B763 aircraft from Rom-Fiumicino (LIRF) to Frankfurt (EDDF) with a delay of d = 67 min with 209 passengers on board (in the high scenario), we assumed 20 passengers on board, who miss their connecting ﬂights. According to the airport statistics of Frankfurt Airport , 14.5%, 62.1%, 23.4% of the connections are going to German, European and intercontinental destinations, respectively. In this example, three of three passengers could be rebooked within Germany to Köln/Bonn EDDK for a ticket price of EUR 240 per passenger. In total, 8 out of 12 passengers could be rebooked within Europe to Reykjavík BIRK for a ticket price of EUR 217 and one out of ﬁve passengers could be rebooked to another intercontinental ﬂight to Sydney Airport YSSY for a ticket price of EUR 787.5. 5.4. Delay of Connecting Flights (DEL AY) Although time buffers are considered in airline networks (especially of network carriers) missed connections of individual passengers cause high costs for compensation and rebooking (REBP). This can be avoided by making the connecting ﬂight wait for the passenger and thus accepting a delay itself. It is examined up to which delay the waiting for passengers is economically reasonable and Aerospace 2020, 7, 165 13 of 22 from when on passengers should be rebooked on the next possible ﬂight. Thereby, the actual off-block time of the connecting ﬂight is considered and a possible delay of the connecting ﬂight is added to the actual off-block time. Passengers who do not miss their connecting ﬂight because the connecting ﬂight is already delayed will not be considered. Only passengers who miss their connecting ﬂight according to the rotation schedule are considered in this strategy. The number of delayed transfer passengers depending on the business model and scenario is listed in Table 1. The allocation of alternative connecting ﬂights is described in Section 3.4. The expected primary and reactionary delay costs for the connecting ﬂight are derived in Section 4. In summary, the costs for DEL AY depend on the scenario (low, base, high) the number and destinations of delayed passengers (i.e., the aircraft size), the number and connectivity of alternative connections, and on the number of aircraft whose departure is delayed. With this strategy, the number of delay minutes cannot be reduced. Therewith, the success of this strategy depends signiﬁcantly on the number of connective passengers and on the amount of reactionary delay. The strategy might be efﬁcient in case of a signiﬁcant number of transfer passengers in an aircraft with a primary delay, which causes a delay of the corresponding connecting ﬂight since otherwise the compensation costs incurred (e.g., additional overnight costs) burden the cost balance disproportionately and signiﬁcantly reduce passenger comfort. In this case, the ﬂight dispatcher carefully weighs up the delay of the planned connecting ﬂight. If no further reactionary delay costs are to be expected due to the delay of the connecting ﬂight, this strategy is recommended. 5.5. Flight Cancellation (C ANCEL) The greater the delay of a ﬂight, the higher the delay costs incurred by an airline. At a critical delay level, the cancellation of a ﬂight will be more economical than the delayed execution of this ﬂight. For this reason, it is being examined at which delay level, the reactionary costs of delay exceed the costs of cancellation. The costs of canceling a ﬂight on the day of its planned execution include the legally prescribed compensation and support services by Regulation (EC) No. 261/2004 (hard costs) and the lost future revenue (soft costs) (see Section 4.4). Besides, the lost revenue due to the canceled ﬂight itself is taken into account, which includes the revenue from the sale of the ﬂight tickets and the revenue from in-ﬂight sales. The costs for delivery of baggage to the passenger ’s destination address are also included. This is offset by savings on the operational side. The costs for kerosene (Section 4.1), charges for the use of airport infrastructure and certain airways, maintenance costs (Section 4.3), and handling costs (Section 5.1) at the destination airport are eliminated . The costs for ﬂight cancellation depend on the business model, the aircraft size, and the number of booked seats and are taken from . The costs range from EUR 97 for a low-cost carrier seat in a narrowbody up to EUR 314 per seat in a half-loaded widebody of a network carrier. In summary, the costs for C ANCEL depend on the scenario (low, base, high) the number and destinations of connective passengers (i.e., the aircraft size) and the number and connectivity of alternative connections. The number of delay minutes cannot be reduced. Therewith, the success of this strategy depends signiﬁcantly on the number of connective passengers and on the amount of reactionary delay. 6. Performance Indicators for the Assessment of a Compensation Strategy As pointed out in Section 5, ﬁve options to reduce reactionary delay costs are associated with a speciﬁc delayed ﬂight. It was also pointed out, that the deployment of a compensation strategy induces costs. In an optimization problem, the difference between the reactionary delay cost reductions and the compensation costs for each ﬂight will be minimized. However, the beneﬁt of the countermeasure depends on the time when they are applied. The beneﬁt of a compensation strategy changes with ongoing time. With the help of the previously outlined cost estimation model, we can quantify the beneﬁts of the different strategies for different situations. For each compensation strategy com p 2 C := fFTA; I ACS; REBP; DEL AY; C ANCELg, Aerospace 2020, 7, 165 14 of 22 we compare the observed costs from the reference scenario without any compensatory measurements with the costs that are observed if we apply com p. We start with the evaluation of each individual relevant ﬂight f and for each of the three cost scenarios s 2 fLow; Base; Highg and determine ﬂight-speciﬁc performance indicators: Time at which the cost reduction is maximum: t ( f , s, com p) (min); max Earliest time from which the compensation strategy com p is beneﬁcial: t ( f , s, com p) (min); begin Latest time until the application of strategy com p is beneﬁcial: t ( f , s, com p) (min); end Maximum cost reduction: DK( f , s, com p) (EUR). Since these points in time depend on the amount of the delay, they are only partly suitable for valuation. More meaningful results can be obtained by comparing the respective point in time with the original delay. For this purpose, we deﬁne key performance indicators (KPIs), which can be calculated for a speciﬁc delay interval between d and d . The total number of ﬂights with delay within d min max min and d is F 2 [d , d ]. max max min The success rate ER(d) F (d) comp d=d ER(d) = . (22) å F(d) d=d indicates the percentage of ﬂights in the delay interval [d , d ] 2 [d , d ] for which the application i j min max of the compensation strategy com p leads to a reduction of the total delay costs. The number of those ﬂights is referred to as F (d). In this study, we investigate delay intervals [d , d ] with a length comp max min of 0.5 min. The success rate ER(d) refers to the performance of a collection of ﬂights for a given compensation strategy. The application of ER(d) to all ﬂights within the delay interval d is shown in Figures 4–6. However, it is also necessary to estimate the impacts of applying a certain strategy to an individual ﬂight. For this purpose, we deﬁne the following three performance indicators. The optimal compensation rate of a ﬂight CR(d) max CR(d) = . (23) indicates the time of the maximum saving t (min) related to the delay d (min). It is a measure of max the extent to which the delay must be compensated to achieve the greatest possible cost reduction. The cost reduction refers to the expected reactionary delay costs in case of non-application of the strategy. To evaluate a single compensation strategy, the mean value of CR(d) of all ﬂights in a given delay interval is calculated and shown in Figures 4 and 5. The break-even point t (min) indicates the point in time up to which the use of the BE compensation strategy is economical. In case more delay is compensated, the costs of using the compensation strategy exceed the possible savings in reactionary delay costs. To evaluate a compensation strategy, the mean value of t of all ﬂights in a given delay interval is calculated. BE The break-even rate BR(d) (min) BE BR(d) = (24) indicates the point in time t in relation to the delay d (min) up to which the use of a compensation BE strategy for a ﬂight is economically. To evaluate the compensation strategy, the mean value of the BR(d) of all ﬂights is calculated in a certain delay interval. In the event that at least a certain number of minutes of delay has to be compensated so that the overall operating expenditure is reduced, the break even rate BR (d) will indicate the time t in min BE,min relation to the delay d from which the use of the compensation strategy for a ﬂight is worthwhile: BE,min BR (d) = (25) min d Aerospace 2020, 7, 165 15 of 22 To evaluate the compensation strategy, the mean value of BR (d) of all ﬂights in a given delay min interval is calculated and shown in Figure 4. CR(d), BR(d), BR (d) and DK(d) further depend on the airline business model. For this reason, min the assessment of each strategy is done for three scenarios low, base, and high with low, medium and high total operating costs, respectively. 7. Results 7.1. Applicability of a Fast Turnaround (FTA) The fast turnaround strategy makes good business sense from a delay of about ten minutes (see Figure 4, left). The economic use of the fast turnaround strategy is possible for both widebody and narrowbody. The success rate ER in Figure 4 middle, differs only slightly for the same delay. As with increasing the cruising speed strategy ( I ACS), a higher proportion of the delay should be compensated with a fast turnaround, if the ﬂight is operated with a wide-body aircraft (Figure 4, right). Figure 4. Applicability of a fast turnaround FTA. (Left): Break-even rate BR for a fast turnaround in min a base scenario with medium total operating costs. (Middle): Success rate ER and (right): compensation rate CR. 7.2. Applicability of Cruising Speed Increase (I ACS) The higher the airline’s total operational costs the earlier the strategy of increasing the cruising speed pays off. The time at which the strategy is worthwhile varies between t = 15, 17, BE,min and 20 min, depending on the business model. In the high scenario, no break-even point BR is achieved later than 20 min. Hence, the strategy leads to a reduction of the reactionary delay costs, for all delays larger than 20 min. Due to missing ﬁxed costs for this strategy, no minimum compensation BR is required. min The values determined for the compensation rate of a ﬂight CR (Equation (23)) do not allow differentiation of different business models. In general, minor delays should be compensated for as fully as possible. For airlines with high operating costs, a slightly higher CR is recorded for the same delay (Figure 5, right). The success rate ER for widebodies is higher for the same delay d. Therefore, the use of the compensation strategy is advisable even for shorter delays with widebodies. Existing delays of a widebody should be compensated to a greater extent than of narrowbodies (Figure 5, left). The higher CR is due to the higher number of passengers on board. The share of passenger costs in the reactionary delay costs and also its absolute value is higher for a widebody than for a narrowbody (Figure 5, left). 7.3. Applicability of Rebooking Passengers (REBP) The evaluation of the strategy could be based on 36 routes. For 33 of these ﬂights, another ﬂight fulﬁlled the criteria for rebooking as discussed in Section 5.3. For the ﬂights examined with a delay of more than two hours, two or three possible alternative connections were identiﬁed. For all ﬂights examined, the optimal number of passengers to be rebooked was determined. An interval [d , d ] of i j minutes was chosen for the evaluation and presentation of the results in diagrams. The results for different operating costs differ only slightly. The mean value ER of all three cost scenarios in Figure 6 Aerospace 2020, 7, 165 16 of 22 indicates, that number of ﬂights examined is very small and the results show great ﬂuctuations. To be able to make reliable statements about the suitability of this strategy, the calculations should be repeated based on a more extensive database. Figure 5. Compensation rate CR and success rate ER of compensating reactionary delay by increasing the cruising speed (I ACS) for narrowbody and widebody aicraft. The rebooking rate U R (Figure 6, right) indicates the proportion of passengers who could be rebooked from a delayed ﬂight to an alternative ﬂight and who therefore reached their destination earlier. The solid red line represents the seat load factor SLF of the alternative ﬂights. Even with the maximum load factor of the alternative ﬂights (SLF = 100%), not all passengers on a delayed ﬂight can be carried. Figure 6. Success rate ER (left) and rebooking rate U R (right) of compensating reactionary delay by rebooking passengers (REBP). The solid red line represents the seat load factor SLF of the alternative ﬂight. 7.4. Eligibility of Delay of Connecting Flights (DEL AY) The deliberate delay in connecting ﬂights causes additional delays. Since the effects of the additional delay minutes can only be predicted to a limited extent (because of the characteristics of reactionary delay), the strategy should be used with caution. The longer the waiting time until the next possible ﬂight, the longer an airline can delay departure to allow delayed transfer passengers to connect (see the time until which the compensation is worthwhile t in Figure 7, left). This applies BE regardless of the airline’s business model. For wide-bodied aircraft, the economically reasonable waiting time t is slightly higher than for aircraft types with a lower number of seats. The exact BE number of delayed transfer passengers does not seem to have a signiﬁcant inﬂuence on the length of the delay (see Figure 7, right). Nevertheless, with a higher number of delayed passengers, higher t BE can be proven. 7.5. Suitability of Flight Cancellations (C ANCEL) Cancellation of a ﬂight makes sense when the reactionary costs of delay are greater than the cost of canceling a ﬂight. This is the case when the expected delay at take-off exceeds a certain value t (see Figure 8). Assuming comparatively low operational costs, it is advisable to cancel a ﬂight BE from a delay of approximately 125 min (left columns in Figure 8). For airlines with higher operating costs, a ﬂight should already be canceled at a lower delay (right columns in Figure 8). For example, Aerospace 2020, 7, 165 17 of 22 the cancellation of a ﬂight in the base scenario is possible from a delay of about 98 min, and in the high scenario from about 90 min delay is advantageous from an economic point of view (see Figure 8). Figure 7. Applicability of delaying connecting ﬂights (DEL AY) as delay cost compensation strategy in a high total operating cost scenario. The time until which the compensation is worthwhile t increases BE with increasing allowed waiting time until the next possible ﬂight. Widebodies are indicated by black triangles, narrowbodies by grey dots. Due to high compensation costs, which do not depend on the number of passengers, but on the number of delayed aircraft, the number of connecting passengers seems to have no direct inﬂuence on the productivity of this strategy. Passenger costs are responsible for most of the reactionary delay costs and cancellation would directly affect more passengers in a widebody aircraft (see Figure 8). Since widebody aircraft are preferred for long-haul ﬂights which destinations are generally less frequent than ﬂights to closer destinations a cancellation of a ﬂight cannot then be easily replaced by an alternative ﬂight. Figure 8. Minimum required delay for a proﬁtability of cancelling the ﬂight (C ANCEL) due to delay and too many missed connections t . BE 8. Conclusions and Outlook In this paper, ﬁve different delay compensation strategies were analyzed and applied to a rotation schedule of 24 h at Frankfurt Airport, Germany. Therefore, important components of reactionary delay costs provided by  were adapted to other aircraft types, enhanced for carbon dioxide costs, adjusted for inﬂation of 4.46% between 2014 and 2019, and enhanced by delay costs, covering transfer passenger ’s concerns. Subsequently, for each strategy, costs for compensating delays were approximated. Finally, all strategies were applied to all delayed ﬂights in the rotation schedule and the productivity was analyzed depending on the amount of delay of each aircraft. The most promising strategies for reducing reactionary delay costs are fast turnaround FTA and the speed increase during cruise I ACS. The use of the fast turnaround as a compensation strategy is Aerospace 2020, 7, 165 18 of 22 preferable to the use of speed increase, because of a higher compensation rate CR (Figure 9, top right), i.e., a larger proportion of the original delay can be compensated for with a cost-optimal solution. The reason for this may be, on the one hand, the lack of a data basis for modeling the strategy fast turnaround. On the other hand, this may be because with FTA the delay can already be compensated before departure. Thus, the ﬂight in question could start on time, compensation for the delay during the ﬂight would no longer be necessary, and reactionary delay costs for this ﬂight would not be incurred. By using the fast turnaround strategy, the reactionary delay costs incurred by an airline can be reduced more than with increased speed (Figure 9, bottom). Both when considering DK per ﬂight and delay minute, the maximum cost reduction DK is higher on average for the fast turnaround. FTA IACS Figure 9. Comparison of success rate ER (top left) , compensation rate CR (top right), cost reduction per ﬂight (bottom left) and cost reduction per delay minute (bottom right) of the most effective delay costs compensation strategies: Fast turnaround (FTA, grey) and increased cruise speed (IACS, black). The inclusion of individual transfer passengers in the delay cost balance of an airline involves the uncertainty of the number of these passengers if the method is to be implemented in a trajectory optimization. The high sensitivity of this number is reﬂected in the efﬁciency of the strategies REBP, DEL AY and C ANCEL. The assumptions made in this study regarding the number and destination of individual transfer passengers were specially adapted to the statistics of Frankfurt Airport. Number and destination vary for each airport and airline business model. It must be emphasized that not only the function of the airport in the network (i.e., hub or spoke), but also the connections to tourist and business destinations, intermodal connectivity (public transport connections), as well as the number and type of airlines operating at the airport have an impact on the efﬁciency of the REBP, DEL AY and C ANCEL strategies. In addition, the efﬁciency of the strategies is strongly dependent on the frequency of air connections to a given destination. These conditions are deﬁned in the ﬂight plan, which is used as an example in this study. This means that the results of this study cannot simply be transferred to other airports or ﬂight plans. The example of Frankfurt Airport was chosen because of its high number of transfer passengers and its good connectivity to give the strategies many possibilities. Despite the high number of transfer passengers and the good connectivity, the example of Frankfurt Airport provides a higher efﬁciency of non-passenger dependent strategies to compensate for delay costs Aerospace 2020, 7, 165 19 of 22 In the next step, the calculation rule for the costs of each compensation strategy and the different cost components of delay costs are going to be implemented in the multi-criteria aircraft trajectory optimization tool TOMATO [16,57] of TU Dresden. Therewith, delay costs will be considered as weighting functions in trajectory optimization and will act as decision support, when balancing environmentally-driven detours (e.g., around condensation trail sensitive areas) and cost-index-driven speed adjustments. This coupling has already been initiated in , but with strongly approximated delay costs. With the new approach, costs for additional fuel burn will be calculated precisely and not approximated, as done in this study. Note, in this study, the numbers, destinations, and costs of connecting passengers are restricted to Frankfurt Airport in 2019. Unfortunately, the assumptions cannot be taken over to an arbitrary airport with different connectivity. From this follows, before implementing the approach in TOMATO, assumptions have to be made to deal with this problem. 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Evaluation of Strategies to Reduce the Cost Impacts of Flight Delays on Total Network Costs