Flight Scheduling through Optimizing Flight Block and ...

Flight Scheduling through Optimizing Flight Block and Ground Times: A Case Study

Volume 21, Number 4 December 2015, pp. 299-315

Massoud Bazargan Embry-Riddle Aeronautical University ([email protected])

Different studies point to a growing and chronic delays with airline flights. The airlines constantly readjust their flight block times and ground times to reduce delays based on their most recent flight and ground times at different airports. In this paper, we propose mathematical models aimed at more reliable schedules by making modest changes to flight departure times within short time windows. The models utilize historical data to minimize total expected delays by simultaneously determining flight block and ground times. The model is first developed for one daily aircraft routing and applied to three US airlines. The model is then expanded to address an entire fleet of aircraft in an airline with individual aircraft daily routing and potentials for crew/passengers connections. The application of this model to a fleet of a US airline is presented, identifying flight block and ground times, with encouraging results. These results imply that more schedule reliability and significant reduction in delays can be achieved through realistic and more synchronized flight block and ground times. Keywords: Airlines, Scheduling, Integer Programming, Transportation

1. Introduction Airline passengers continue to experience chronic delays every year. According to the Bureau of Transportation Statistics (BTS), a US government entity, more than 20% of all flights in US were delayed or cancelled in 2013. This figure rose to 30% in the first 3 months of 2014 (BTS). According to the Federal Aviation Administration (FAA), a flight is considered to be delayed if it departs more than 15 minutes later than its scheduled departure time. Various industry, government and academic studies (see for example Ball, et. al. 2010, airlines.org, BTS, Bazargan 2011) highlight the enormous cost of delays to airlines and passengers. When developing schedules, airlines incorporate many complex and often conflicting parameters including time of the day, maintenance, crew, hub capacities, gate, slot availabilities and government mandatory regulations (Lee, et. al. 2007). However, the trends suggest that the airlines need better planning to reduce or avoid these chronic and persistent delays. The delays and their increasing costs have prompted researchers and practitioners to study and propose methods and strategies to develop more robust and reliable schedules. In these studies more flexibility is embedded in the schedule so that it cannot be easily damaged by external or internal disturbances.

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Currently, there exist a large number of academic studies to improve the robustness and reliability of flight schedules. A majority of these studies attempt to build better schedules by readjusting flight departure times with different set of objectives and constraints. Lan et al (2006) and Aloulou, et. al. (2013) allow changes to flight leg departure times within a given window in an effort to minimize passenger misconnections. Stjkovic and Soumis (2001) attempt to readjust the daily flight departure times while simultaneously generating crew duties. Mercier and Soumis (2007), propose an integrated model for aircraft routing, crew scheduling through flight retiming. The proposed model attempts to minimize the total cost of all crew scheduling costs by identifying routes and pairings for each flight leg allowing retiming of departures within a certain window. Sohoni, et. al. (2011) propose that airlines assign block times based on their most recent past similar flights. They offer models to make perturbations to flight departure times in an effort to increase reliability and passenger service levels. Deshpande and Arikan (2012) indicate that the airlines periodically use ad-hoc techniques to decrease or increase their flight block times based on the most recent data. They propose models to estimate on-time arrival probabilities based on historical flight block times. Lee et. al (2007) propose a multi-objective model to minimize delays and crew cost and offer genetic algorithm and simulation methods to solve it. Retiming the departure times have been studied under different contexts too. These contexts include streamlining operations (see for example Sherali et. al (2013)) or increase profitability (see for example Jiang and Barnhart (2013)). Duran, et. al. (2015) divide the flight block times into cruise times which are controllable and noncruise times which are stochastic. They offer models to incorporate robustness into the flight schedule by a tradeoff between cruise and non-cruise times. Some studies attempt to readjust the departure times by identifying and minimizing delays that propagate through downstream flights. Dunbar, et. Al (2012), Lan et. Al (2006) and AhmadBegi, et. al. (2010) take advantage of slacks in the flight schedule and redistribute them by retiming the departure times in an effort to minimize the propagated delays and costs. This paper also attempts to build more reliability into the flight schedule by modifying and readjusting the flight departure times within a short given window. However, the approach, focus and the models are different from those cited earlier. In this paper, we attempt to minimize the total expected delays by simultaneously determining more realistic flight block and ground times and their impact on departure times. The models consider passenger and crew connections at different airports. The concept of simultaneously optimizing flight block and ground times and their impact on delays has not received much attention. Lee, et. Al (2007) include the scheduled flight block and ground times in their multi-objective model. However, the scopes, approaches and models are different from this paper. They do not determine the optimum values which can affect the retiming of departure times in their model. The other limited existing ground delay studies (see for example Mukherjee, et. al. 2012) consider this issue in the context of airport capacity, ground services and slot allocations. Wu and Caves (2000) study the stochastic nature of airline turnaround times and propose a model to minimize a weighted total cost to airlines, passengers and schedule punctuality by identifying schedule buffer times. However, this study focuses only at ground times and does not include optimizing the flight block times.

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The main contribution of this paper is that it considers both the flight block and ground times and attempts to sync them with their daily routing in an effort to minimize their total expected delays subject to operational and other side constraints. It demonstrates that the commonly adopted strategy by the airlines to inflate the flight block times hoping to cover any irregularities in ground times will not produce the expected results. The application of the models discussed in this paper, to select airlines, shows good potentials to reduce delays by synchronizing the scheduled block and ground times with their actual values. Section 2, introduces the problem of variability and stochastic natures of flight block and ground times. Section 3, explores the mathematical models and their applications for one daily aircraft routing and an entire fleet. Section 4, discusses the perturbation of parameters and their impact on total expected delays and finally section 5 concludes this paper.

2. Problem Definition and Formulation This study was initiated by an airline in US. The main scope is to determine more realistic flight block and ground times to reduce delays. The airlines estimate and constantly readjust their flight block and ground times based on their most recent data. However, as we will see later in this paper, in many cases, these adjustments are not correct and lead to additional delays. The focus of this paper is therefore to identify more realistic flight block and ground times based on historical data in an effort to minimize total expected delays. Flight block time is basically defined as „gate to gate‟ time. It is the time interval from leaving a gate in the departing airport to the gate in arriving airport. Turn or ground time is define as the time between the arrival of an aircraft at a gate until it leaves that gate for the next flight. The fluctuations in flight block and ground times have been major causes of delays. Figures 1 presents a randomly selected flight block for a US airline flying New York City (JFK) to West Palm Beach in Florida (PBI). The figure presents the actual and scheduled flight block time series (in minutes) over a 6 month timeframe in 2013, flying this leg1. This chart presents the flight block time for the same flight, same departure time, same fleet and in many cases the same aircraft (tail number). We excluded weekend flights for consistency. As the figure suggests, the airline readjusts the flight block time periodically, reacting to recent patterns of actual flight times. It should be noted that no correlation was found (correlation coefficient=-.06) between the actual flight block times and the date of flights, indicating that the flight block time does not get any better or worse over time during the six months of the collected data. The coefficient of variation (standard deviation/mean) for the actual flight block times is 0.09.

1

Source: Bureau of Transportation Statistics (BTS)

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Figure 1 Scheduled and Actual Block Times for JFK-PBI in Minutes (Source: BTS)

Figure 2 presents the fitted histogram to the actual block time for this flight leg (JFK-PBI). The airline specifies 168 minutes as the most revised schedule block time. As figure 2 implies, based on historical data, the probability that the flight block takes 168 minutes or less is 50.8%.

Figure 2 Histogram for Flight Block Time for Flight Leg JFK-PBI

Figure 3, presents the ground time for this same flight once arriving at PBI. It presents the scheduled and actual turn/ground time in minutes at PBI. These times represent the scheduled and actual ground times of the same flights and timeframe arriving at PBI as discussed in figure 1. The correlation coefficient and coefficient of variation are .09 and .22 respectively, implying no correlation with respect to time but higher variability compared to actual flight block times.

Figure 3 Scheduled and Actual Ground Times in Minutes (Source: BTS)

Figure 4 presents the histogram for turn/ ground time at PBI. On average more than 75% of ground times at PBI exceed the scheduled 47 minutes turn time specified by the airline.

Figure 4 Histogram for Ground Time at PBI

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As indicated before, this flight was randomly selected, and by no means an exception. Other randomly selected flights showed similar patterns in terms of fluctuations in flight block and ground times. To address these slacks or delays, a typical approach that the airlines adopt is to periodically revisit and adjust the flight block and/or ground times as seen in figures 1 and 3. However, as the histograms presented in figures 2 and 4, suggest these minor adjustments, do little to resolve the chronic delay issues. Section 3 presents our attempt to minimize the total expected delays by identifying more realistic flight block and ground times for one daily aircraft and an entire fleet routings.

3. Mathematical Model The development of the mathematical model is focused at minimizing the total expected flight block and ground delays by identifying optimum flight block and ground times. Two models are presented. Model 1 provides the mathematical model and computational experimentations for daily routing of a single aircraft. Model 2 expands this model by considering an entire fleet for an airline and incorporating new constraints for crew and passenger connections. Both models attempt to identify the optimum:  Flight block time for each flight  Ground/ turn rime at each airport  Revised departure times 3.1 Model 1 – One Daily Aircraft Routing This section explores the development of one daily aircraft routing. The model assumes the availability of the following parameters:  The daily routing for a single aircraft  Historical data on flight block and turn times for the aircraft daily routing  Curfews and ground restrictions at airports within the daily routing  The allowable time window(s) for departure retiming. The model attempts to identify optimal flight block and ground times by potentially making minor changes to scheduled departure times. These allowable departure time windows provide the flexibility to the model to find the optimal flight block and ground times while staying within the desired boundaries. The mathematical model for a daily aircraft routings is presented as follows: Sets Set of all flights on a specific aircraft daily routing Set of all airports on a specific aircraft daily routing Set of paired flights and arriving airports on aircraft daily routing R Set of airports with ground time restrictions. Index

(, )

Index for flight ( ) Index for airport ( ) index for flight arriving into airport , ( , ) Index for airport having ground time restrictions ( Index for time for flight block and ground times

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Parameters ) Expected flight block delay in min for flight i when the flight block time is set to t minutes ) Expected ground time delay in min at airport j when the ground time is set to minutes Discrete allowable fluctuations in flight block time in minutes for flight i Discrete allowable fluctuations in ground time in minutes at airport j Scheduled flight block time for flight i Scheduled ground time at airport j Current scheduled departure time for flight i Earliest possible departure time for the first flight in the daily routing Last flight in the aircraft daily routing Latest arrival time for the last flight in the daily routing Maximum deviation time allowed between proposed and current departure times for flight i Decision Variables Binary decision variable taking a value of 1 if flight takes block time t minutes ( and 0, otherwise; Binary decision variable taking a value of 1 if ground time at airport takes ( and 0, otherwise; Proposed departure time for flight i The model is therefore formulated as. Minimize ∑

∑

(

∑

)

∑

(

)

(1)

Subject to ∑

∑

(2)

∑

(3)

∑

(4)

(5) ∑

| ∑

(6)

|

(7) (8)

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{

} and

In this model the objective function (1) minimizes the total expected flight block and ground delays. All expected delays ( ( ) ( )) are calculated offline and entered into the model. Therefore the above model is a deterministic mixed integer linear program. The process of how these expected delays were calculated is explained later in section 3.2. The set of constraints (2) provides continuity and connections among the sequential flights. They insure that all proposed departure times ( ) occur later than the previous departure time ( ) plus the flight block time for that previous flight ∑ plus the ground time at the current airport ∑ . Constraints (3) and (4) allow only one flight block and ground time from the set of allowable times. Constraints (5) and (6) insure the curfews are not violated for the departure of the first and arriving of the last flights. Constraint (7) limits the deviations of the proposed and scheduled flight departures to be within a desired time window. Constraint (8) provides the flexibility to limit the ground times at select airports if such restrictions exist. 3.2 Computational Experimentation In order to better evaluate the performance of the model, we searched for larger number of flight legs on a daily aircraft routing. The following presents three such applications. These applications include two major airlines (Delta and United Airlines) and a low cost carrier (JetBlue) operating in US. The rationale for selecting these airlines was to observe if potential improvements on flight block times and ground times are different among the airlines with different network plans and business models. It should be noted that these routings were randomly selected among the three airlines‟ 5-flights daily aircraft routings. Delta: ATL-EWR EWR-ATL ATL-EWR EWR-ATL ATL-JFK JetBlue: ROC-JFK JFK-PBI PBI-JFK JFK-MCO MCO-SJU United: DEN-IAD IAD-ORD ORD-DCA DCA-ORD ORD-IAD The historical data on these flight legs over a six months period in 2013 were collected2. As indicated in section 2, these historical data relate to the same fleet type, same departure times, and in many cases to the same aircraft. The expected delays were calculated for each routing and entered in the model. The expected delays were calculated using @Risk 3, a commercial software used for probability and statistical analyses. The software was utilized to determine the histograms fitted to historical data for each airline‟s flight block and ground times. The simulation module of the software was then utilized to determine the expected delays based on the ranges of allowable changes to flight block and ground times as described below. These expected delays were then entered into the objective function of the mathematical model. Without loss of generality, and after consulting with the airline, we used the following assumptions for parameters in the model. 2 3

Source: Bureau of Transportation Statistics (BTS) www.palisade.com

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

Allowable time window for changes to the current scheduled departure times ( : ±30 minutes. This time window, as specified in constrain 7, implies that the proposed departure times by the model can only deviate by a maximum of 30 minutes earlier or later than the current scheduled times provided they do not violate curfews (constraints 5 and 6).  Allowable changes to current flight block times : ±20 minutes. These fluctuations imply that the proposed flight block times can be reduced or increased by a maximum of 20 minutes from current scheduled times.  Allowable changes to current ground times : ±15 minutes. These fluctuations imply that the proposed ground times at airports can be reduced or increased by a maximum of 15 minutes from current scheduled times.  Earliest and latest flight curfews: 0600 am and 2300 local times respectively. These times were converted into minutes for 360 (6 60) and =1380 (23 60). Each model has more than 350 binary and integer variables and 380 constraints. The model was solved using Cplex4 and the solutions were generated instantly. Figure 5, presents the solutions for one-day routing expected delays under current and optimum scenarios in minutes. As the figure implies, the current total expected delays on all five daily routing for Delta, JetBlue and United airlines are 76.1, 65.8 and 87.5 minutes respectively. The optimum expected delays are 34, 38.5 and 62.3 minutes which are reduced by 55%, 42% and 29% from their current expected delays respectively. Figure 5 shows the breakdown of each of the expected delays for block and ground times.

Figure 5 Current and Proposed Expected Block, Ground and Total Delays in Minutes

Table 1 provides the detailed solutions of the mathematical model for optimum flight block, ground times and changes to departure times in minutes for each flight leg and airport for the three airlines. For comparison purposes the current scheduled flight block and ground times are also presented. The solutions recommend more ground times at all airports for all three airlines. These additional ground times are compensated by minor changes to flight departure times. 4

www.IBM.com

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The negative changes to departure times indicate earlier and positive implies later than current scheduled departure times. Table 1 Scheduled, Optimum Flight Block, Ground & Changes to Departure Times in Minutes Flight

Delta

ATLEWR EWRATL ATLEWR EWRATL ATL-JFK

Opt flight Block

Opt Ground

Current Block

Current Ground

Changes to Dept. times

135

58

137

43

-25

133

82

131

69

-12

136

55

150

40

8

150

71

146

56

14

156

140

24

Totals ROCJFK JFK-PBI

710

266

704

208

80

109

86

94

173

62

184

47

9

PBI-JFK JetBlue JFKMCO MCOSJU Totals DENIAD IADORD ORDUnited DCA DCAORD ORDIAD Totals

161

71

163

63

19

177

60

184

45

23

180

160

0

25

771

302

777

249

192

62

190

47

-25

116

50

123

47

-13

110

52

105

37

-18

123

52

128

37

-9

99 640

99 216

645

0 168

Tables 2 presents the breakdown of the total expected delays in minutes for optimum and current schedules as discussed in figure 5, in terms of flight block and ground times, for each individual flight leg and airport. In this table Totals presents the sum of all expected delays attributed to flight block and ground times for both optimum and current schedules for each airline respectively. Ob. Func (Objective function) is the sum of flight block and ground times as shown in figure 5 and reported by the model. PC represents the percentages of expected delays for each of the flight block and ground times in the Obj. func. It is calculated by totals divided by Obj. Func.

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According to this table, the model is redistributing the current percentages of flight block and ground times expected delays. For all three airlines, the optimum solutions have larger percentages of flight block expected delays compared to current schedules. Instead, they are assigning a smaller percentages to ground time expected delays than the current ones. Perhaps one reason is that flight block times are more standardized in terms of equipment, speed of the aircraft and other unforeseen factors. The model therefore attempts to assign larger ground time buffers than the current scheduled, to address the higher variability in ground times Table 2 Breakdown of Expected Delays for Optimum and Current Schedules Flights

Delta

Opt Block Opt Ground Current Block Current Ground

ATL-EWR

0.1

1.1

0.1

10.5

EWR-ATL

2.3

0.9

4.6

6.9

ATL-EWR

2.8

16.7

1.4

28.5

EWR-ATL

2.9

7.0

5.8

15.4

ATL-JFK

0.3

Totals

8.3

Obj func PC

JetBlue

25.7

14.9

34.0

61.3 76.1

24%

76%

20%

80%

ROC-JFK

4.9

4.2

3.1

14.4

JFK-PBI

5.2

4.3

2.1

13.4

PBI-JFK

4.0

3.6

3.0

7.3

JFK-MCO

6.1

6.1

3.7

16.4

MCO-SJU

0.1

Totals

20.3

Obj func PC

United

2.9

2.4 18.2

14.2

38.5

51.6 65.8

53%

47%

22%

78%

DEN-IAD

2.3

21.5

3.1

32.0

IAD-ORD

4.7

7.8

2.8

6.4

ORD-DCA

3.5

7.4

5.5

14.9

DCA-ORD

3.1

10.2

1.8

19.1

ORD-IAD

1.9

Totals

15.5

Obj func PC

1.9 46.8

15.0

62.3 25%

72.5 87.5

75%

17%

83%

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3.3 Model 2 – Entire Fleet Routing The mathematical model presented in the previous section is expanded to address all daily routings within the entire fleet. In the previous model, for a single aircraft, we did not address passenger, cabin and flight crew connections. This model provides the flexibility for crew and passengers to connect to their next flights on the same fleet type. The expanded entire fleet mathematical model is explained as follows. We assume the availability of data as discussed in model 1. Sets Set of all aircraft/tail numbers in the fleet Set of daily flights for a specific aircraft a Set of airports on a daily routing for a specific aircraft a Set of airports with ground time restrictions for daily routing of aircraft a Set of paired arriving flights and airports for aircraft a Set of paired airports and departing flights for aircraft a Set of all paired feasible connecting aircraft and flights for cabin crew, flight crew and passengers. FC Set of flights for flight crew Index Index for aircraft within a fleet ) Index for daily flight routing of aircraft a Index for airports visited by daily routing of aircraft a Index for airports having ground time restrictions on daily routing of aircraft a Index for time for fluctuating flight block and ground times (, ) Index for flight arriving into airport , (, ) Index for flight departing from airport Index for flight sequences for flight crew , ( Index for connecting flight crew, cabin crew and/or passengers from arriving aircraft flight to departing aircraft flight , Parameters Expected flight block delay in min for aircraft a, flight i when the flight block time is set to t minutes ) Expected ground time delay in min for aircraft a, at airport j when the ground time is set to minutes. Discrete fluctuations for flight block time in minutes for aircraft a, flight i Discrete fluctuations for ground time in minutes for aircraft a, at airport j Scheduled flight block time for aircraft a, flight i Scheduled ground time for aircraft a, at airport j Flight crew connection time for aircraft a, at airport j Cabin crew connection time for aircraft a, at airport j Passenger connection time for aircraft a, at airport j Current scheduled departure time for aircraft a, flight i

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Earliest possible departure time for the first flight in the daily routing of aircraft a Latest arrival time for the last flight in the daily routing of aircraft a Maximum deviation time allowed between proposed and current departure times for aircraft a, flight i Legal Maximum flight minutes for flight crew per day to stay legal Decision Variables Binary decision variable taking a value of 1 if aircraft a on its flight takes block time t minutes ( and 0, otherwise; Binary decision variable taking a value of 1 if ground time at airport for aircraft a takes ( and 0, otherwise; Proposed departure time for aircraft a, flight i The model is then formulated as Minimize ∑

∑

∑

∑

∑

∑

(

)

(9)

Subject to ∑

∑

∑ [ ∑

]

(10)

{

}

(11)

∑

(12)

∑

)31(

∑

(14)

(15) (16)

∑ |

|

(17)

∑

(18) {

}

The objective function (9), similar to model 1, attempts to minimize the total expected delays among all aircraft in a fleet. The set of constraints (10), make sure

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the departure times for any aircraft is greater or equal to its last departure time plus flight block and current airport ground times. Constraints (11) insures the flight, cabin crew and passengers connect from one arriving to another departing aircraft in the fleet. The right hand side of this set of constraints select the largest value among all the connection times for crew and passengers. The set of constraints (12) insure that the total daily flying time for flight crew stays legal. The set of constraints (13) to (18), similar to model 1, insure one flight block and one ground time are selected, curfews not violated, maximum allowable deviations and ground restriction times are imposed Similar to model 1, all expected delays in the objective function are calculated offline and included in the model making it a deterministic mixed integer linear program. 3.4 Computational Experimentation The following presents the application of this model to a fleet of Boing 737-700 belonging to AirTran Airways operating in US (this airline was acquired by Southwest in 2011). There are 12 aircraft/routings with a total of 41 daily flights. Each aircraft/routing has 3-5 flight legs per day. The historical data for each flight block and ground times were compiled and analyzed5. We used the same assumptions as model 1 in terms of allowable changes to flight block, ground and departure times. The legal flying times for flight crew are assumed to be 8 hours. The model reported more than 3500 variables and 1200 constraints. Again, Cplex was used to solve the model in less than 2 seconds. Figure 6 present the total expected delays under current and optimum solutions for the entire fleet. According to this figure, the optimum solution represents more than 63% improvement in reducing expected delays compared to current scheduled flight block and ground times for the entire fleet.

Figure 6 Total Expected Delays in Minutes for Current and Optimum Solutions

Figure 7 presents the breakdown of expected delays for all 12 daily routings for current and optimum solutions.

Figure 7 Breakdown of Expected Delays in Minutes for Current and Optimum Solutions 5

Source: Bureau of Transportation Statistics (BTS)

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Figure 8 presents the breakdown of the optimal solutions of the total expected delays into flight block and ground times. Similar to table 2, this figure shows the percentages of expected delays in flight block and ground times in the objective functions.

Figure 8 Percentages of expected delays for flight block and ground times in the objective functions

This figure confirms and supports the results obtained by model 1 in terms of percentages attributed to expect delays for flight block and ground times. On average, in the optimal solutions, flight and ground time expected delays make up 30% and 70% of total expected delays respectively. Similar to model 1, the solutions reported minor changes to departure times for each flight leg.

4. Sensitivity Analysis It was of interest to observe how the optimal solutions for this 12 aircraft fleet are impacted if we modify the allowable fluctuation times for flight block, ground and departure times. As indicated in section 3, we allowed changes to flight block, ground and departure times by ±20, ±15 and ±30 minutes respectively. This section examines how the optimal solutions change as we fluctuate these time windows. In particular, we want to identify which parameter out of flight block, ground and departure time windows has a larger impact on reducing the total expected delays. The model was run by allowing changes to one parameter at a time. First, we ran the model by letting the flight block times to fluctuate from 0 to ±20 min in increments of 1 minute while allowing no changes to ground times windows ( =0 for all ). The changes to departure times are same and fixed to ±30 minutes. Next we let changes to only ground times from 0 to ±15 min in increments of 1 minute while setting changes to flight block times to zero ( =0 for all ). Again the departure times are set to ±30minutes. Figure 9 presents the optimum solutions for total expected delays as we let changes to flight block and ground times in increments of 1 minute. As the figure suggests ground time windows have a higher impact on reducing the expected delays than flight block windows.

Figure 9 Total Optimum Expected Delays as Flight Block or Ground Time Windows Change

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Next, we explore the fluctuations to departure time windows from current (0) to ±50 minutes. We ran multiple models letting changes to departure times in increments of 5 minutes from ±5 minutes to ±50 minutes. We kept all other parameters fixed ( = ±20 and =±15). Figure 10 presents the total expected delays in minutes for the optimum solutions as we change the departure time windows. Based on figures 9 and 10, the following table presents the reductions in current total expected delays (348.12 minutes) as we make changes to their respective time windows. It should be noted that this table shows the percentages by making changes to only one parameter at a time as discussed earlier. As the table implies increasing ground time and departure time windows have the largest impact on reducing the total expected delays.

Figure 10 Total Optimum Expected Delays vs Changes to Departure Time Windows Table 3 Percentage Reductions in Current Total Expected Delays as we Fluctuate Time Windows Changes to time window (min) Ground time Block time Departure time 5

19%

13%

8%

10

30%

20%

21%

15

39%

24%

33%

25%

46%

20 25

56%

30

63%

35

68%

40

71%

45

73%

50

74%

5. Conclusions This paper presents an optimization approach to help the airline design a more reliable schedule. Airlines should consider more realistic flight block and ground times based on their historical data. Changing just flight block or ground time in isolation, without considering the sequence of daily routing for the aircraft, will not have the desired effect in reducing the total delays.

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Two mathematical models were proposed to minimize the total expected delays for more reliable airlines schedules. The flight block and ground times are revised and linked together for a daily aircraft routing or an entire fleet. The proposed models make moderate changes to departure times based on airlines‟ allowed timeframe windows. The expanded model accommodate crew and passenger connections and enable the flight crew to stay legal based on changes to flight block times. Sensitivity analyses highlighted the impact of fluctuations of model parameters on total expected delays. The two models demonstrated that significant savings in expected delays can be realized. It was shown that a high portion of these savings are attributed to changes to ground times than flight block times.

6. References 1.

AhemeBeygi, S., Cohn, A., Lapp, M., (2010), Decreasing airline delay propagation by re-allocating scheduled slack, IIE Transactions, Volume 42, Issue 7, pp. 478-489. 2. Airlines.org, http://www Airlines.org 3. Aloulou, M., Haouari, M., Mansour, F., (2013), A model for enhancing robustness of aircraft and passenger connections, Transportation Research Part C, Vol. 32, pp. 48-60. 4. Ball, M., Barnhart, C., Dresner, M., Hansen, M., Neels, K., Odoni, A., Peterson, E., Sherry, L., Trani, A., Zou , B., (2010), Total Delay Impact Study A Comprehensive Assessment of the Costs and Impacts of Flight Delay in the United States, Final report submitted to Nextor. 5. Bazargan, M., (2011), A Linear Programming approach for wide-body two-aisle aircraft boarding strategy, International Journal of Operations & Quantitative management, Vol. 17, No. 3, pp. 193-210. 6. BTS, Bureau of Transportation Statistics, http://www.rita.dot.gov/bts/home. 7. Deshpande, V. & Arıkan, M., (2012), The Impact of Airline Flight Schedules on Flight Delays, Manufacturing & Service Operations Management, Vol. 14, pp 423-440. 8. Dunbar, M., Froyland, G., Wu, C., (2012), Robust Airline Schedule Planning: Minimizing Propagated Delay in an Integrated Routing and Crewing Framework, Transportation Science, Vol. 46, No. 2, May 2012, pp 204–216. 9. Duran, S., Gurel, S., Akturk, S., (2015), Robust airline scheduling with controllable cruise times and chance constraints, IIE Transactions, 47, pp 64–83. 10. Jiang, H., Barnhart, C., (2013), Robust airline schedule design in a dynamic scheduling environment, Computers & Operations Research, Vol. 40, No.3, pp 831-840. 11. Lan, S., Clarke, J.-P. & Barnhart, C. 2006. Planning for Robust Airline Operations: Optimizing Aircraft Routings and Flight Departure Times to Minimize Passenger Disruptions, Transportation Science, 40, pp 15-28. 12. Lee, L. H., Lee, U.L., Tan, Y.P. , (2007), A multi-objective genetic algorithm for robust flight scheduling using simulation, European Journal of Operational Research, Vol. 177-3, pp. 1948–

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13. Mercier, A., Soumis, F. (2007), An integrated aircraft routing, crew scheduling and flight retiming model, Computers & Operations Research, vol. 34, pp 2251 – 2265. 14. Mukherjee, A., Hansen, M., Grabbe, S., (2012), Ground delay program planning under uncertainty in airport capacity, Transportation Planning and Technology, vol. 35, issue 6, pp 611-628. 15. Sherali, H. D., Bae, K.-H. & Haouari, M. 2013. An Integrated Approach for Airline Flight Selection and Timing, Fleet Assignment, and Aircraft Routing, Transportation Science, Vol.47, pp 455-476. 16. Sohoni, A., Lee, Y., Klabjan, D., (2011), Robust Airline Scheduling Under Block-Time Uncertainty, Transportation Science, Vol. 45, No. 4, pp 451-464. 17. Stojković, M. & Soumis, F. 2001. An Optimization Model for the Simultaneous Operational Flight and Pilot Scheduling Problem, Management Science, 47, pp 1290-1305. 18. Wu, C., Caves (2000), Aircraft operational costs and turnaround, Journal of Air Transport Management, 6, pp 201-208 About Our Author Dr. Bazargan is currently a Professor of Operations Research, Operations Management and the Associate Dean for Research at the College of Business, Embry-Riddle Aeronautical University. He is the author of “Airline Operations and Scheduling”. He has worked on extensive funded research grants from the FAA, Florida Department of Transportation (FDOT) and the aviation industry. Some of his industry research projects include aircraft boarding strategy, aircraft replacement strategy, optimizing flight block and ground times, aviation safety studies, manpower planning, airports funding strategies and airports productivity and efficiency. He has extensive publications and research interests in optimization and simulation applied to transportation and aviation industries.