Optimized Itinerary Generation for NAS Performance Analysis

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1 Optimized Itinerary Generation for NAS Performance Analysis Feng Cheng, Bryan Baszczewski, John Gulding Federal Aviation Administration, Washington, DC, FAA s long-term planning process is largely supported by NAS-wide simulation modeling of future operational scenarios. Among many factors that are considered for future schedule generation, the itinerary structure of a future schedule also affects the projected NAS performance as itineraries that reflect low aircraft utilization are expected to have less propagated delay than those with high aircraft utilization. However, algorithms that seek to maintain network connectivity for future years are usually complex even for a single airline in single year. This paper proposes a new method for creating future itineraries based on the Mixed-Integer Programming solution by optimizing the itinerary structure of the flights. The underlying solution technique is based on an adaptation of the Fleet Assignment Model. The results of the new method show improved operational efficiency and less ground idle time. Two partitioning methods for itinerary generation are developed. One method is based on the combination of Airline and Equipment Type. The other method uses the seat category to provide greater flexibility for assigning aircraft to flights. This paper also provides a quantified analysis to demonstrate a trade-off between the de-peaking strategies that minimize the number of aircraft in service and the banking strategies that maintain schedule banks. I. Introduction Historically, future schedules developed for aviation planning have used a flight operations based forecast in order to project traffic growth for benefits analysis. This type of forecast makes key assumptions on the aircraft equipment and airline load factor that allow an operations forecast to satisfy a complimentary passenger forecast. The annual flight operations growth rates for FAA facilities as well as passenger growth rates are published in the Department of Transportation, FAA Aerospace Forecast and FAA Terminal Area Forecasts (TAF) which are released annually (Ref. 17). Both forecasts provide annual growth rates at the regional/market level without details that are necessary to develop a future day of operations required to assess aviation performance. Another key design point for algorithms is that all FAA forecasts provided are unconstrained which, if used directly without concern for operating constraints, would produce unrealistic trends. Therefore, producing future schedules requires a module that transforms an unconstrained scheduled into a feasible schedule that is at least representative of high delay conditions that have existed prior to government action requiring schedule limitations (Ref. 3). The requirements of building a set of future schedules, consistent with official forecast, while reflecting operational constraints mark the key design features of the current future schedule process. The future schedules are created by merging the annual growth rates as given by the TAF with operations data that provide specific demand at the airport by time of day. This involves a multi-step process in which decisions on the departure and arrival flight time are performed independently of each other. The first step produces a set of future flights that reflect an unconstrained demand where demand throughout the day grows proportionally to the existing hourly demand distribution, regardless of other constraints (Ref. 4). In a second step, demand capacity ratios based on conditions prior to schedule limitations are used to smooth, and if necessary trim the unconstrained schedule until a feasible condition is reached (Ref. 3). These two steps preserve schedule peaks consistent with what is observed in the historical data. In the third step, a process of linking flight legs in a schedule into itineraries, called itinerary generation, is applied. Finally in step 4, fleet evolution is performed to determine future aircraft types of the itineraries to match with an FAA provided airline specific fleet forecasts. In practice, an airline would not make these types of decisions in a non-integrated manner as the first steps involve the assignment of times and the last step would be influenced by passenger demand. However, FAA s planning process typically requires estimates be made for years in the future and for different types of

2 operations (General Aviation, Schedule, and Non-scheduled). At best this process is an approximation that replicates certain schedule characteristics that are believed to heavily influence the performance of NAS. The ultimate goal of the research described in this paper is to balance the requirement of the forecast process while keeping a consistency across future years that will not bias future planning for aviation. The end result is a future schedule that is input into a NAS-wide simulation model (Refs. 9 and 10). The NASwide simulation results will be sensitive to how the future schedule is constructed. Previous work on future schedule sensitivity has largely focused on schedule peaks and demand capacity-imbalances as well as ensuring Instrument Flight Rules (IFR) conditions are accurately represented across the major facilities. With demand near capacity, the NAS model will report large variation in delay depending on whether the schedules become more peaked or more smoothed. Airline business models will reflect the trade-off between the cost due to congestion and the revenue gained by minimizing passenger connection times or by operating at a preferred time. This trade-off on cost saved through de-peaked schedules and the potential effect on airline revenue has been evaluated in various sources (Ref. 20). A more integrated schedule generation process ideally will approximate airline behavior and project it into the future without knowing an airline s exact practice. In broad terms, an airline will want to minimize the number of aircraft required to cover a network as well as operate during times preferred by the passengers. Data for baseline historical years provide insight into how banks grow relative to the capacity of an airport and the magnitude peaks reach before the system responds with constraints in the form of slot control or schedule limitation policy. These airport specific demand capacity ratios serve as the guide to how passenger demand is served today. The observed flight-legs per itinerary achieved by airlines provide an indicator of how well an airline can cover passenger demand given the current fleet and bank structure. The turn-around times observed also provide a key input into the requirements of developing airline itineraries. The purpose of this paper is to develop a process that maintains patterns seen in the historical data, projected into the future in a way that is believed to not bias NAS-wide model results. A summary of the key design parameters and key data input parameters is provided in Table 1 below: Table 1. Key Design Parameters for Future Schedule Process Key Design Parameter Forecast is based on operations not passengers. Forecast is at the annual airport, not daily city-pair level Forecast is Unconstrained Forecast contains airline-specific projections Itineraries will be developed at the airlineequipment level based on current airline operations and future airline equipment types. Description No priority on which aircraft size covers a given flight leg. Aircraft size on flight leg is based on historical data. Up-gauging is random to match a fleet forecast and not directly based on passenger information. Traffic between city-pairs is derived from an algorithm that insures overall traffic level scales to the airport wide forecast. Results of city-pair forecast will exceed practical limits of airport. A separate process is required to create a feasible schedule from the constrained forecast. Algorithm will operate at the airline level. Future airline demand is a consequence of airline demand observed in the baseline and projected using growth rates that do not contain airline specific projections. Network connectivity is determined by how flights are added in the future for a particular airline. The design parameters given above are largely the product of the level of detail given in the FAA forecast. Airport growth is generic and not specific to an airline while fleet growth is airline specific. City pair growth is not provided. If a daily, city-pair schedule with airline specific itineraries is required, forecast with very different degrees of detail must be linked together. In the past, this process has been approximated with separate modules that 1) create city pair forecast (with times assigned), 2) constrain the schedule to feasible levels, 3) link flight legs into airline specific itineraries and 4) evolve the fleet to match an airline specific fleet forecast. Previous papers have described how this is accomplished and approximated with separate modules (Refs. 3, 4, 8). Key parameters

3 observed in historical data such as demand/capacity ratios can be matched using the existing process. City pair specific future demand can also be created so as to match airport-wide demand levels. However several other key baseline parameters that are believed to affect NAS-Performance are not guaranteed to be replicated with the existing process. They are related to network connectivity and include baseline measures such as flight legs per itinerary and the idle time between flight legs. Idle time is defined as surface time in excess of the modeled required turnaround time. In general the longer the idle time and less flight legs per itinerary, the less connected the airline network and the less likely the model will result in more propagated delay due to late arriving aircraft. This is not a surprising result given the independent nature of the processing in which schedule times are assigned independent of the production or aircraft itineraries. The main purpose of this paper is to develop a new approach for the above process by modeling the inter-dependencies between schedule growth and itinerary generation, and by capturing the trends observed in historical data to be reflected in the future. It would also provide means for assessing the potential for a trade-off in performance gain achieved by maximizing the aircraft usage versus maintaining schedule peaks. A key metric affected by a carrier s network connectivity is late arriving aircraft delay, measured as a flight s late departure and arrival caused by a previous flight s late arrival (Refs. 12, 16, 18). The later arrival delay incurred by downstream flight legs is known as propagated delay (Ref. 12). According to a Bureau of Transportation Statistics data extract (Ref. 17), the overall On-Time arrival performance for Fiscal Year 2011 (October 2010 through September 2011), excluding canceled and diverted flights, was 80.7%. The delay category Late Arriving Aircraft was the highest contributor to total FY11 scheduled arrival delay with 41.2%. BTS Data Query Percent of Arrival Delay (>=15 mins) Minutes by Delay Category October September 2011 Carrier Delay 41.2% 29.7% Weather Delay NAS Delay Security Delay Late Arr Del 4.3% 0.1% 24.7% Figure 1. Percent of Arrival Delay Minutes by BTS Category In the rest of this paper, we begin with a description of the requirements for an itinerary generation algorithm in the next section. Section III provides a review of the basic fleet assignment model and its extension with time windows for flights, which is adapted for our itinerary generation solution. Then Section IV describes the core mathematical models used in this research, with a formulation showing how the use of time windows can provide a choice for an optimization algorithm to minimize the aircraft usage in itinerary generation. An extension of the formulation models the use of preferred times as approximated with existing banks while minimizing the number of aircraft required. Numerical and sensitivity analysis are provided in Sections VI and VII. We discuss the computation considerations related to further enhancement of the models. The paper is concluded with a summary in Section IX. II. Itinerary Generation An itinerary generation algorithm requires two input arguments: a schedule which is a collection of flights and a set of non-negative numbers called the minimum turnaround times. For the purposes of the algorithm each flight

4 9:00 9:45 10:30 11:15 12:00 12:45 13:30 14:15 15:00 15:45 16:30 17:15 18:00 18:45 19:30 20:15 21:00 21:45 22:30 23:15 0:00 0:45 1:30 2:15 3:00 3:45 4:30 5:15 6:00 Flight Counts Accumulative Flight Counts plan in the input schedule needs to have information that will identify its carrier, aircraft type, departure airport, scheduled departure time, arrival airport, and scheduled arrival time. The minimum turnaround time input which is a function of a carrier and aircraft type represents a lower bound on the time between an airframe s arrival and its departure from the same airport. The itinerary generator algorithm s goal is to link flight legs into a set of itineraries using a given set of turnaround times. By an itinerary we mean a collection of flight plans, ordered by scheduled departure time, such that the flight plans in the set have the same carrier and aircraft type (i.e. represent a single airframe) and they satisfy the minimum turnaround time condition. The future schedule generation process obtains historical flight plans from the Enhanced Traffic Management System (ETMS) which provides each flight s final filed departure and arrival times, scheduled times, origindestination pair, carrier code, equipment type, user class and filed altitude, airspeed, and trajectory. This historical data forms the core of the baseline flight dataset for future schedule generation. When the forecasted number of flights for an origin-destination pair exceeds the number of baseline flights, it requires the creation of additional flights to fill the demand. The creation and population of these notional future flights is derived from each origindestination pairs baseline flight dataset. After a network algorithm determines the additional flights required among city pairs necessary to meet projected airport growth, these future flights are chosen randomly from the baseline flights, according to a uniform distribution. The times assigned to the new flights are based on current times shifted according to a normal distribution with mean of 0 minutes and standard deviation of 5 minutes. This narrow time window for shifting the new flights times was chosen to preserve existing bank structures and maintains peaks consistent with what is observed in the historical data. The other data elements are considered static and the newly created flights are added to the expanded future demand set. For a decrease in demand, flights are randomly deleted as necessary. 6 5 SFO-LAX: (All) Base2011 Unconst Figure 2. Departure Peak Identification Figure 2 above illustrates the process of adding new flights to an existing city-pair (SFO-LAX) distribution using the baseline schedule of with a target year of The solid columns are the flight counts by 15-minute bin. The dotted lines are the accumulative flight counts over the course of the day. The colors represent different scenarios (blue as FY11 baseline, and red as unconstrained forecast for FY30). At the daily level, the total number of new flights to be added to the baseline schedule is determined by the Fratar algorithm based on the projected growth rate. In the unconstrained forecast scenario, 14 new flights are needed to increase the number of flights from 38 to 51. The next step is to distribute these new flights over the carriers as well as across the operational hours of the day. Currently, the distribution of the new flights is largely proportional to the existing profile of the baseline schedule. As the results, the new flights are likely to overlap with the existing flights. This may cause several effects including reduced flight legs per itinerary; longer idle time between linked flights and a larger number of short

5 headways than are observed in historical schedules. Short headways between flights with the same origin and destination may bias the operational performance in some models by concentrating flights in a particular gate area or over a particular fix. These impacts will be particularly strong for heavy and super-heavy aircraft, since these have greater separation requirements and particular gate requirements. A number of strategies could be considered to alleviate the shortcomings of the existing future schedule generation method. One approach is to delevop a smart shifting algorithm to spread out the new flights in a bigger time window, or to shift to a less busy time window; another approach is to change the way that the new flights are assigned to airlines. Instead of assigning the new flights to the same airline in the base schedule, a competitive or a generic airline could be used for the new flights. This paper will investigate the first option by changing the time assignments of the new flights and, if needed, the time assignments of the baseline flights to optimize the expected performance of a future schedule. It is conceivable that by allowing flexibility in flight departure times particularly for flights added to reflect increased demand, an optimization routine could minimize aircraft required and produce schedules with less idle time and greater aircraft utilization. However as noted in previous work, this may result in de-peaked schedules (Ref. 20). With this objective in mind, we develop a generalized itinerary generation solution for simultaneously assigning aircraft types to flights and scheduling flight departures. In our model, a time window is assigned to each flight allowing flight departure times to be adjusted so that the total number of itineraries is minimized. Although not necessarily the most likely scenario for the future demand, the minimum number of itineraries provides a benchmark that the NAS can reach in a best-case scenario. The use of time windows in an optimization algorithm has been previously experimented by a group of researchers from MIT (Refs. 2, 11). We have extended their modeling techniques to solve our itinerary generation problems with time windows of various widths used for different types of flights. A new method of shifting flights is also developed for the purpose of preserving the existing bank structures that many airlines currently have in place. Using the FY2011 data from ETMS (Peak Summer Day July 21 st, 2011; and Bad Weather Day November 4 th, 2010), we show that our model can solve real, large-scale problems that approximate itinerary characteristics observed in the historical data. In every test scenario, the model produces a fleet assignment with significantly lower costs in terms of number of aircraft required than the baseline model. Additionally, in a separate analysis, the model is used to tighten the schedule, potentially saving aircraft. III. Review of Fleet Assignment Models The itinerary generation model can be viewed a variant of the fleet assignment model, which has been studied extensively in the literature. See, for example, Hane, et al. (Ref. 5), Abara (Ref. 1), and Jacobs, Smith and Johnson (Ref. 7). We begin with a review of the basic fleet assignment model. The following are commonly given as input data and associated rules for a fleet assignment problem, Flight Schedule: each flight covered exactly once by one fleet type Number of Aircraft by Equipment Type: Can t assign more aircraft than are available, for each type Turn Times by Fleet Type at each Station Other Restrictions: Maintenance, Gate, Noise, Runway, etc. Operating Costs, Spill and Recapture Costs, Total Potential Revenue of Flights, by Fleet Type The objective of the basic fleet assignment model is to find the flight to Aircraft assignment that minimizes the total cost. The decision variables are x k,i equals 1 if fleet type k is assigned to flight leg i, and 0 otherwise y k,o,t is the number of aircraft of fleet type k, on the ground at station o, and time t The parameters include C k,i is the cost of assigning fleet k to flight leg i N k is the number of available aircraft of fleet type k t n is the count time

6 We further define the following. I is the set of all flight legs i K is the set of all fleet types k O is the set of all stations o CI(k) is the set of all flight arcs for fleet type k crossing the count time The MIP Formulation of the basic fleet assignment model is then given by Subject to: min c k,i x k,i (0) k K i I x k,i = 1, i I (1) k K y k,o,t + x k,i y k,o,t + x k,i i I(k,o,t) i O(k,o,t) = 0, k, o, t (2) y k,o,tn + x k,i N k, k K (3) o O i CI(k) x k,i {0,1}, y k,o,t 0. (4) In this formulation, the objective is to minimize the cost to cover all flights with available aircraft. Constraint (1) makes sure that all activities are covered exactly once. Constraint (2) ensures that the aircraft flow is conserved at each node. The third constraint implies a limited number of aircraft of each type are available for use at any given time and location. A generalized fleet assignment model has been presented by Rexing, et al. (Ref. 11) for simultaneously assigning aircraft types to flights and scheduling flight departures. By allowing variability in scheduled flight departure times, the generated fleet assignment model with time windows for departure times allows more flight connection opportunities, and therefore, results in more cost effective fleet assignment. The formulation of the model is provided below. The objective function of this model is again to minimize the total cost as defined. The constraints ensure flight coverage, conservation of flow at each node, restricted aircraft utilization (constraints 3), and variable integrality (constraints 4 and 5). Note that there are far more nodes in the network when time windows are used. By choosing a single arc copy among multiple candidates in a given time window, the model effectively chooses the departure time of each flight. This model also allows the user to apply a different cost coefficient to every flight copy. For example, one can make it more expensive to fly a flight the further it is moved from a target time that satisfies a schedule bank requirement. Rexing, et al. s work is relevant to the topic of our paper. In general, Itinerary Generation (IG) differs from the Basic Fleet Assignment Model (BFAM) in certain ways. But the most important one is that BFAM only assigns the flights to aircraft of specific equipment type while IG assigns flights to aircraft in order to form an itinerary. IG requires modeling the aircraft at a specific future tail number level. Based on this observation, it is obvious that the complexity of IG problems is far greater than BFAM. However, the BFAM solution can be used as the first step toward the solution of an IG problem. Hence the fleet assignment problem with time windows is closely related to the problem addressed in this paper, i.e., itinerary generation with time windows for flight departures. Furthermore, future schedules consist of two types of flights: the original flights derived from a baseline schedule and the new flights added to reflect the growth of future demand. In our formulation, the newly added flights have a higher degree of freedom for time adjustments required to achieve the desired performance target while meeting the increasing future demand. Other important differences between BFAM and IG are summarized in the following table.

7 Table 2. Key Differences between BFAM and IG Models Issue BFAM IG Description Fleet Optimization objective Time Fleet size known for an airline Minimizing total cost Complete cycle (planes return to origins) Fleet size given by forecast for each airline Minimizing number of aircraft needed Single day (not complete cycle) Future Flights Flight legs are given Future Flights are based on the existing flight network observed in current schedules Flight Allocation N/A Based on FRATAR algorithm. Flight/Itinerary Statistics N/A Maintenance, Gate, Operating, Spill and Recapture Costs, etc. Included in the objective function Distribution for Trip Length, Airline/Equip, Block Hours Not considered Allocation among airlines based on current or forecasted fleet size Minimizing objective may not be consistent with fleet forecast Remove the corresponding constraint Current network provides Airline, Equip and Time Mimic current allocation or fleet forecast (Airline, Equip and Time) Trip length is not explicitly modeled in formulation. Other factors could be modeled at different levels of details (i.e. airline specific) Use constant (or estimated) costs Output Fleet Assignment Itineraries Additional algorithm required for mapping fleet assignment to itineraries IV. Itinerary Generation Model with Time Windows With the same reasoning behind the fleet assignment model with time windows, we would also introduce a time window for the departure time of each flight for the purpose of itinerary generation. By allowing each flight to shift within a time window, it adds additional flexibility for itinerary generation. We would specify different time windows for different types of flights. In this formulation, new flights have more flexibility in shifting their departure times, while the changes to the original flights should be kept at minimum to preserve the original patterns of existing schedules. A. Mixed-Integer Programming Formulation The generalized itineration generation problem with time windows is formulated as a Mixed-Integer Programming (MIP) problem similar to the fleet assignment problems, with an additional set of integer variables defined to allow time windows for each flight. Here we first provide a formulation of the Itinerary Generation model. min c k,i x k,j,i (5) k K j J(i) i I Subject to: x k,j,i = 1, i I k K j J(i) (6) y k,o,t + x k,j,i y k,o,t + x k,j,i = 0, k, o, t j J(i) i I(k,o,t) j J(i) i O(k,o,t) (7)

8 y k,o,tn + x k,j,i N k, k K o O j J(i) i CI(k) (8) x k,j,i {0,1}, k, j, i y k,o,t 0, k, o, t. (10) (9) Note that J(i) represents a set of alternate flights for flight i by shifting within a time window around the original scheduled departure time. For example, a time window of +/- 15 minutes is assigned to the original flights, meaning that a flight can deviate from its departure time specified in the input schedule by as much as 15 minutes in either direction (15 minutes earlier or 15 minutes later than the departure time in the input schedule). For newly added flights, we assign a larger time window (for example up to 40 minutes) around their scheduled departure times.. A larger time window for new flights would also allow time assignments in other departure/arrival banks or even potentially less congested times. The larger time window allows an optimization routine to find a suitable flight time meets the key objectives established above. At present a time slot is provided every five minutes from a reference time up to the window interval limit. For this research, a time window of +/- 30 minutes results in 13 potential time assignments per flight. Furthermore, this research does not use flight specific cost. Therefore, minimizing cost is equivalent to minimizing the number of aircraft required to cover a network. B. Modeling the Effect of Banking As pointed out in other studies, strategies that minimize idle time may cause a smoothing or de-peaking of the schedule if consideration is not given to preserving departure peaks or banks. The effects of the smoothing or depeaking may benefit carrier-equipment idle time but may also artificially lower delay by assigning shifted flights to non-peak periods. Thus, there exists a tradeoff between competitive departure placements within a bank structure versus maximizing a carrier s equipment utility. To remain consistent with the assumption of the carriers preference to satisfy demand at peak demand period, we must identify the local departure peaks in any future schedule for any airport and shift our flights accordingly. The departure peaks are identified for each airport in the baseline and future schedules by counting the number of IFR operations by 15-minute bins, and applying a rolling centered Bin +/- 2 Bins window (i.e., Bin +/- 30 minutes = 1.25 hour window) to find the maximum number of departures for each window considered the local maximum. Contiguous peaks are permitted. Another approach involves labeling the end point of a positive-sloped line segment as a peak resulting in tagging every up-tick as a local peak. Using a narrower window may also result in labeling false peaks, whereas a wider window risks ignoring true peaks. The results of the centered 1.25 hour time window are seen below for ATL in Figure.

9 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00 0:00 1:00 2:00 3:00 70 ATL November 4, 2010 Projected to Binned Deparutre Local Max: Bin +/- 30 Minute Max Moving Window Figure 3. Departure Peak Identification A set of additional parameters and rules are required in the new model for capturing the behavior of departure peaks. For example, Bank width is used to represent the width of a bank. Typically we use +/- 30 minutes around each peak for the bank width. Although a flight can be shifted to any bank if no further restriction is imposed, we assume that a flight is shifted forward (or backward) to its nearest peak. With the banking structure captured in the modified model, future flights for the same city-pair are more likely moved to nearby banks. The mathematical formulation of the itinerary generation model with banking structure is in fact identical to the formulation for the same model without banking structure as described in the previous subsection, except that the set of alternate flights J(i) should be chosen within a time window around the peak period that is closest to the departure time of flight i, instead of a time window around its departure time. C. Partitioning Methods Compared to the BFAM problems, both versions of the IG problems as presented above have far more integer variables in the formulation, which makes the problem much more difficult to solve. Hence, to reduce the computation complexity involved, we will introduce a partitioning approach based on two different grouping methods as discussed below. 1. Partitioning Schedules by Airlines and BADA Equipment Types The MIP solution is computationally intensive when the size of the model is large (particularly when the number of integer variables is large). Even with a reduced network consisting of a selected subset of airports, it is still quite challenging to solve the Itinerary generation problem with flights allowed to shift around within a time window. To further reduce the computation, a decomposition method is developed using partitions based on airlines and equipment types. As mentioned in the introduction, the input flight schedule to the itinerary generation model includes flight plans from multiple airlines. In addition, the equipment type (for examples, MD80, A320, or 737) used for a flight is typically chosen by airlines using more complex decision making involving passenger demand, crew equipment available, and competitive market forces. For this implementation, the itinerary generation problem can be partitioned by airline and by equipment type using baseline data and airport forecast as the best available estimate of airlines demand in the future. Within the group of a single partition (i.e., an airline and equipment type combination), the cost parameter c r can be treated as a constant. So the objective function simplifies to minimizing the total number of aircraft required to cover all the flights in the group. The number of flights within a partition with specific airline and equipment type is obviously much less, and therefore the size of the corresponding itinerary

10 generation problem for a single partition is significantly smaller than the original problem. Given the fact that the solution time of an MIP problem typically grows exponentially with the problem size, the decomposition method makes the problem much more tractable. 2. Partitioning Schedules by Common Airline Equipment Groups Another grouping method is based on the Seat Category. The seat category is defined as the range of passenger seating capacity for commercial aircraft. Typically, a seat category consists of multiple equipment types with seating capacity in the same range. For example, A and B are different equipment types but have similar seating capacity. Therefore, A and B are in the same seat category. Grouping by seating capacity allows additional flexibility of assigning aircraft of different equipment types to flights. With a greater range of aircraft to choose from for the itinerary generation, we should expect to see better operating efficiency. V. Test Scenarios and Evaluation Criteria The overall objective of introducing a MIP solution to the future schedule process is to link together independent modules that currently 1) Assign Flight Times and 2) create linked flights into itineraries. It is believed that if kept independent, future schedules may exhibit less network connectivity and therefore underestimate propagated delay. Furthermore, as the end process must create a constrained schedule, which also involved making decisions on flight times, the evaluation of the new logic would be performed with and without constraints. In the end, three itinerary generation algorithms were evaluated. The Baseline algorithm represents the current process where modules are processed sequentially with flight time assignments independent of itinerary generation. The alternative scenario involved two itinerary generation processes using the time windows described above. In the first, the time windows are chosen with an existing city-pair flight used for the reference time. In the second, time windows are chosen relative to an alternative bank observed at the facility. Table 3. Test Scenarios for MIP Solution Demand Scenario Itinerary Generation Description Process Unconstrained Baseline/Sequential A non-integrated, sequential process assigning notional future flights with short headways for subsequent standard greedy itinerary generation. The original bank structure is generally preserved. No consideration for the airports physical constraints or carrier connectivity and aircraft utilization. Unconstrained Optimized Performs integrated flight-time assignments (time-shifting) on the unconstrained schedule to optimize aircraft utilization and carrier network connectivity. Does not explicitly maintain a bank structure, and may assign flights in periods of low passenger demand (smoothing). Unconstrained Optimized for Banks Performs integrated flight-time assignments (time-shifting) on the unconstrained schedule to optimize aircraft utilization and carrier network connectivity with additional constraints preserving the bank structure detected in the raw unconstrained schedule. Constrained Baseline/Sequential A non-integrated, sequential process subjecting the unconstrained demand to a constraining algorithm designed to shift (smooth) or remove (trim) flights according to each airport s capacity limits to achieve the single goal of yielding a feasible demand set. There is no control for preserving banks or improving

11 connectivity and utilization. Constrained Optimized An integrated process in which the altered feasible schedule s flight-time assignments are optimized for aircraft utilization and carrier network connectivity. But does not explicitly maintain bank structure. Constrained Optimized for Banks An integrated process in which the altered feasible schedule s flight-time assignments are optimized for aircraft utilization and carrier network connectivity with additional constraints preserving the bank structure detected in the feasible schedule. The scenarios above were evaluated for the two sample days (Peak Summer day July 21 st, 2011; and Fall bad weather day November 4 th, 2010) over five demand years (2011, 2015, 2020, 2025, 2030). The testing would track if key measures observed in the baseline such as schedule peaks and network connectivity are maintained in the future or kept consistent. Lastly, the logic is evaluated on its final effect on the delay numbers that would be realized in the NAS-wide simulation model. For this work, the FAA System-Wide Analysis Capability (SWAC) was used for delay projections. Table 4. Evaluation Criteria Metric Legs per Itinerary Idle Time Schedule Peaks Propagated Delay Total Delay Indicator Measures for each carrier and equipment type the average number of flight legs per itinerary. Computed and compared at the carrier-equipment and system level to the respective corresponding baseline values. The excess amount of time an aircraft remains on the ground. Computed and compared at the carrier-equipment and system level to their respective baseline values. Monitor changes in schedule peaks using various criteria. One example metric tracked was the number of operations scheduled at 90% capacity or greater. The scheduled arrival delay >=15 minutes incurred by subsequent flight legs due to the late arrival of a previous flight leg. A flight must be delayed on its departure and arrival to qualify. (Refs. 12, 18). It is expected an increase in connectivity will affect an increase in propagated delay. The total delay (combined gate, surface, and airborne) delay incurred by a flight. Delay is not rounded or floored. It is expected that demand smoothing, due to optimized flightshifting, will result in operations during non-peak times and possibly result in decreased total delay. VI. Numerical Results and Analysis We have tested the MIP model with data from fiscal year 2011 for all major airlines and equipment types. As described above, the current algorithm is a multi-step process that first produces a future schedule based on an unconstrained forecast and then produces a constrained or feasible schedules that reflects that capacity constraints of the airports. For each future year and each combination of airline and equipment, we solve the itinerary generation problem with time windows to generate the optimized itineraries such that the total number of aircraft required would be minimal. The primary goal of the MIP is to improve the performance of network connectivity as measured by flight legs per itinerary and % flight idle time. Figure below shows the key network connectivity measures for the baseline and future years under the 3 alternative itinerary generation algorithms. The benchmark is measured against the values observed in the historical data for For 2011, there were system wide flight legs per itinerary of 4.5 and percent idle time of 15.5%. For the Baseline/Non-Integrated scenarios, these measures degrade over time. Without a direct link between flight assignment and itinerary generation, it is as if the process adds more aircraft to the supply and airlines cover the future networks with proportionately more aircraft. When the process is optimized

12 5:00 AM 6:00 AM 7:00 AM 8:00 AM 9:00 AM 10:00 11:00 12:00 1:00 PM 2:00 PM 3:00 PM 4:00 PM 5:00 PM 6:00 PM 7:00 PM 8:00 PM 9:00 PM 10:00 11:00 12:00 1:00 AM 2:00 AM 3:00 AM 4:00 AM 5:00 AM 6:00 AM 7:00 AM 8:00 AM 9:00 AM 10:00 AM 11:00 AM 12:00 PM 1:00 PM 2:00 PM 3:00 PM 4:00 PM 5:00 PM 6:00 PM 7:00 PM 8:00 PM 9:00 PM 10:00 PM 11:00 PM 12:00 AM 1:00 AM 2:00 AM 3:00 AM 4:00 AM using a simple application of time windows, the model is able to cover the same network with proportionately the same number of aircraft. However, if an attempt is made to preserve schedule banks, the trend reverts to the baseline/non-integrated scenario. 6.0 Flight Leg/Itinerary Ratio 25% % Ground Idle Time % % % 1.0 5% 0.0 0% Greedy Optimized Optimized/Bank Greedy Optimized Optimized/Bank Figure 4. Network Connectivity Measures by Itinerary Scenarios The results demonstrated the effectiveness of the optimization method in generating optimized itineraries with its capability to adjust flight schedules with time windows. However the improvement in aircraft utilization may come at the expense of schedule smoothing unless schedule banks are explicitly accounted for by the itinerary generation modules. Figure shows example demand profiles for IAH for the forecast year of Optimized - IAH :: Baseline Optimized Capacity 70 Optimized w/banks - IAH :: Baseline Optimized/Bank Capacity Figure 5. IAH Demand Profiles by Itinerary Generation Method There are many choices available in assessing the significance in the schedule peaks between the 3 scenarios. Ultimately the effect of schedule peaks will involve the complex interaction of all the events and constraints in the model. To first order, we can measure the number of operations that occur in 15 minute time bins that are a 90% of capacity or above. For the IAH 2030 example, there are 65 less flights at the 90% capacity or above limit for the optimized as opposed to only 24 fewer in the Optimized for Banks. For the optimized for banks scenarios, the MIP

13 Minutes of Total Delay Number of Departures consistently moves more operations back into peak periods. Although it never achieves the same degree of Schedule Peakiness, an improvement can be detected. Ultimately the effect of network connectivity and schedule peaks will be determined by the delay values realized by the NAS-wide simulation model. VII. Schedules and NAS Wide Model Sensitivity A Future Schedule contains many elements that influence delay results. However the primary driver may be simply described as demand/capacity imbalances. Imbalances may exist for all weather conditions or a facility may routinely handle current traffic levels but experience imbalances during bad weather. In the latter case, it is important that future schedules or the model process accurately reflect weather conditions. FAA currently accounts for weather effects through its sample day selection process. Figure below shows how delay increases over time when demand is unconstrained versus a constrained (feasible) demand set. The total delay at facilities would decrease if demand remained feasible Core 30 Forecasted Non-Networked (Single Legs) Demand and Total Delay Summer Day Constrained Total Delay Constrained Flights Unconstrained Total Delay Unconstrained Flights Figure 6. Projected flight departures and total delays The manner in which airlines chain flights together into an itinerary and connect passengers is also a contributor to delay. If airlines and airports had unlimited resources, they could purchase and accommodate enough aircraft to minimize the effect of late arriving flights on pending departure. The Baseline/non-integrated approach unintentionally models aircraft in this way. Without, a direct attempt to minimize aircraft, they are regarded as a free resource. A. Simulation and Delay Calculations The effect of itineraries on delay is evaluated for each scenario through the use of a fast-time NAS-wide simulation model. We chose the System Wide Analysis Capability (SWAC) simulation, developed and hosted by the Systems Analysis and Modeling Division in the office of NextGen to evaluate the effects on delays (Ref. 14). This model simulates the performance of NAS resources (airports, sectors, fixes, and en-route restrictions) at the system wide level. The following sections describe the rules used of extracting total delay and total propagated delay from the SWAC model. The intent is to use definitions that most closely match the definitions used by the Bureau of Transportation Statistics (BTS). 1. Measurement I: Simulated Late Arriving Aircraft Delay

14 For each aircraft evaluate the following from the simulation timestamps and calculate late arrival aircraft delay consistent with the rules provided from BTS (Refs 12, 16, 18): 1.) Itinerary has >= 2 Flight Legs 2.) Leg i Actual Gate Arrival Time > Leg i+1 Scheduled Gate Departure Leg i+1 Turnaround Time 3.) Leg i+1 Actual Gate Arrival Time Leg i+1 Scheduled Gate Arrival >= 15 minutes 4.) Minimum Value of: a. Leg i+1 Actual Gate Arrival Time Leg i+1 Scheduled Gate Arrival Time b. Leg i Actual Gate Arrival Time (Leg i+1 Scheduled Gate Departure Leg i+1 Turnaround Time) To validate the simulated propagated delay as a percent of total scheduled arrival delay against historical BTS data, and estimate potential error, a single baseline schedule (Summer day: July 21 st, 2011) was run using a standard baseline data file (2011) and the greedy itinerary algorithm through SWAC. Table 5. Late Arrival Delays: Historical vs. Simulation Scenario Late Arrival Delay ASQP NAS Wide 41.7% ASQP Core % Simulation Core % This underestimation of Late Arrival delay may be attributed to several factors including the lack of consideration for crew scheduling, mechanical or connecting passenger issues, and sensitivity to turnaround times. 2. Measurement II: Simulated Total Delay Another measure of flight delay, provided from SWAC output (Ref. 13), is the difference of the Total Delay between test scenarios. The Total Delay is calculated as the sum of the delay components by flight phase contained within the simulation s Flight Output Report aggregated for each flight: B. Results Total Delay = Total Gate Delay + Total Surface Delay + Total Airborne Delay The expected consequence of an improvement in a carrier s network connectivity through increased legs/itinerary and decreased idle time is increased propagated delay. However, any smoothing of the overall demand set may ultimately shift flights from peak demand periods into lower demand periods and shift delay to the gate and incur a lower level of total departure (taxi-out) and airborne delay. Arranging this assumption into a scenario test matrix serves as a guide to verify the models are performing as expected and validates the core assumption of the relationships between network connectivity and delays. The expected directions of the key metrics are provided below in Table 6. Table 6. Test Matrix: Expected Directions of Evaluation Criteria Test Scenario Comparison Scenario Legs/Itinerary Idle Time Propagated Delay % Total Delay Optimized Non-Integrated Increase Decrease Increase Increase Optimized for Banks Non-Integrated Increase Decrease Increase Increase Optimized Optimized for Banks Increase Decrease Increase Increase The results for the Summer Day Constrained demand set are presented in Figure. The trends in Total Delay and Propagated Delay generally agree with the expectations except for a slight disagreement in the earlier years of Total Delay for the comparison of Optimized and Optimized-for-Banks. However, the trend shows in later years that a

15 less peaked schedule results in lower Total Delay. The Propagated Delay as a Percent of Total Arrival Delay is highest for the optimized scenario which also has the highest flight legs per itinerary and lowest percent of idle time. However the scenario with the highest total delay is the baseline which also has the highest score for schedule peaks. This indicates schedule peaks have a higher order effect on delay than tighter networks with higher aircraft utilization. 900, , , , , , , , ,000-35% 30% 25% 20% 15% 10% 5% 0% Constrained: Total Delay Minutes Propagated Delay as a % of Total Scheduled Arrival Delay (>=15 mins) Baseline Optimized Optimized/Bank Figure 7. Delay Measurements by Itinerary Scenario The resulting differences between a test scenario and the comparative scenarios key metrics are compiled in Table 7 for our summer baseline day s constrained demand set. The change in values for Flight Legs/Itinerary, Idle Time and Propagated Delay are a straight difference of the test scenario and the comparison scenario output. The change in Total Delay is the percent change from the comparison scenario s result. The shading indicates if the direction of the metric change follows our expected results for a comparison in a given year. The green-shading indicates agreement with our expectation, and the red shading indicating a conflict with our expected result. Test Scenario Comparison Scenario Table 7. Comparison of Constrained Demand Itinerary Scenarios, Summer Day Constrained Legs/Itinerary Idle Time Propagated Delay as a % of Scheduled Arrival Delay Total Delay Optimized Non-Integrated % -3.4% -3.4% -3.7% 6.4% 4.4% 5.3% 5.6% -2.7% -5.1% -8.8% -7.9% Optimized for Banks Optimized Non-Integrated % -1.3% -0.2% -0.1% 2.4% 0.9% 0.5% 0.3% -3.6% -6.2% -5.9% -3.9% Optimized for Banks % -2.1% -3.1% -3.6% 4.0% 3.4% 4.7% 5.3% 1.0% 1.1% -3.1% -4.1%

16 VIII. Itinerary Generation with Grouping by Seat Category The seat category is defined as the range of passenger seating capacity for commercial aircraft. Typically, a seat category consists of multiple equipment types with seating capacity in the same range. Grouping by seating capacity allows additional flexibility of assigning aircraft of different equipment types to flights. With a greater range of aircraft to choose from for the itinerary generation, we should expect to see better operating efficiency. Figure 8 below shows the key network connectivity measures for the baseline and future years for the same 3 scenarios as shown in Figure 5. Since the seat category is used for grouping the flights, the results show improved performance in terms of leg/itinerary ratios and ground idle times achieved by the MIP method. Particularlly, the results for the optimized for banks scenario are noticeably better than the cases with grouping by equipment type. 6.0 Leg/Itinerary Ratio 25% % Ground Idle Time % % 10% 1.0 5% 0.0 0% Greedy Optimized Optimized/Bank Greedy Optimized Optimized/Bank Figure 8. Network Connectivity Measures by Itinerary Scenarios To simulate the delay performance for the scenarios with grouping by seat category, we assume that a generic equipment type is used for all flights of the same seat category. The simulation results provided in Figure 9, show the average performance of Total Delay and Propagated Delay. These results are quite similar to those with grouping by equipment type as shown in Figure 7. However, the Propagated Delay appears to be less than that in Figure 7. This may be explaned by the fact that the seat category is a larger group than the equipment type, therefore, it provides greater flexibility for the MIP method to generate itineraries with less potential delays. Figure 9. Delay Measurements by Itinerary Scenario with Grouping by Seat Category

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