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A Tale of Two Aisles

Control #2158 February 12, 2007

Contents

1 Introduction 1.1 Disturbances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Boarding Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 The Problem 2.1 Performance Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 The Aircraft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 The Model 3.1 Modelling Arrivals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Modelling Movement Within Aircraft . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 The Results 5 Conclusions 1 2 2 5 5 6 6 6 7 8 8

1

Introduction

Mounting financial pressure, from rising oil prices to low-cost carriers, make high operational efficiency an imperative for the airline industry [3]. One important metric of operational efficiency is airplane turn time, the time between arrival and next departure. This metric is considered noteworthy because it is a measure of an aircraft's utilization, and may be a key point of difference between low-cost carriers and traditional carriers, with low-cost carriers being known for quick turn times [9]. Aircraft generate revenue only when they're flying; turn times spent on the ground are lost revenue opportunities. Contributors to aircraft turn time include taxiing, passenger enplaning and deplaning, cargo loading and unloading, airplane fueling, cabin cleaning, and galley servicing [6]. The most significant of these is passenger enplaning and deplaning, a component that is not only one of the biggest factor in turn times for most airlines, but also a component that has steadily deteriorated over the last three decades [6], as can be seen in Figure 1. In addition, passenger enplaning and deplaning also leave impressions of service quality on customers, with slower, more inefficient processes frustrating passengers and tempting them to switch airlines. For these reasons decreasing boarding time is an important consideration for airlines these days.

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Figure 1: Historical trends of enplane and deplane rates [6]

1.1

Disturbances

Boarding times are often lengthened by interruptions to the boarding process; these interruptions are termed "disturbances". Common disturbances are aisle interference, seat interference, and lack of nearby overhead bin vacancies [5]. Aisle interference This type of delay occurs when one passenger is obstructed by another passenger who is stowing his luggage, seating himself, or obstructed himself. The first passenger must wait behind the other passenger until he removes himself from the aisle or moves forward. Seat interference This type of delay occurs when one passenger's seat is closer to the window than another passenger nearer to the aisle in the same half-row already seated. This interference necessitates that the seated passenger rise and move back into the aisle to allow the other passenger access to his seat. Lack of nearby overhead bin vacancy This type of delay occurs when a passenger needing to stow their luggage in overhead bins cannot do so because the overhead bins near his seat are full. He must then move either upstream or downstream in an attempt to find a vacancy for his luggage. Boarding strategies attempt to minimize boarding time by minimizing the number of disturbances [8, 3]. Only a couple of previous works take into account the bin vacancy issue [5, 4]; the others focus on seat and aisle interferences.

1.2

Boarding Strategies

To exert control over the boarding process, airlines assign passengers to boarding groups or zones, calling each boarding group to board in order. For example, the traditional and most oft-used boarding group assignment is the "back-to-front method", wherein boarding groups composed of contiguous rows are called in reverse order, with boarding groups in the back called first and those

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Figure 2: Flow chart of solution approaches to the aircraft boarding problem. in front called last. Thus, a boarding strategy is the method by which passengers are assigned to boarding groups and the in order which these groups are called. In the past few years, new boarding strategies have been innovated by researchers in both academia and industry. However, the body of literature on this problem is surprisingly small, given the aviation industry's long and close relationship with operations research [3]. Some in academia and industry have used simulation to compare sometimes exhaustive lists of boarding strategies [6, 5], while others in academia have taken an analytical approach. Within the analytical approaches, there has been further branching, with some using mathematical programming [3, 8] and others analyzing the problem using Lorentzian geometry and random matrix theory [2]. Analytical approaches can reveal unknown optimal solutions, wile simulations compare strategies and evaluate them under various conditions [3]. The various approaches and their relationships to each other are illustrated in Figure 2. As a result of these efforts, various other boarding strategies besides the back-to-front method are now in use in the airline industry [7]: Rotating-zone boarding Boarding groups are contiguous rows, but called in alternating order, with boarding groups in the back called, then those in the front, then those second to the back, etc., until the groups meet in the middle of the plane. See Figure 3(b). Used by AirTran. Outside-in boarding Boarding groups are assigned by type of seat: window, middle or aisle. They are boarded in that order, as well, to minimize seat interference. See Figure 3(c). Used by Ted/United. Block boarding A combination of outside-in and back-to-front boarding such that boarding groups composed of window seats board before boarding groups composed of middle and aisle seats. Within boarding groups, rows are contiguous, and boarding occurs in back-to-front order. See Figure 3(d). Used by Delta. Reverse-pyramid boarding Another combination of outside-in and back-to-front, this method is best explained through illustration. See Figure 3(e). Used by US Airways.

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(a) Back-to-front boarding

(b) Rotating-zone boarding

(c) Outside-in boarding

(d) Block boarding

(e) Reverse-pyramid boarding

Figure 3: Illustration of boarding systems currently in use. The number on each seat indicates the boarding group assignment. Random boarding with assigned seats Essentially one boarding group. Used by JetBlue, Maxjet, Northwest. Random boarding with unassigned seats Much like random boarding with assigned seats, except the seats aren't assigned. Used by EasyJet, RyanAir, and Southwest, the most prominent among which is Southwest. Southwest actually uses three boarding groups, assigned based on check-in time, so random boarding with unassigned seating does not necessarily imply a single boarding group. The reverse-pyramid boarding strategy illustrated in Figure 3(e) is the direct product of research effort in academia. First developed by van den Briel et al. at Arizona State University for America West Airlines, the optimal solutions to a nonlinear integer program minimizing seat and aisle interferences (a proxy for boarding times) turned out to be reverse-pyramid strategys [8, 9]. The strategy was later confirmed and refined by Bazargan [3], who characterized the impact of betweengroup interference (that is, the overlap between one boarding group and the next; specifically, Bazargan defines a parameter , the fraction of passengers from the previous group trying to reach their seats) on the optimality of the outside-in/reverse-pyramid/back-to-front strategies. The reverse-pyramid boarding strategy is successful because it minimizes seat interferences by using an element of the outside-in boarding strategy, as well as simultaneously minimizing aisle interferences by boarding over a larger span of rows. This strategy is in contrast to the back-to-front

Control #2158 Size Class Small Midsize Large Number of Seats 85-210 210-330 450-800

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Table 1: Specification of aircraft size classification method, which concentrates passengers in contiguous sections, thus increasing aisle interferences. In fact, Ferrari [4] showed that random boarding with assigned seating was a better strategy than the back-to-front method, precisely because random boarding allows boarding over the entire span of the aircraft. While the literature has addressed a great number of boarding strategies, they have almost without exception used only one aircraft model, the Airbus A320. The one exception was the use of a modified A320, with 8 seats across rather than 6, but with the same number of total seats [4]. The best strategies in the A320 case proved also to be the most stable, while the other strategies "showed great instability" [4]. However, the modification made to the A320 layout was modest at best, and it would be interesting to see how far the robustness of strategies like the reverse-pyramid extended, particularly to a plane like the Boeing 747, which is much larger and has two aisles.

2

The Problem

This paper attempts to build on the results of previous work to provide a more comprehensive answer to the question of optimal boarding strategy. In particular, this paper will focus on boarding strategy comparison using simulation across different size classes of aircraft, specified in Table 1. The objective is to find the best strategy for each size class.

2.1

Performance Measures

Performance measures for each strategy will be based on aircraft boarding time and personal boarding time, defined below: · Aircraft boarding time: duration between when the first passenger enters the airplane to when the last passenger is seated · Personal boarding time: duration between when a passenger joins the jetway queue or enters the airplane (if there is no jetway queue) and when he is seated for the first time (if there is a seat interference for which he must rise then reseat himself) The four performance measures used, in order of importance, will be: 1. Average aircraft boarding time: the average aircraft boarding time 2. Average personal boarding time: the expected average personal boarding time 3. Maximum personal boarding time: the expected maximum personal boarding time 4. Maximum aircraft boarding time: the maximum aircraft boarding time

Control #2158 Size Class Small Midsize Large Aircraft Model Boeing 737 Boeing 757 Boeing 747

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Table 2: Specification of aircraft size classification

2.2

The Aircraft

The aircraft models selected for boarding strategy are listed in Table 2. Selection was based on popularity within each size class, as measured by number of models currently in service [1]. Note that variants of models (e.g., 757-200, 757-300) were not considered separately; variant populations were included in the model population (e.g., 757-200s and 757-300s were both counted as 757s).

3

The Model

The model of the boarding process can be divided into two functions: modelling the arrival of the passengers in the jetway or the plane (if there is no jetway queue), and modelling the movement of passengers once within the aircraft. Boarding strategy changes the former; the latter model remains the same no matter the boarding strategy.

3.1

Modelling Arrivals

This part of the model consists of the jetway queue, which occurs when passengers are arriving more quickly than they are seating themselves. A queue develops in the jetway when passengers fill up the aisle(s) in the plane due to aisle interference. Passengers enter the queue at a fixed rate of one passenger every 7 seconds, which is the observed service rate for one gate agent [3]. They leave the queue when the entrance to the airplane is clear (that is, when the first cell in the aircraft is unoccupied). The boarding strategy chosen influences the order of passengers entering the queue. Boarding strategies assign boarding groups to the passengers as well as order the call-off for boarding groups. Passengers are assumed to follow their boarding group assignment without exception (that is, there are no early boarders or no late boarders), but the order of passengers within each boarding group is random. The boarding strategies evaluated were: · Back-to-front boarding · Rotating zone boarding · Outside-in boarding · Reverse-pyramid boarding · Random boarding with assigned seats Note that in all boarding strategies, first class and business class are boarded first. Special needs passengers are also conventionally boarded first, but this type of passenger is not included in the model.

Control #2158 Model Boeing 737­400 Boeing 757­300 Class First Economy First Economy Business Economy Economy Economy Rows 3 22 6 35 4 4 42 4 Row Configuration 2­2 3­3 2­2 3­3 2­2­2 2­3­2 3­4­3 2­4­2 Total Seats 144 234

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Boeing 747­400

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Table 3: Aircraft dimensions and interior layout used in simulations. Note that numbers in the row configurations indicate number of seats in a row and dashes indicate an aisle. Average boarding time Aircraft 95% CI Personal 10.5 [10.4, 10.6] 5.3 10.7 [10.6, 10.8] 5.7 17.2 [16.8, 17.5] 9.0 18.4 [18.0, 18.8] 9.5 Maxmimum boarding time Personal 95% CI Aircraft 10.3 [10.2, 10.3] 10.9 10.1 [10.1, 10.2] 11.2 16.7 [16.5, 16.8] 18.9 17.9 [17.8, 18.1] 20.9

Boarding Strategy Outside-in Reverse-pyramid Back-to-front Rotating-zone

95% CI [5.3, 5.3] [5.6, 5.7] [9.0, 9.1] [9.4, 9.6]

Table 4: Performance measures for small aircraft by boarding strategy.

3.2

Modelling Movement Within Aircraft

This part of the model consists of passenger movement within the aircraft. In this part of the model, passengers move along the aisle(s) to their destinations, resolving aisle and seat interferences (note that bin occupancy is not modelled). The aircraft is discretized into cells that can be occupied by no more than one passenger or not occupied at all. Every seat is represented by one cell, and aisle cells occur at the same intervals as seat cells. Aisle interferences are resolved by waiting until the aisle cell in front is clear. Seat interferences are resolved by waiting until the seated passenger(s) can leave the seat and move into the aisle, downstream of the waiting passenger. After they have successfully moved into the aisle, the waiting passenger seats himself. The passengers behind the previously waiting passenger do not move forward, waiting instead for the previously seated passenger(s) to reseat himself (themselves). The specific aircraft dimensions and layouts used for each aircraft model are given in Table 3. Average boarding time 95% CI Personal 95% CI [17.1, 17.4] 8.8 [8.8, 8.8] [18.1, 18.4] 9.4 [9.3, 9.4] [25.7, 26.4] 13.7 [13.6, 1.7] [26.8, 27.5] 14.0 [13.9, 14.0] Maxmimum boarding time Personal 95% CI Aircraft 17.0 [16.9, 17.0] 18.2 17.7 [17.6, 17.7] 19.0 25.4 [25.3, 25.6] 28.7 26.6 [26.4, 26.7] 29.0

Boarding Strategy Outside-in Reverse-pyramid Back-to-front Rotating zone

Aircraft 17.2 18.2 26.0 27.1

Table 5: Performance measures for midsized aircraft by boarding strategy.

Control #2158 Average boarding time 95% CI Personal 95% CI [28.8, 29.2] 15.3 [15.3, 15.4] [32.6, 33.0] 15.4 [15.4, 15.4] [32.7, 33.2] 16.2 [16.1, 16.2] [35.4, 35.6] 16.5 [16.5, 16.5]

8 Maxmimum boarding time Personal 95% CI Aircraft 28.1 [28.0, 28.1] 29.7 32.2 [32.2, 32.2] 33.6 32.0 [32.0, 32.1] 34.4 35.3 [35.2, 35.3] 36.2

Boarding Strategy Back-to-front Reverse-pyramid Rotating zone Outside-in

Aircraft 29.0 32.8 33.0 35.5

Table 6: Performance measures for large aircraft by boarding strategy.

4

The Results

The results in Tables 4, 5, 6 show that outside-in and reverse-pyramid strategies are the best strategies for small and midsized aircraft, as expected from the results seen in the literature. However, very surprisingly, the back-to-front method is the best strategy by far for the Boeing 747, a much larger plane with a different interior layout (2 aisles) than the planes previously investigated. This discrepancy may be due to the fact that on a larger plane, the boarding groups are much larger, so seat and aisle interference are more spread out. In all cases, the rotating zone strategy performed the worst.

5

Conclusions

While airlines should switch to the reverse pyramid strategy for small and midsized aircraft, they should keep their traditional back-to-front strategy for large aircraft. As with any model, numerous simplifications were made to the model. Several refinements, such as bin occupancy, person compressibility, early/late boarding, and multiple doors, may yield more realistic results significantly different from the current results. Bin occupancy As noted in [5], one of the chief disturbances to the boarding process is lack of nearby overhead bin vacancy. Lack of bin vacancy forces passengers to move upstream or downstream past their seat row in order to find vacancies, lengthening individual boarding time and increasing aisle interferences. Wide rows and late boarding groups exacerbate this problem, and a more realistic model would take into account the effect of bin occupancy on boarding times. Person compressibility In this discrete model, passengers always occupy one cell, no more and no less. In reality, passengers can often compress themselves into other passengers, into occupied seats, and hold their personal belongings closer to themselves, decreasing the amount of space they occupy. While deadlock may occur in this model during a seat interference, in reality, some passengers may be able to squeeze by in a space somewhat less than a cell. Early/late boarding In this model, passengers were modelled as following their boarding group assignment without exception. However, in reality, passengers often arrive at their gates late, after their boarding groups have been called. Other passengers may also attempt to board before their boarding groups have been called, either accidentally or intentionally. Presumably, gate agents may prevent early-boarders, but perhaps such prevention would not be in the best interest of customer service. The effect of late boarding was examined in [4], but only one the boarding strategies found in [5]. In particular, the reverse-pyramid boarding strategy was not examined for robustness with respect to early/late boarding.

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References

[1] AirguideOnline.com. Commercial aircraft: Jet aircraft world fleet summary. http://www. airguideonline.com/aircr_wfleet.htm, [Online, accessed February 2007]. [2] E. Bachmat, D. Berend, L. Sapir, S. Skiena, and N. Stolyarov. Analysis of aeroplane boarding via spacetime geometry and random matrix theory. Journal of Physics A: Mathematical and General, 39(29), July 2006. [3] M. Bazargan. A linear programming approach for aircraft boarding strategy. European Journal of Operational Research, 2006. doi:10.1016/j.ejor.2006.09.071. [4] P. Ferrari and K. Nagel. Robustness of efficient passenger boarding in airplanes. In 84th Annual Meeting, Washington, DC, January 2005. Transportation Research Board. [5] H. V. Landeghem and A. Beuselinck. Reducing passenger boarding time in airplanes: A simulation based approach. European Journal of Operational Research, 142(2):294­308, October 2002. [6] S. Marelli, G. Mattocks, and M. Remick. The role of computer simulation in reducing airplane turn time. AERO Magazine, 1(1), January 1998. [7] M. van den Briel. Airplane boarding. http://www.public.asu.edu/~dbvan1/projects/ boarding/boarding.htm, [Online, accessed February 2007]. [8] M. H. L. van den Briel, Villalobos J. R., and G. L. Hogg. The aircraft boarding problem. In Proceedings of the 12th Industrial Engineering Research Conference, 2003. Nr 2153, CD-ROM. [9] M. H.L. van den Briel, R. Villalobos, G. L. Hogg, T. Lindemann, and A. Mul´. America West e Airlines develops efficient boarding strategies. Interfaces, 35(3):191­201, May 2005.

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