Flight delays and passenger preferences: an axiomatic approach.

AuthorBishop, John A.

The U.S. Department of Transportation (DOT) defines a flight as "delayed" if it arrives 15+ minutes late. The DOT "flight counting" delay definition is used to rank airline/airport service quality. An obvious caveat of counting flight delays is that the duration of delay plays no role in the delay count. The purpose of this article is to propose an aggregate delay measure that is sensitive to the distribution of time delayed among passengers. The importance of this work is that our derived delay measure reflects passenger preferences rather than the arbitrary delay cutoff established by the DOT. We model passengers' preference ordering using the criteria that passengers prefer fewer, shorter, and more equal delay times.

JEL Classification: L93, R42

  1. Introduction

    Airline flight delays, like any other form of waiting for service, may negatively affect customers (passengers) in many ways. Delays can increase passengers' anger, uncertainty, and dissatisfaction with the service provided (Taylor 1994). In addition, flight delays are costly. A recent Joint Economic Committee report estimates that domestic flight delays cost the airline industry and passengers $40.7 billion in 2007. (1) In December 2007, U.S. airline delays reached their highest monthly level since the Bureau of Transportation Statistics began tracking flight delays in 1995, as 32% of domestic flights arrived late. Furthermore, in 2007, U.S. airline delays reached their highest annual level since 1999, as 24% of all domestic flights arrived late. To address this problem, the Federal Aviation Administration is imposing financial penalties of up to $25,000 per violation on chronically delayed flights. (2)

    In ranking flight delays among airlines and airports, the sole (and official) measure used by the U.S. Department of Transportation (DOT) is the proportion of flights delayed (i.e., a flight is counted as "delayed" if it arrives 15 or more minutes behind schedule). This DOT "flight-counting" measure of delays has been adopted by the industry and is widely reported by the media as the de facto standard with which to measure on-time performance. In fact, the

    DOT's Air Travel Consumer Report provides a monthly ranking of airlines based on the percentage of on-time arrivals. (3) The purpose of this article is to propose an alternative aggregate delay measure based on passenger preferences rather than an arbitrary DOT delay definition.

    There are several flaws with using the DOT standard to measure airline service quality. Foremost is the arbitrariness in assigning 15 minutes as the delay threshold. Why not 10 minutes or 20 minutes? Second, by counting the occurrence of delays, the duration of delay plays no role in the calculation (e.g., no distinction is made between flights delayed 16 minutes vs. 60 minutes). Third, a discrete designation for each flight, either "on-time" or "delayed," ignores the distribution of flight delays. Even carriers with identical average minutes of delay are likely to be viewed differently if they provide some passengers with severe delays. We believe that extreme delays are viewed as particularly upsetting for travelers (i.e., a one-hour delay is more painful for travelers than two 30-minute delays).

    Airline researchers recognize the statistical shortcomings of the 15-minute delay standard; hence, various measures of flight delays have been considered, including the following: counting the number of flight delays (Brueckner 2002), calculating the minutes of travel time on a route in excess of the monthly minimum (Mayer and Sinai 2003), and determining the minutes of arrival (Mazzeo 2003) and departure delay (Rupp 2009). Moreover, Bratu and Barnhart (2006) show that when factors such as flight cancellations and missed connections are factored in, actual passenger waiting times are nearly two-thirds higher than the minutes of aircraft arrival delay (the DOT-reported measure). The unique contribution of our article is that we derive a delay measure based on passenger preferences, not simply based on a measure's statistical properties or arbitrary delay standards. Of course, any measure of airline delays must assert a passenger preference ordering; we model passengers as preferring fewer, shorter, and more equal delay times.

    The article is organized as follows. Section 2 provides the axiomatic framework for measuring aggregate flight delays. We examine the notion of flight delay and propose a set of axioms governing the measurement of flight delays for a group of airline (or airport) passengers. We then propose a class of decomposable measures of flight delays as well as a partial dominance condition for the rankings of flight delays. In section 3, we apply the proposed measures and dominance condition to measure and rank flight delays of two major U.S. airlines. Section 4 provides some extensions and discussion.

  2. Measuring Aggregate Flight Delays

    Consider a group of N passengers with possibly different delay times, [x.sub.i], where i = 1, 2 ..., n. Here the group can be viewed as all passengers of an airline or an airport. Clearly, not all passengers have their flights delayed; some may even depart and arrive early. In this sense, [x.sub.i], can be positive (delayed), negative (arrived early), or zero (on time). For the group as a whole, we denote X = ([x.sub.1], [x.sub.2] ..., [x.sub.N]) as the flight-delay profile of the group.

    For the passengers as a group, we want to construct a summary measure of delays so that comparisons and rankings among different groups of passengers are feasible. To this end, we

    define a measure of flight delays as a single value function, D=D([x.sub.1], [x.sub.2], ..., [x.sub.N]), that reflects the aggregate level of flight delays for the group as a whole. To characterize D(.), we follow the axiomatic approach that Sen (1976) pioneered in poverty measurement. The similarity between these two measurements indicates that much of the calibration crafted to measure poverty can be applied when measuring flight delays. (4) In this approach, we first lay out the basic ideal properties that an index of flight delays should possess and then generate satisfactory flight-delay measures within the boundaries of the axioms.

    Axioms on D(*)

    We first require that the flight-delay index be a continuous function of all flight-delay times.

    CONTINUITY. D(*) is a continuous function of X = ([x.sub.1], [x.sub.2], ..., [x.sub.N]).

    The second axiom is the anonymity axiom, which states that the identities of the passengers play no role in the computation of D(*): If two populations have the same flight-delay profile, then the two groups should have the same level of flight delays. Profiles X = ([x.sub.1], [x.sub.2], ..., [x.sub.N]) and Y = ([y.sub.1], [y.sub.2], ..., [y.sub.N]) have the same level of flight delay if Y = PX for some permutation matrix P. A permutation matrix is a square matrix with elements 0 and 1 where each row and column sums to 1. Formally, the anonymity a[x.sub.i]om is stated as follows:

    ANONYMITY. D(Y) = D(X) if Y = PX for some permutation matrix P.

    The next axiom is the focus axiom, which states that an index of flight delays is concerned only with delays; hence, arriving early by 20 minutes or by two hours makes no difference for the calculation of D(*). That is, recalling that early arrival means [x.sub.i]

    Focus. D(Y) = D(X) if Y is obtained from X via [y.sub.i] = [x.sub.i] for all [x.sub.i] > 0 and [y.sub.i] [less than or equal to] [x.sub.i] for all [x.sub.i] [less than or equal to].

    Contrary to an early arriving flight, if a flight has been delayed, then any further delay will increase the level of aggregate delays. This is the monotonicity axiom to which we alluded earlier in the Introduction. In the following statement, a passenger's delay time increases from [x.sub.i] to [y.sub.i] = [x.sub.i] + [[epsilon].sub.i].

    MONOTONICITY. D(Y) > D(X) if Y is obtained from X via [y.sub.i] = [x.sub.i] + [[epsilon].sub.i] for some [x.sub.i] > 0 with some [[epsilon].sub.i] > 0 and [y.sub.i] = [x.sub.i] for all other [x.sub.i] > O.

    While an index D(*) that satisfies the monotonicity axiom...

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