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Airline fare and seat management strategies with demand dependency
Journal of Air Transport Management 24 (2012) 42e48
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Airline fare and seat management strategies with demand dependency K. Obeng a, *, R. Sakano b a b
Department of Marketing, Transportation and Supply Chain, School of Business and Economics, North Carolina A&T State University, Greensboro, NC 27411, USA Department of Economics and Finance, School of Business and Economics, North Carolina A&T State University, Greensboro, NC 27411, USA
a b s t r a c t This paper conceptualizes various discount strategies used by airlines. Using a constrained revenue maximization model that assumes interdependent demand, it develops rules to guide decision-making, and shows that the large fare discount-many discount seats and small fare discount-few discount seats strategies are optimal. Empirical support is provided for the large fare discount-many discount seats, the no fare discount-moderate discount seats and small fare premium-few discount seats strategies. In addition it identifies the large fare premium-very few discount seats strategies. We argue that these strategies are used in various demand situations and allow airlines to price discriminate. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction The 1978 US Airline Deregulation Act removed many of the economic regulations over airlines. Events since then, especially the development of computer-assisted reservation systems and the internet, have led airlines to introduce yield management systems to provide a variety of pricing schemes and itineraries to induce passengers to self-select services according to their willingness to pay. The result is second degree price discrimination with travelers paying different fares for the same flight. Airlines also practice third degree price discrimination by grouping their customers according to elasticity of demand and charging each group a different fare. Since airlines face capacity constraints in terms of limited aircraft seats, they must make decisions in terms of how many discount seats to offer and the discount fares to charge to maximize revenues. We consider demand dependency and conceptualize the following fare-discount and discount-seats strategies: small fare discount-many discount seats, small fare discount-few discount seats, large fare discount-many discount seats, large fare discountfew discount seats as well as a fare premium-no discount seat strategy and ask if there are others not revealed by this conceptualization. 2. A typology of strategies A number of strategies are used by airlines practicing price discrimination. Among them is the large fare discount-few discount * Corresponding author. Tel.: þ1 3363347231; fax: þ1 3363347093. E-mail address: [email protected] (K. Obeng). 0969-6997/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jairtraman.2012.06.001
seats strategy that is used when demand is very less elastic and a large fare discount is required to attract few additional travelers to fill capacity (Pels and Rietveld, 2004). The second, is large fare discount-many discount seats and it is applicable when demand is less price elastic but when many seats must be sold as in off-peak (Mantrala and Rao, 2001). A third strategy is a small fare discount-few discount seats and applies were demand is elastic, and a fourth is offering small fare discount-many discount seats such as in tourist or other markets where demand is very elastic. While they are important, these strategies do not represent a complete list of what airlines do. Despite this void, theoretical support for some of the more common strategies can be seen by considering the seat allocation problem of a constant average cost airline that offers a two-class coach service (high- and discount-fare seats) in a given origindestination market.1 The discount-fare seats are restricted and those unable to meet them buy high-fare seats. The demand of each fare class is down-sloping and, following Botimer and Belobaba (1999), are interdependent. There are a limited number of highfare paying passengers all of whom buy seats every time and the airline faces the constraint that it cannot overbook flights, and everyone who buys a ticket shows up for the trip. The airline operates an aircraft of capacity Vc seats, and assuming inverse demand functions, the fare for each class depends upon the number of seats demanded by each of the classes. These quantities are Q1 seats for the high-fare F1 and Q2 seats for the discount-fareF2. Thus, F2 ¼ F2(Q1,Q2) and F1 ¼ F1(Q1,Q2) are the inverse demand functions 1 This assumption of constant cost means average cost and marginal cost are the same for each passenger regardless the class of ticket purchased. This assumption also avoids a marginal cost function that depends on the outputs of both classes.
K. Obeng, R. Sakano / Journal of Air Transport Management 24 (2012) 42e48
where discount fare is less than the high-fare and the derivatives of the fares with respect to the quantities Q1 and Q2 are negative. In maximizing its revenue TR ¼ Q1F1(Q1,Q2) þ Q2F2(Q1,Q2), the airline faces the constraint that the number of passengers cannot exceed plane capacity. Thus, Q1 þ Q2 Vc and the Lagrangian of this optimization problem is,
Max L ¼ Q1 F1 ðQ1 ; Q2 Þ þ Q2 F2 ðQ1 ; Q2 Þ þ lðQ1 þ Q2 Vc Þ
(1)
where, l is a Lagrangian multiplier. From this, if the demands for high- and discount-fare seats are completely independent as when there is no switching then revenues are Q2F2(Q2) and Q1F1(Q1) for discount- and high-fare paying passengers. Substituting them into Eq. (1) and taking the partial derivatives with respect to Q1 and Q2, setting the results equal to zero and solving gives MR1 ¼ MR2. Where MR1 ¼ F1(11/ε11) is the marginal revenue from each additional high-fare paying passenger, MR2 ¼ F2(11/ε22) is the marginal revenue from each additional passenger paying a discount fare, ε11 and ε22 are high- and discount-fare elasticities of demand. It implies that absent demand dependency, fewer discount seats should be offered if the marginal revenue MR2 of an additional discount-fare passenger is less than the marginal revenue MR1 of an additional high-fare paying passenger. However, if there is demand dependency, which implies that switching is allowed, the airline chooses Q1 and Q2 to maximize revenue and from Eq. (1), the first order conditions for revenue maximization are,
vF1 ðQ1 ; Q2 Þ vF ðQ ; Q Þ Q2 2 1 2 þ l vQ1 vQ1 Q F ðQ ; Q Þ 2 2 1 2 ~ ¼ MR þl 1 ε12 Q1
vL=vQ1 ¼ F 1 ðQ1 ; Q2 Þ Q1
~ Q1 F1 ðQ1 ; Q2 Þ þ l vL=vQ2 ¼ MR 2 ε21 Q2
(2)
(3)
Where, ε21 is the cross-elasticity of discount seat demand from changes in high fares and ε12 is the cross elasticity of high-fare seat ~ demand from changes in discount fares. Also, MR 1 ¼ F1 ðQ1 ; Q2 Þ ~ ½1 1=ε11 and MR 2 ¼ F2 ðQ1 ; Q2 Þ½1 1=ε22 are own price contributions to the marginal revenues of an additional high- and discount-fare paying passenger. The second terms in Eqs. (2) and (3) are the contributions of switching to marginal revenue. Alternatively, they are the additional revenues lost when an additional passenger switches from one fare class to another. Solving these equations for l and equating the results gives.
43
from high- to discount-fare seats than from discount- to high-fare seats. Fig. 1 shows marginal revenue equalization for high- and discount-fare paying passengers. For clarity, we have included high-fare seats demand Dh, its corresponding marginal revenue b , MR b MR1, the demand and marginal revenue D 1 when the high h fare changes, discount-fare seats demand Dd and its corresponding b and MR b marginal revenue MR2, as well as D 2 depicting where both d demand and the marginal revenue of a discount-fare passenger have changed. MR1 and MR2 show where switching is not considered and the two demands are independent. Here, marginal revenues equalization is at “a” where MR1 ¼ MR2. To the right of “a” the marginal revenue from an additional discount fare passenger is greater than the marginal revenue from an additional high-fare passenger and the airline benefits by offering many discount seats. To the left, the reverse is true and each additional high-fare paying passenger adds more to revenue than does an additional discount-fare paying passenger. With switching, the marginal revenue of high-fare seats MR1 b and MR2 shifts to M R b . If the downward shift of shifts down to M R 1 2 MR1 is less than a similar shift of MR2 the number of discount seats would increase and vice versa. For the case where the downward shift of discount fare seat demand is larger than the downward shift in high-fare seat demand marginal revenues are equalized at “b” and there are more discount-seats than high-fare seats. Regardless of where marginal revenues are equalized Fig. 1 shows that capacity is fully reallocated between high- and discount-fare paying passengers with demand diversions occurring. Additionally, both the seat allocation and optimal fares are simultaneously determined. For example, drawing vertical lines through the marginal revenue equalization point “b” to the demand lines of high- and discount-fare paying passengers gives their respective optimal fares b F and b F 2 , the fare discount as the difference between them b . b and Q and the optimal seat allocation as Q 1 2 Also, solving Eq. (4) for the discount fare gives F2 ¼ F1[1(1/ ε11) þ (Q1/ε21Q2)/1(1/ε22) þ (Q2/ε12Q1)]. Since the discount fare is less than the high fare the term in brackets in this equation takes values between zero and one. Further, since discount seat demand is more elastic than high-fare seat demand, for the discount fare to be less p than the ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi high fare Q1/ε21Q2 < Q2/ε12Q1 from which Q1 < Q2 ε21 =ε12 . This shows that there must be more high-fare seats than discount-fare seats because the cross-elasticity of
High Fare ($)
Discount Fare MR1
MR2
Q2 F2 ðQ1 ; Q2 Þ Q1 F1 ðQ1 ; Q2 Þ ~ ~ MR ¼ MR 1 2 ε12 Q1 ε21 Q2
(4)
F1 F1
b ~ b ~ Let MR 1 ¼ MR1 Q2 F2 =Q1 ε12 and MR2 ¼ MR2 Q1 F1 =Q2 ε21 be the marginal revenues of high- and discount-fare paying passengers with switching. Then, with demand dependency revenues are maximized where both marginal revenues are equal. ~ ~ Furthermore, since MR 1 > MR2 the sufficient condition for marginal revenue equalization with switching is Q2F2/ε12 Q1 > Q1F1/ε21Q2. This implies that with switching the decrease in the marginal revenue of an additional high-fare passenger is larger than the decrease in the marginal revenue of a discount fare passenger; a condition met with more passengers switching
F2 F2
Dd Dh MR1
Dd b
O
a
Q1
MR2
Dh
Q2 = V C – Q 1 Q2 = V C – Q 1
Q1 Seats
Fig. 1. Marginal Revenue Equalization.
O
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K. Obeng, R. Sakano / Journal of Air Transport Management 24 (2012) 42e48
discount-fare seat demand from changes in the high fare (ε21) is greater than the cross-elasticity of high-fare seat demand from changes in the discount fare (ε12). Given that, the term in brackets in the equation is positive and less than one, it approximates the probability of having more high-fare seats than discount-fare seats if the airline optimizes its seat allocation to maximize revenue or Pr(Q1 > Q2). Substituting this into the discount fare equation gives F2 ¼ F1*Pr(Q1 > Q2), that is the expected revenue from a discount fare.2 An advantage of our equation is that it provides a relatively simple way of approximating the probability of more high- than discount-fare seats and avoids having to make distributional assumptions about this probability. Using the expected revenue equation, the fare-discount (DF) is the product of the high-fare and the probability of having more discount seats than high-fare seats:
DF ¼ F1 F2 ¼ F1 *f1 PrðQ1 >Q2 Þg ¼ F1 *PrðQ2 >Q1 Þ
(5)
If the probability of finding a discount seat is high, then discount seat demand is less elastic and Eq. (5) shows the amount of the farediscount is large and vice versa. These results show that as the probability of finding a discount seat increases a large fare discount-many discount seats strategy is required for revenue maximization. Alternatively, as the probability of finding a discount seat reduces a small fare discount-few discount seats strategy is required for revenue maximization. Thus, revenue maximization supports only two of the conceptualized strategies. Perishable asset pricing studies have also found that the large fare discount-many discount seats strategy applies to products whose demands are less elastic, or which are hard to sell and whose elasticities of demand increase as the end of a shopping period approaches. Early in a shopping period the discounted quantity is large and for a product whose elasticity increases toward the end of a shopping period the strategy of a large fare reduction early and a small fare reduction later could bring about large changes in quantity demanded. For airlines this strategy implies offering a large fare discount well ahead of a flight date when there are many seats and a small fare discount as the flight date approaches and there are few discount seats.3 It could also apply when airlines are returning their planes from low to high demand markets where premium fares can be charged.4 To fill seats airlines can minimize their losses by charging low fares possibly reflecting variable costs. Similarly, it could apply to off-peak situations when airlines attempt to fill many seats by offering large fare discounts, e.g., weekend flights. Comparatively, the small fare discount-few discount seats strategy applies when airlines face elastic demand. Although the revenue maximization model captures only two strategies, the peak pricing studies have supported the fare premium-no discount seats strategy, while perishable asset pricing studies have supported the other two. The latter suggests a large price markdown close to the end of a shopping period for products whose price elasticities decrease with time, for example large fare discounts on stand-by tickets to fill few available airplane seats. This is the case of the large fare discount-few
2 Replacing a discount fare with a bid price makes this result identical to Littlewood’s (1972) formula. 3 Obeng’s (2008) work on temporal variation in airfares confirm this strategy by showing that the amount of the fare discount airlines offer reduces as the flight day approaches. 4 Airlines park their planes overnight in low demand markets where there is space and return them to high demand markets early morning.
discount seats strategy. Also, Coulter (1999) shows that some companies have price markdowns that increase from the beginning to the ending of shopping periods. That is, small markdowns at the beginning of a shopping period when the available quantity is large (i.e., a small price discount-large discounted quantity), and large markdowns close to the end of a shopping period when available quantity is low to dispose of hard-to-sell inventory (i.e., a large price discount-few discounted quantities). 3. Methodology The revenue maximization, peak pricing and the perishable asset analysis support five fare-seat management strategies. Still the question is what empirical evidence is there to support them? Are there other fare-seat management strategies which airlines use besides those noted? Answers to these questions are obtained using a two-step approach. First, we assume flights with similar fare discount-discount seats characteristics form distinct groups and then use cluster analysis to identify these groups. The characteristics of the groups provide some indications of fencing, and a comparison of their mean discount fares and mean discount seats to the overall mean values of the observations provides a basis for identifying the strategies airlines use. That is, the difference between the mean discount fare for available airplane seats of a cluster and the mean discount fare for similar seats for all observations is the amount of the extra discount over the average discount fare if negative, or a premium above the average discount fare (less discount than the average) if positive. This approach recognizes that airline consolidators buy tickets in bulk at discounts from airlines and pass some of the discounts to passengers in the fares they advertise. Further, it uses observed discount fares, which are those offered on consolidators’ websites, as an instrument for actual fares since both are highly correlated. Once the strategies are identified, the second step orders them by offered discount fare and identifies their statistically significant characteristics using an ordered logit model whose independent variables include those used in the cluster analysis. The signs and sizes of the marginal effects of the variables in this model are used to describe the strategies. We assume that y*i is a continuous latent variable representing the strategies, where i is a strategy, xj a set of j variables that affect the choice of each strategy and b a set of coefficients. Then the latent regression for the strategies is:
y*i ¼
X
bj xij þ εi
(6)
j
Where, εi is a random error and the ordered true values of the strategies are yi ¼ 0,1,2,3,.,i and are assumed to be generated by the process,
8 0 if yi < m0 > > > > < 1 if m0 < yi < m1 yi ¼ 2 if m1 < yi < m2 > > ::::::::::::::::: > > : i if yi mi1
(7)
In Eq. (7), m is a set of threshold parameters that defines the boundaries of the strategies. If the cumulative density function of the error term εi is logistic, then the probability of observing each strategy is,
K. Obeng, R. Sakano / Journal of Air Transport Management 24 (2012) 42e48
9 hP i > > Pðyi ¼ 0Þ ¼ 1 1 þ exp > j bj xij m0 n h P io n h P io > > > > > b m b m 1 1 þ exp Pðyi ¼ 1Þ ¼ 1 1 þ exp = j j xij 1 j j xij 0 n h P io n h P io > b m b m x x 1 1 þ exp Pðyi ¼ 2Þ ¼ 1 1 þ exp 2 1 > j j ij j j ij > > > ::::::::::::::::::::::::::::n h io P > > > ; Pðyi ¼ iÞ ¼ 1 1 1 þ exp j bj xij mi1
The ordered logit model is non-linear and, as a result, inferences cannot be made from the signs and sizes of its coefficients but from the marginal effects of the variables. Following Greene (2007) the effect of an increase in a variable on the probability that a flight is based on a particular strategy is,
0 0 vPi =vxj ¼ f mi1 b x f mi b x bj
(9)
The left-hand-side is the partial derivative of the probability of strategy i with respect to variable j and f(,) is the logistic density function. In the case of a continuous exogenous variable, its marginal effect shows how a unit increase in that variable affects the probability that a flight is based upon a particular strategy. On the other hand for a discrete exogenous variable its marginal effect is the change in the probability that a flight is based upon a particular strategy when that variable takes a value of one versus a value of a zero. Among these variables is the cost of providing service. This cost affects the choice of a strategy in two ways. One, a higher average cost may make an airline choose a small fare discountfew discount seats strategy because its profit margin is small prior to any discount. Two, lower average cost may make an airline choose a large fare discount-many discount seats strategy especially when a large capacity aircraft is used. If an aircraft must be returned to a high demand market, the airline chooses a large capacity aircraft even if the demand for the first leg of the flight is relatively low because profits from the second leg will outweigh the cost of the first. However, pilot and fuel costs can be considered fixed because they must be borne whether or not there are passengers. Hence, variable costs are those associated with flight attendants and on-board services. If in charging full fares the aircraft would return empty, the airline minimizes its losses by pricing based on variable cost and this results in very low fares with many discount seats. One cost factor is network complexity; airlines with complex networks with many nodes and circuitous routes have high costs and higher fares unless there are network economies of scale. Berry (1990) found that serving a large number of routes reduces cost which in turn reduces fares. In comparison longer routes increase cost and fares. Hayes and Ross (1998) and Borenstein and Rose (1994) found route length is associated with high fare dispersion. To account for trip length we use trip time which is the sum of inflight time, layover time, and departure delay. Because in mediumand small-size markets, direct flights may use smaller planes, their costs per seat mile may be high leading to attempts to recoup them in higher fares and few discount seats. For example, while the cost per seat mile to operate a 235 seat Boeing 757-300 is $0.0244, the corresponding costs for 50 seats Embraer Regional Jet (ERJ-145) and 49 seats Canada Regional Jet (CRJ-145) both used in short haul services are $0.0863 and $0.0945 (Coyle et al., 2011). Therefore, direct flights are a characteristic that affects cost and is included. In addition, direct flights are interacted with the number of days
45
(8)
before a flight to capture the scarcity of seats on them as the departure date approaches. Of course, competition from airlines emerging from bankruptcies affects fare levels as well. American Airlines echoes this point in its pricing policy by noting that in markets where its competitors have reorganized the competitors’ costs are low and result in low fares that American must match (AMR, 2010). Though reorganization affects fare dispersion it is not included as a variable but is captured, along with other omitted variables, through airline fixed effects. Besides cost, demand factors affect strategy choice. Pels and Rietveld (2004), for example, show that airfares are cheaper if bought well in advance of trip dates when there are many discount seats. Therefore, the days left for a flight when a seat is available is included. Other demand variables are discount seats on originating and connecting flights. Further, airline passengers have a disutility for layover time just as they have for waiting time. This disutility is likely higher than that associated with in-flight time because layover is a greater inconvenience especially if it involves changes in concourses, gates and long waiting times. We include squared layover time to emphasize this greater inconvenience and to capture the possibility that it could lead to a strategy choice emphasizing fare discounts and discount seats. Finally, to capture passenger demand the geometric mean of the passengers on both flights is included.5 Differences in strategy choice may also be temporal such as daily to reflect peak and off-peak conditions. As such the days left before a flight when an itinerary is available is again a variable in the equation. 4. Data The data were collected for a weekday airline round-trip from a non-hub airport, Greensboro, North Carolina to Boston, Massachusetts, a distance of 645 airline miles. The trip began from 5:30ame11:30am on a Monday and returned any time on Friday of the same week. American, Delta, US Airways, Continental, United, and Northwest provided services in this corridor with Canada Regional Jets, Embraer and Boeing 737 aircrafts.6 Data were collected using the online search engine, ORBITZ, because it provided information on aircraft type and aircraft diagrams from which to determine airplane seat capacity and available discount seats. The on-line search was a 100% enumeration of listed flights during a specified 2 h in the afternoon of each weekday of the three weeks prior to the trip.7 The enumeration collected information on flight numbers, posted fares and the seats available at those fares on originating and connecting flights, in-flight and layover times.
5
Initially, we used the arithmetic mean and did not get good results. The rationale for studying this market is to capture fare dispersion in non-hub airports where the absence of low-cost carriers makes established airlines charge premium fares. 7 The data were collected between 4pm and 6pm each weekday during the three weeks prior to the trip. 6
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K. Obeng, R. Sakano / Journal of Air Transport Management 24 (2012) 42e48
The posted fares are interpreted as the discount fares because some seats are unavailable at these fares. Data were also collected on seats on originating and connecting flights, direct service, and number of carriers involved in connecting flights, airline name, and departure time among others. These data were supplemented by service factors at the airport such as airline load factors, on-time performance and departure delays available from the website of the US Bureau of Transportation Statistics (2008). Multiple-carrier flights are treated as if offered by separate carriers, and we assume symmetry so that Delta-US Airways or US Airways-Delta flight for example is the same.8 Because the on-line data did not include passenger load, that information is obtained by multiplying the capacity of each aircraft used by an airline to provide the service by the corresponding load factor of that airline at the airport the month of the trip. For all flights the geometric mean of the calculated passenger loads on both flights was used in our equation. With these modifications the data are an unbalanced panel of 604 itineraries whose characteristics show that the average fare is $812.69 for a round trip, originating flights use aircrafts with 64 seats per flight and connecting flights 107.5 seats per flight. On the average there are 17.3% discount seats on originating flights compared to 38.6% on connecting flights, while average in-flight and layover times are 2.9 h and 1.4 h. 5. Results Because the dataset is large we use the FASTCLUS procedure in SAS (1985) to perform the cluster analysis with normalized variables: days before flight, geometric mean of passengers, fare, seats on originating plane; seats on connecting plane, layover time in hours, direct flight times, and trip time. Several cluster solutions were obtained and compared in terms of pseudo F-statistic and the cubic clustering criterion. These statistics peaked when there were three-clusters and five-clusters suggesting that either of them could be a solution. Further analysis, however, showed that in both solutions a cluster had very few observations. Consequently, a fourcluster solution is used. Table 1 shows cluster characteristics in terms of the means of the variables used and progressively large fares from Cluster 1 to Cluster 4 permitting an ordering of the strategies from the least to the most expensive in terms of fares. Comparing the clusters, Cluster 2 is the base to which the others may be compared because it is where airlines sell at the average (discount) price and reserve the average number of discount seats for their passengers. When demand is small relative to capacity, there are many vacant high fare seats making airlines increase the number of discount seats they offer. If demand is less elastic, deep fare discounts must be used to sell more discount seats than the average as in Cluster 1. Alternatively, if demand is much more elastic and capacity is slightly more than demand, a small fare discount can be used to sell more discount seats than the average. However, if demand is less elastic a large fare discount than the average only leads to a small increase in the number of discount seats demanded above the average. For the case where capacity is less than demand, competition for seats makes an airline offer more high fare seats and fewer discount seats than the average. It does so by charging premiums above the average fare. Here, if demand is elastic, a small fare increase over the average reduces the number of discount seats below average as in Cluster 3. And if demand is less elastic a large premium on discount seats makes their fares higher than the average resulting in fewer number of discount seats than the average as in Cluster 4. The four clusters
8
Further, only flights with available seats on all legs at the offered fares are considered.
thus represent different demand, elasticity, and aircraft capacity situations and offer strategies for airline management. Using the ordered clusters, we modify Eq. (6) to account for airline fixed effects. If there are m ¼ 1,2,3,.,M airlines and n ¼ 1,2,3,.,N, observations then considering each row of the data the probability that an observation belongs to a particular airline is P Pnm ¼ F(m, m, b0 þ jbjxjn þ εn þ ym > 0) where m is a threshold parameter, ym is airline fixed effect, and b0 þ ym is an airline-specific constant term. To avoid identification in estimating this equation P we impose the constraint mym ¼ 0. This fixed effects ordered logit model is estimated, and Table 2 shows its results and fit statistics. All the coefficients are highly significant statistically except that of the squared layover term.9 From the cluster analysis and the ordered logit results we identify the following strategies: Large fare discount-many discount seats strategy: This strategy characterizes Cluster 1 because its average discount fare of $556 is far smaller than the mean discount fare of $812.69, and originating planes have 44.2% discount seats and connecting planes 51.4% discount seats. This strategy could represent where demand is less elastic, plane capacity is average and loads factors are relatively low; i.e. it represents weak high-fare seat demand requiring increasing the number of discount seats and offering a large fare discount to fill them (i.e., a shift to the right of discount-seats supply). From the marginal effects of the statistically significant coefficients in Table 2 the probability of using this strategy reduces by 6.5% when fares increase compared to a 21.9% increase when discount seats on originating and connecting flights increase. In addition, the probability of using this strategy increases by 6.3% for an increase in the number of days in advance when a ticket is purchased. Comparatively, the probability of using it reduces by 24.4% and 12.2% when trip time increases, and when there is an increase in the number of days when direct flights are available. Other results in Table 1 show that there are no direct flights for this strategy; tickets are offered on the average 13.0 days in advance; and the average trip takes 4.58 h including 2.5 h layover, which may contribute to lower demand. Additionally, 42.5% and 30.5% of the flights affected by this strategy are from 5:30ame6:30am and 10:30ame11:30am and medium-size planes seating approximately 132 passengers on the average are used on connecting flights. No fare discount-moderate number of discount seats strategy: This strategy describes Cluster 2 where small planes seating 52 passengers on average are used to provide service and 33.9% of the seats are discounted, a percentage close to the overall average of 35.9% discount seats on connecting flights. All flights affected by this strategy are direct and airlines charge a discount fare of $815.24 that is almost the same as the overall mean discount fare of $812.69 per round trip. Because the fare is almost the same as the mean discount fare for all observations, it is described as the no fare discount-moderate discount seats strategy. Alternatively, we characterize it as the norm to which others can be compared. The results show that the probability of airlines using this strategy increases by 10.6% with each increase in the number of days in advance a ticket is purchased, and by 36.8% when the number of discount seats increases. Conversely, the probability of using it reduces by 11.0% as fares increase and by 9.6% with each additional passenger. The factors that mostly reduce this probability are
9 In the discussion following the supply of discount seats assumes fixed plane size. If aircraft size increases, the supply of discount seats shifts to the right, the reverse being also true.
K. Obeng, R. Sakano / Journal of Air Transport Management 24 (2012) 42e48
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Table 1 Characteristics of clusters. Variable
Fare Days before flight Layover time squared Discount seats on originating flight Discount seats on connecting flight Direct flight days before flight Trip time (in-flight time þ layover time þ departure delay) Geometric mean of passengers on pffiffiffiffiffiffiffiffiffiffiffiffi originating (Q1) and connecting flights (Q2) i.e., ð Q2 Q1 Þ Direct flight (%) Capacity of originating plane Capacity of connecting plane
Mean
Mean
Mean
Mean
Cluster 1 (N ¼ 167)
Cluster 2 (N ¼ 120)
Cluster 3 (N ¼ 257)
Cluster 4 (N ¼ 60)
556.19 13.0 2.5 27.6 67.7 N/A 4.58 66.0
815.24 8.3 N/A 17.7 N/A 8.3 2.55 38.1
823.79 6.0 2.9 12.3 41.7 N/A 4.69 65.7
1474.00 6.3 16.7 9.9 21.7 0.0 8.54 67.8
0.00% 62.5 131.7
100% 52.1 N/A
0.00% 71.1 127.3
trip time and how many days in advance direct flights are available. For instance, an increase in trip time reduces this probability by 41.1%, whereas each additional day a direct flight is offered reduces the probability of using this strategy by 20.6%. Tickets for these flights are offered on the average a week in advance; trip time is 2.55 h, 38.1 passengers per plane take flights affected by this strategy and 92.5% of the affected flights depart from 6:30ame7:30am Small fare premium-few discount seats strategy: This strategy (Cluster 3) is when increased demand from airlines channeling passengers through their hubs results in flying larger planes, and offering few discount seats at a very small premium of $9.10 over the overall mean discount fare of $812.69. The main characteristics of this strategy include the absence of direct flights and offering 17.2% and 32.8% discount seats on originating and connecting flights. The marginal effects of the variables are the largest here than they are in the other
1.67% 58.1 170.2
Overall mean
812.69 8.4 3.6 17.3 38.6 1.7 4.62 52.9 20.33% 63.7 107.5
strategies discussed earlier. For example, the probability of using this strategy reduces by 16.9% with an increase in the number of days in advance a ticket is purchased, and by 58.5% when there is an increase in the number of discount seats. However, increases in fares, trip time and the number of days in advance on which direct flights are available increase the probability of using this strategy by 17.5%, 65.4% and 32.7%. And, an increase in the number of passengers increases the probability of using this strategy by 15.2%. From Table 1, the mean discount fare of $823.79 for flights in this cluster is offered on the average six days before the flight day, the flights have 2.9 h layover and as many passengers as in the first cluster. Additionally, 45.1% of the flights affected by this strategy depart from 10:30ame11:30am, while 29.2% depart from 5:30ame6:30am Large Fare premium-very few discount seats strategy: The final cluster (Cluster 4) gives the large fare premium-very few
Table 2 Maximum likelihood results of fixed effects ordered logit model. Fixed effects ordered probability model Log likelihood function AIC information criterion AIC finite sample BIC Information criterion
372.261 1.2889 1.2907 1.4129
Variable Days before the flight Fare ($) Discount seats on originating flight Discount seats on connecting flight Geometric mean of passengers on originating (Q1) pffiffiffiffiffiffiffiffiffiffiffiffi and connecting flights (Q2) i.e., ð Q2 Q1 Þ Layover time squared Direct flight days before flight Trip time (in-flight + layover + departure delay) Mu(1) Mu(2)
Coefficient 0.4578* 0.4734* 1.3284* 0.2584* 0.4129*
Marginal Effects Variable Days before the flight Fare ($) Discount seats on originating flight Discount seats on connecting flight Geometric mean of passengers on originating (Q1) pffiffiffiffiffiffiffiffiffiffiffiffi and connecting flights (Q2) i.e., ð Q2 Q1 Þ Layover time squared Direct flight days before flight Trip time (in-flight + layover + departure delay) Note: * is 1% significant.
0.1373 0.8879* 1.7731* 1.0687* 4.9065*
Y ¼ 00 0.0630 0.0652 0.1830 0.0356 0.0569
Y ¼ 01 0.1062 0.1098 0.3082 0.0599 0.0958
Y ¼ 02 0.1688 0.1746 0.4898 0.0953 0.1523
Y ¼ 03 0.0005 0.0005 0.0014 0.0003 0.0004
0.0189 0.1223 0.2442
0.0319 0.2060 0.4114
0.0506 0.3274 0.6538
0.0001 0.0009 0.0019
48
K. Obeng, R. Sakano / Journal of Air Transport Management 24 (2012) 42e48
discount seats strategy because there is indeed a large premium of $661 when its mean discount fare of $1474 is compared to the overall mean discount fare of $812.69. And, its 17.0% and 12.3% discount seats on originating and connecting flights are far lower than the mean reported earlier despite airlines flying larger planes on connecting flights which have 170.2 seats on the average. An explanation for this strategy is that both high-fare seats and discount-fare seats are substitutes in production, especially on connecting flights which fly near capacity without discounts due to less elastic high demand relative to capacity. With this less elastic demand a large fare premium over the mean is needed making few discount seats available at regular fares. Thus, if the number of high-fare seats increases to meet increased demand, the supply of discount seats decreases because with fixed capacity fewer discount seats become available at each discount-fare level. If the demand for discount seats is relatively less elastic, then this decrease in supply would result in high fares and fare premiums. However, the very small marginal effects of the variables on the probability of choosing this strategy show that they do not affect this strategy much. For example, increases in fares, trip time and the number of days in advance when direct flights are available increase the probability of using this strategy by 0.1%, 0.2% and 0.1%. Comparatively, an increase in discount seats reduces this probability by 0.2% whereas an increase in passenger load increases it by 0.04%. In Table 1 most of the flights in this strategy connect with others and only 1.7% are direct. Because of these connections travel time and layover time are long; 8.5 h and 4.1 h. Also, only 60 flights are affected by this strategy with 51.7% departing between 6:30am and 7:30am
6. Conclusion This paper classifies the fare discount-discount seats strategies which airlines use in yield management into stylized groups and identify the characteristics of each group to inform decision making. At least five such strategies are conceptualized: small fare discount-many discount seats, small fare discount-few discount seats strategy, large fare discount-few discount seats, large fare discount-many discount seats strategies and fare premium-no discount seats strategies. It was argued that these strategies are
chosen on the basis of elasticity of demand and plane capacity relative to demand. Using a constrained revenue maximization model in which switching is explicitly considered a marginal revenue equalization rule is derived and used to show that the strategies to adopt are the small fare discount-few discount seats and large fare discount-many discount seats. While the revenue maximization rule is standard, because both demands shift down and discount-fare seats demand is more elastic than high-fare seats demand when there is switching, marginal revenue equalization is reached where there are more discount seats. Additionally, alternate derivation of Littlewood’s rule are presented, which is that the discount fare is the product of the high-fare and the probability that there are more high-fare seats than there are discount-fare seats. An approximation for this probability based on price elasticities of demand, cross-elasticities of demand and the seats allocated to high- and discount-fares is estimated.
References AMR Corporation, 2010. Annual Report. http://phx.corporate-ir.net/External.File? item¼UGFyZW50SUQ9NDIyOTIzfENoaWxkSUQ9NDM3MDEwfFR5cGU9MQ¼¼ &t¼1. Berry, S.T., 1990. Airport presence as product differentiation. American Economic Review 80, 394e399. Borenstein, S., Rose, N.L., 1994. Competition and price dispersion in the US airline industry. Journal of Political Economy 102, 653e683. Botimer, T.C., Belobaba, P.P., 1999. Airline pricing and fare product differentiation: a new theoretical framework. The Journal of the Operational Research Society 50, 1085e1097. Coulter, K.S., 1999. The application of airline yield management techniques to a holiday retail shopping setting. Journal of Product and Brand Management 8, 61e72. Coyle, J.J., Novack, R.A., Gibson, B.J., Bardi, E.J., 2011. Transportation, seventh ed. South-Western Cengage Learning, Mason. Greene, W.H., 2007. LIMDEP Version 9.0. In: Econometric Modeling Guide, vol. 1. Plainview. Press. E22e6. Hayes, K.J., Ross, L.B., 1998. Is airline price dispersion the result of credit planning or competitive forces? Review of Industrial Organization 13, 523e541. http:// www.transtats.bts.gov/Data_Elements.aspx?Data¼1 (accessed 30.04.08.). Littlewood, K., 1972. Forecasting and control of passenger bookings. Presented at the 12th AGI-FORS Symposium. Mantrala, M.K., Rao, S., 2001. A decision support system that helps retailers decide order quantities and markdowns for fashion goods. Interfaces 31, S146eS165. Obeng, K., 2008. Airline daily fare differentiation in a medium-size market. Journal of Air Transport Managmennt 14, 168e174. Pels, E., Rietveld, P., 2004. Airline pricing behaviour in the London-Paris market. Journal of Air Transport Management 10, 279e283. SAS, 1985. SAS User Guide: Basics, Version, fifth ed. SAS Institute Inc, Cary. US Bureau of Transportation Statistics, 2008.
Contents lists available at SciVerse ScienceDirect
Journal of Air Transport Management journal homepage: www.elsevier.com/locate/jairtraman
Airline fare and seat management strategies with demand dependency K. Obeng a, *, R. Sakano b a b
Department of Marketing, Transportation and Supply Chain, School of Business and Economics, North Carolina A&T State University, Greensboro, NC 27411, USA Department of Economics and Finance, School of Business and Economics, North Carolina A&T State University, Greensboro, NC 27411, USA
a b s t r a c t This paper conceptualizes various discount strategies used by airlines. Using a constrained revenue maximization model that assumes interdependent demand, it develops rules to guide decision-making, and shows that the large fare discount-many discount seats and small fare discount-few discount seats strategies are optimal. Empirical support is provided for the large fare discount-many discount seats, the no fare discount-moderate discount seats and small fare premium-few discount seats strategies. In addition it identifies the large fare premium-very few discount seats strategies. We argue that these strategies are used in various demand situations and allow airlines to price discriminate. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction The 1978 US Airline Deregulation Act removed many of the economic regulations over airlines. Events since then, especially the development of computer-assisted reservation systems and the internet, have led airlines to introduce yield management systems to provide a variety of pricing schemes and itineraries to induce passengers to self-select services according to their willingness to pay. The result is second degree price discrimination with travelers paying different fares for the same flight. Airlines also practice third degree price discrimination by grouping their customers according to elasticity of demand and charging each group a different fare. Since airlines face capacity constraints in terms of limited aircraft seats, they must make decisions in terms of how many discount seats to offer and the discount fares to charge to maximize revenues. We consider demand dependency and conceptualize the following fare-discount and discount-seats strategies: small fare discount-many discount seats, small fare discount-few discount seats, large fare discount-many discount seats, large fare discountfew discount seats as well as a fare premium-no discount seat strategy and ask if there are others not revealed by this conceptualization. 2. A typology of strategies A number of strategies are used by airlines practicing price discrimination. Among them is the large fare discount-few discount * Corresponding author. Tel.: þ1 3363347231; fax: þ1 3363347093. E-mail address: [email protected] (K. Obeng). 0969-6997/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jairtraman.2012.06.001
seats strategy that is used when demand is very less elastic and a large fare discount is required to attract few additional travelers to fill capacity (Pels and Rietveld, 2004). The second, is large fare discount-many discount seats and it is applicable when demand is less price elastic but when many seats must be sold as in off-peak (Mantrala and Rao, 2001). A third strategy is a small fare discount-few discount seats and applies were demand is elastic, and a fourth is offering small fare discount-many discount seats such as in tourist or other markets where demand is very elastic. While they are important, these strategies do not represent a complete list of what airlines do. Despite this void, theoretical support for some of the more common strategies can be seen by considering the seat allocation problem of a constant average cost airline that offers a two-class coach service (high- and discount-fare seats) in a given origindestination market.1 The discount-fare seats are restricted and those unable to meet them buy high-fare seats. The demand of each fare class is down-sloping and, following Botimer and Belobaba (1999), are interdependent. There are a limited number of highfare paying passengers all of whom buy seats every time and the airline faces the constraint that it cannot overbook flights, and everyone who buys a ticket shows up for the trip. The airline operates an aircraft of capacity Vc seats, and assuming inverse demand functions, the fare for each class depends upon the number of seats demanded by each of the classes. These quantities are Q1 seats for the high-fare F1 and Q2 seats for the discount-fareF2. Thus, F2 ¼ F2(Q1,Q2) and F1 ¼ F1(Q1,Q2) are the inverse demand functions 1 This assumption of constant cost means average cost and marginal cost are the same for each passenger regardless the class of ticket purchased. This assumption also avoids a marginal cost function that depends on the outputs of both classes.
K. Obeng, R. Sakano / Journal of Air Transport Management 24 (2012) 42e48
where discount fare is less than the high-fare and the derivatives of the fares with respect to the quantities Q1 and Q2 are negative. In maximizing its revenue TR ¼ Q1F1(Q1,Q2) þ Q2F2(Q1,Q2), the airline faces the constraint that the number of passengers cannot exceed plane capacity. Thus, Q1 þ Q2 Vc and the Lagrangian of this optimization problem is,
Max L ¼ Q1 F1 ðQ1 ; Q2 Þ þ Q2 F2 ðQ1 ; Q2 Þ þ lðQ1 þ Q2 Vc Þ
(1)
where, l is a Lagrangian multiplier. From this, if the demands for high- and discount-fare seats are completely independent as when there is no switching then revenues are Q2F2(Q2) and Q1F1(Q1) for discount- and high-fare paying passengers. Substituting them into Eq. (1) and taking the partial derivatives with respect to Q1 and Q2, setting the results equal to zero and solving gives MR1 ¼ MR2. Where MR1 ¼ F1(11/ε11) is the marginal revenue from each additional high-fare paying passenger, MR2 ¼ F2(11/ε22) is the marginal revenue from each additional passenger paying a discount fare, ε11 and ε22 are high- and discount-fare elasticities of demand. It implies that absent demand dependency, fewer discount seats should be offered if the marginal revenue MR2 of an additional discount-fare passenger is less than the marginal revenue MR1 of an additional high-fare paying passenger. However, if there is demand dependency, which implies that switching is allowed, the airline chooses Q1 and Q2 to maximize revenue and from Eq. (1), the first order conditions for revenue maximization are,
vF1 ðQ1 ; Q2 Þ vF ðQ ; Q Þ Q2 2 1 2 þ l vQ1 vQ1 Q F ðQ ; Q Þ 2 2 1 2 ~ ¼ MR þl 1 ε12 Q1
vL=vQ1 ¼ F 1 ðQ1 ; Q2 Þ Q1
~ Q1 F1 ðQ1 ; Q2 Þ þ l vL=vQ2 ¼ MR 2 ε21 Q2
(2)
(3)
Where, ε21 is the cross-elasticity of discount seat demand from changes in high fares and ε12 is the cross elasticity of high-fare seat ~ demand from changes in discount fares. Also, MR 1 ¼ F1 ðQ1 ; Q2 Þ ~ ½1 1=ε11 and MR 2 ¼ F2 ðQ1 ; Q2 Þ½1 1=ε22 are own price contributions to the marginal revenues of an additional high- and discount-fare paying passenger. The second terms in Eqs. (2) and (3) are the contributions of switching to marginal revenue. Alternatively, they are the additional revenues lost when an additional passenger switches from one fare class to another. Solving these equations for l and equating the results gives.
43
from high- to discount-fare seats than from discount- to high-fare seats. Fig. 1 shows marginal revenue equalization for high- and discount-fare paying passengers. For clarity, we have included high-fare seats demand Dh, its corresponding marginal revenue b , MR b MR1, the demand and marginal revenue D 1 when the high h fare changes, discount-fare seats demand Dd and its corresponding b and MR b marginal revenue MR2, as well as D 2 depicting where both d demand and the marginal revenue of a discount-fare passenger have changed. MR1 and MR2 show where switching is not considered and the two demands are independent. Here, marginal revenues equalization is at “a” where MR1 ¼ MR2. To the right of “a” the marginal revenue from an additional discount fare passenger is greater than the marginal revenue from an additional high-fare passenger and the airline benefits by offering many discount seats. To the left, the reverse is true and each additional high-fare paying passenger adds more to revenue than does an additional discount-fare paying passenger. With switching, the marginal revenue of high-fare seats MR1 b and MR2 shifts to M R b . If the downward shift of shifts down to M R 1 2 MR1 is less than a similar shift of MR2 the number of discount seats would increase and vice versa. For the case where the downward shift of discount fare seat demand is larger than the downward shift in high-fare seat demand marginal revenues are equalized at “b” and there are more discount-seats than high-fare seats. Regardless of where marginal revenues are equalized Fig. 1 shows that capacity is fully reallocated between high- and discount-fare paying passengers with demand diversions occurring. Additionally, both the seat allocation and optimal fares are simultaneously determined. For example, drawing vertical lines through the marginal revenue equalization point “b” to the demand lines of high- and discount-fare paying passengers gives their respective optimal fares b F and b F 2 , the fare discount as the difference between them b . b and Q and the optimal seat allocation as Q 1 2 Also, solving Eq. (4) for the discount fare gives F2 ¼ F1[1(1/ ε11) þ (Q1/ε21Q2)/1(1/ε22) þ (Q2/ε12Q1)]. Since the discount fare is less than the high fare the term in brackets in this equation takes values between zero and one. Further, since discount seat demand is more elastic than high-fare seat demand, for the discount fare to be less p than the ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi high fare Q1/ε21Q2 < Q2/ε12Q1 from which Q1 < Q2 ε21 =ε12 . This shows that there must be more high-fare seats than discount-fare seats because the cross-elasticity of
High Fare ($)
Discount Fare MR1
MR2
Q2 F2 ðQ1 ; Q2 Þ Q1 F1 ðQ1 ; Q2 Þ ~ ~ MR ¼ MR 1 2 ε12 Q1 ε21 Q2
(4)
F1 F1
b ~ b ~ Let MR 1 ¼ MR1 Q2 F2 =Q1 ε12 and MR2 ¼ MR2 Q1 F1 =Q2 ε21 be the marginal revenues of high- and discount-fare paying passengers with switching. Then, with demand dependency revenues are maximized where both marginal revenues are equal. ~ ~ Furthermore, since MR 1 > MR2 the sufficient condition for marginal revenue equalization with switching is Q2F2/ε12 Q1 > Q1F1/ε21Q2. This implies that with switching the decrease in the marginal revenue of an additional high-fare passenger is larger than the decrease in the marginal revenue of a discount fare passenger; a condition met with more passengers switching
F2 F2
Dd Dh MR1
Dd b
O
a
Q1
MR2
Dh
Q2 = V C – Q 1 Q2 = V C – Q 1
Q1 Seats
Fig. 1. Marginal Revenue Equalization.
O
44
K. Obeng, R. Sakano / Journal of Air Transport Management 24 (2012) 42e48
discount-fare seat demand from changes in the high fare (ε21) is greater than the cross-elasticity of high-fare seat demand from changes in the discount fare (ε12). Given that, the term in brackets in the equation is positive and less than one, it approximates the probability of having more high-fare seats than discount-fare seats if the airline optimizes its seat allocation to maximize revenue or Pr(Q1 > Q2). Substituting this into the discount fare equation gives F2 ¼ F1*Pr(Q1 > Q2), that is the expected revenue from a discount fare.2 An advantage of our equation is that it provides a relatively simple way of approximating the probability of more high- than discount-fare seats and avoids having to make distributional assumptions about this probability. Using the expected revenue equation, the fare-discount (DF) is the product of the high-fare and the probability of having more discount seats than high-fare seats:
DF ¼ F1 F2 ¼ F1 *f1 PrðQ1 >Q2 Þg ¼ F1 *PrðQ2 >Q1 Þ
(5)
If the probability of finding a discount seat is high, then discount seat demand is less elastic and Eq. (5) shows the amount of the farediscount is large and vice versa. These results show that as the probability of finding a discount seat increases a large fare discount-many discount seats strategy is required for revenue maximization. Alternatively, as the probability of finding a discount seat reduces a small fare discount-few discount seats strategy is required for revenue maximization. Thus, revenue maximization supports only two of the conceptualized strategies. Perishable asset pricing studies have also found that the large fare discount-many discount seats strategy applies to products whose demands are less elastic, or which are hard to sell and whose elasticities of demand increase as the end of a shopping period approaches. Early in a shopping period the discounted quantity is large and for a product whose elasticity increases toward the end of a shopping period the strategy of a large fare reduction early and a small fare reduction later could bring about large changes in quantity demanded. For airlines this strategy implies offering a large fare discount well ahead of a flight date when there are many seats and a small fare discount as the flight date approaches and there are few discount seats.3 It could also apply when airlines are returning their planes from low to high demand markets where premium fares can be charged.4 To fill seats airlines can minimize their losses by charging low fares possibly reflecting variable costs. Similarly, it could apply to off-peak situations when airlines attempt to fill many seats by offering large fare discounts, e.g., weekend flights. Comparatively, the small fare discount-few discount seats strategy applies when airlines face elastic demand. Although the revenue maximization model captures only two strategies, the peak pricing studies have supported the fare premium-no discount seats strategy, while perishable asset pricing studies have supported the other two. The latter suggests a large price markdown close to the end of a shopping period for products whose price elasticities decrease with time, for example large fare discounts on stand-by tickets to fill few available airplane seats. This is the case of the large fare discount-few
2 Replacing a discount fare with a bid price makes this result identical to Littlewood’s (1972) formula. 3 Obeng’s (2008) work on temporal variation in airfares confirm this strategy by showing that the amount of the fare discount airlines offer reduces as the flight day approaches. 4 Airlines park their planes overnight in low demand markets where there is space and return them to high demand markets early morning.
discount seats strategy. Also, Coulter (1999) shows that some companies have price markdowns that increase from the beginning to the ending of shopping periods. That is, small markdowns at the beginning of a shopping period when the available quantity is large (i.e., a small price discount-large discounted quantity), and large markdowns close to the end of a shopping period when available quantity is low to dispose of hard-to-sell inventory (i.e., a large price discount-few discounted quantities). 3. Methodology The revenue maximization, peak pricing and the perishable asset analysis support five fare-seat management strategies. Still the question is what empirical evidence is there to support them? Are there other fare-seat management strategies which airlines use besides those noted? Answers to these questions are obtained using a two-step approach. First, we assume flights with similar fare discount-discount seats characteristics form distinct groups and then use cluster analysis to identify these groups. The characteristics of the groups provide some indications of fencing, and a comparison of their mean discount fares and mean discount seats to the overall mean values of the observations provides a basis for identifying the strategies airlines use. That is, the difference between the mean discount fare for available airplane seats of a cluster and the mean discount fare for similar seats for all observations is the amount of the extra discount over the average discount fare if negative, or a premium above the average discount fare (less discount than the average) if positive. This approach recognizes that airline consolidators buy tickets in bulk at discounts from airlines and pass some of the discounts to passengers in the fares they advertise. Further, it uses observed discount fares, which are those offered on consolidators’ websites, as an instrument for actual fares since both are highly correlated. Once the strategies are identified, the second step orders them by offered discount fare and identifies their statistically significant characteristics using an ordered logit model whose independent variables include those used in the cluster analysis. The signs and sizes of the marginal effects of the variables in this model are used to describe the strategies. We assume that y*i is a continuous latent variable representing the strategies, where i is a strategy, xj a set of j variables that affect the choice of each strategy and b a set of coefficients. Then the latent regression for the strategies is:
y*i ¼
X
bj xij þ εi
(6)
j
Where, εi is a random error and the ordered true values of the strategies are yi ¼ 0,1,2,3,.,i and are assumed to be generated by the process,
8 0 if yi < m0 > > > > < 1 if m0 < yi < m1 yi ¼ 2 if m1 < yi < m2 > > ::::::::::::::::: > > : i if yi mi1
(7)
In Eq. (7), m is a set of threshold parameters that defines the boundaries of the strategies. If the cumulative density function of the error term εi is logistic, then the probability of observing each strategy is,
K. Obeng, R. Sakano / Journal of Air Transport Management 24 (2012) 42e48
9 hP i > > Pðyi ¼ 0Þ ¼ 1 1 þ exp > j bj xij m0 n h P io n h P io > > > > > b m b m 1 1 þ exp Pðyi ¼ 1Þ ¼ 1 1 þ exp = j j xij 1 j j xij 0 n h P io n h P io > b m b m x x 1 1 þ exp Pðyi ¼ 2Þ ¼ 1 1 þ exp 2 1 > j j ij j j ij > > > ::::::::::::::::::::::::::::n h io P > > > ; Pðyi ¼ iÞ ¼ 1 1 1 þ exp j bj xij mi1
The ordered logit model is non-linear and, as a result, inferences cannot be made from the signs and sizes of its coefficients but from the marginal effects of the variables. Following Greene (2007) the effect of an increase in a variable on the probability that a flight is based on a particular strategy is,
0 0 vPi =vxj ¼ f mi1 b x f mi b x bj
(9)
The left-hand-side is the partial derivative of the probability of strategy i with respect to variable j and f(,) is the logistic density function. In the case of a continuous exogenous variable, its marginal effect shows how a unit increase in that variable affects the probability that a flight is based upon a particular strategy. On the other hand for a discrete exogenous variable its marginal effect is the change in the probability that a flight is based upon a particular strategy when that variable takes a value of one versus a value of a zero. Among these variables is the cost of providing service. This cost affects the choice of a strategy in two ways. One, a higher average cost may make an airline choose a small fare discountfew discount seats strategy because its profit margin is small prior to any discount. Two, lower average cost may make an airline choose a large fare discount-many discount seats strategy especially when a large capacity aircraft is used. If an aircraft must be returned to a high demand market, the airline chooses a large capacity aircraft even if the demand for the first leg of the flight is relatively low because profits from the second leg will outweigh the cost of the first. However, pilot and fuel costs can be considered fixed because they must be borne whether or not there are passengers. Hence, variable costs are those associated with flight attendants and on-board services. If in charging full fares the aircraft would return empty, the airline minimizes its losses by pricing based on variable cost and this results in very low fares with many discount seats. One cost factor is network complexity; airlines with complex networks with many nodes and circuitous routes have high costs and higher fares unless there are network economies of scale. Berry (1990) found that serving a large number of routes reduces cost which in turn reduces fares. In comparison longer routes increase cost and fares. Hayes and Ross (1998) and Borenstein and Rose (1994) found route length is associated with high fare dispersion. To account for trip length we use trip time which is the sum of inflight time, layover time, and departure delay. Because in mediumand small-size markets, direct flights may use smaller planes, their costs per seat mile may be high leading to attempts to recoup them in higher fares and few discount seats. For example, while the cost per seat mile to operate a 235 seat Boeing 757-300 is $0.0244, the corresponding costs for 50 seats Embraer Regional Jet (ERJ-145) and 49 seats Canada Regional Jet (CRJ-145) both used in short haul services are $0.0863 and $0.0945 (Coyle et al., 2011). Therefore, direct flights are a characteristic that affects cost and is included. In addition, direct flights are interacted with the number of days
45
(8)
before a flight to capture the scarcity of seats on them as the departure date approaches. Of course, competition from airlines emerging from bankruptcies affects fare levels as well. American Airlines echoes this point in its pricing policy by noting that in markets where its competitors have reorganized the competitors’ costs are low and result in low fares that American must match (AMR, 2010). Though reorganization affects fare dispersion it is not included as a variable but is captured, along with other omitted variables, through airline fixed effects. Besides cost, demand factors affect strategy choice. Pels and Rietveld (2004), for example, show that airfares are cheaper if bought well in advance of trip dates when there are many discount seats. Therefore, the days left for a flight when a seat is available is included. Other demand variables are discount seats on originating and connecting flights. Further, airline passengers have a disutility for layover time just as they have for waiting time. This disutility is likely higher than that associated with in-flight time because layover is a greater inconvenience especially if it involves changes in concourses, gates and long waiting times. We include squared layover time to emphasize this greater inconvenience and to capture the possibility that it could lead to a strategy choice emphasizing fare discounts and discount seats. Finally, to capture passenger demand the geometric mean of the passengers on both flights is included.5 Differences in strategy choice may also be temporal such as daily to reflect peak and off-peak conditions. As such the days left before a flight when an itinerary is available is again a variable in the equation. 4. Data The data were collected for a weekday airline round-trip from a non-hub airport, Greensboro, North Carolina to Boston, Massachusetts, a distance of 645 airline miles. The trip began from 5:30ame11:30am on a Monday and returned any time on Friday of the same week. American, Delta, US Airways, Continental, United, and Northwest provided services in this corridor with Canada Regional Jets, Embraer and Boeing 737 aircrafts.6 Data were collected using the online search engine, ORBITZ, because it provided information on aircraft type and aircraft diagrams from which to determine airplane seat capacity and available discount seats. The on-line search was a 100% enumeration of listed flights during a specified 2 h in the afternoon of each weekday of the three weeks prior to the trip.7 The enumeration collected information on flight numbers, posted fares and the seats available at those fares on originating and connecting flights, in-flight and layover times.
5
Initially, we used the arithmetic mean and did not get good results. The rationale for studying this market is to capture fare dispersion in non-hub airports where the absence of low-cost carriers makes established airlines charge premium fares. 7 The data were collected between 4pm and 6pm each weekday during the three weeks prior to the trip. 6
46
K. Obeng, R. Sakano / Journal of Air Transport Management 24 (2012) 42e48
The posted fares are interpreted as the discount fares because some seats are unavailable at these fares. Data were also collected on seats on originating and connecting flights, direct service, and number of carriers involved in connecting flights, airline name, and departure time among others. These data were supplemented by service factors at the airport such as airline load factors, on-time performance and departure delays available from the website of the US Bureau of Transportation Statistics (2008). Multiple-carrier flights are treated as if offered by separate carriers, and we assume symmetry so that Delta-US Airways or US Airways-Delta flight for example is the same.8 Because the on-line data did not include passenger load, that information is obtained by multiplying the capacity of each aircraft used by an airline to provide the service by the corresponding load factor of that airline at the airport the month of the trip. For all flights the geometric mean of the calculated passenger loads on both flights was used in our equation. With these modifications the data are an unbalanced panel of 604 itineraries whose characteristics show that the average fare is $812.69 for a round trip, originating flights use aircrafts with 64 seats per flight and connecting flights 107.5 seats per flight. On the average there are 17.3% discount seats on originating flights compared to 38.6% on connecting flights, while average in-flight and layover times are 2.9 h and 1.4 h. 5. Results Because the dataset is large we use the FASTCLUS procedure in SAS (1985) to perform the cluster analysis with normalized variables: days before flight, geometric mean of passengers, fare, seats on originating plane; seats on connecting plane, layover time in hours, direct flight times, and trip time. Several cluster solutions were obtained and compared in terms of pseudo F-statistic and the cubic clustering criterion. These statistics peaked when there were three-clusters and five-clusters suggesting that either of them could be a solution. Further analysis, however, showed that in both solutions a cluster had very few observations. Consequently, a fourcluster solution is used. Table 1 shows cluster characteristics in terms of the means of the variables used and progressively large fares from Cluster 1 to Cluster 4 permitting an ordering of the strategies from the least to the most expensive in terms of fares. Comparing the clusters, Cluster 2 is the base to which the others may be compared because it is where airlines sell at the average (discount) price and reserve the average number of discount seats for their passengers. When demand is small relative to capacity, there are many vacant high fare seats making airlines increase the number of discount seats they offer. If demand is less elastic, deep fare discounts must be used to sell more discount seats than the average as in Cluster 1. Alternatively, if demand is much more elastic and capacity is slightly more than demand, a small fare discount can be used to sell more discount seats than the average. However, if demand is less elastic a large fare discount than the average only leads to a small increase in the number of discount seats demanded above the average. For the case where capacity is less than demand, competition for seats makes an airline offer more high fare seats and fewer discount seats than the average. It does so by charging premiums above the average fare. Here, if demand is elastic, a small fare increase over the average reduces the number of discount seats below average as in Cluster 3. And if demand is less elastic a large premium on discount seats makes their fares higher than the average resulting in fewer number of discount seats than the average as in Cluster 4. The four clusters
8
Further, only flights with available seats on all legs at the offered fares are considered.
thus represent different demand, elasticity, and aircraft capacity situations and offer strategies for airline management. Using the ordered clusters, we modify Eq. (6) to account for airline fixed effects. If there are m ¼ 1,2,3,.,M airlines and n ¼ 1,2,3,.,N, observations then considering each row of the data the probability that an observation belongs to a particular airline is P Pnm ¼ F(m, m, b0 þ jbjxjn þ εn þ ym > 0) where m is a threshold parameter, ym is airline fixed effect, and b0 þ ym is an airline-specific constant term. To avoid identification in estimating this equation P we impose the constraint mym ¼ 0. This fixed effects ordered logit model is estimated, and Table 2 shows its results and fit statistics. All the coefficients are highly significant statistically except that of the squared layover term.9 From the cluster analysis and the ordered logit results we identify the following strategies: Large fare discount-many discount seats strategy: This strategy characterizes Cluster 1 because its average discount fare of $556 is far smaller than the mean discount fare of $812.69, and originating planes have 44.2% discount seats and connecting planes 51.4% discount seats. This strategy could represent where demand is less elastic, plane capacity is average and loads factors are relatively low; i.e. it represents weak high-fare seat demand requiring increasing the number of discount seats and offering a large fare discount to fill them (i.e., a shift to the right of discount-seats supply). From the marginal effects of the statistically significant coefficients in Table 2 the probability of using this strategy reduces by 6.5% when fares increase compared to a 21.9% increase when discount seats on originating and connecting flights increase. In addition, the probability of using this strategy increases by 6.3% for an increase in the number of days in advance when a ticket is purchased. Comparatively, the probability of using it reduces by 24.4% and 12.2% when trip time increases, and when there is an increase in the number of days when direct flights are available. Other results in Table 1 show that there are no direct flights for this strategy; tickets are offered on the average 13.0 days in advance; and the average trip takes 4.58 h including 2.5 h layover, which may contribute to lower demand. Additionally, 42.5% and 30.5% of the flights affected by this strategy are from 5:30ame6:30am and 10:30ame11:30am and medium-size planes seating approximately 132 passengers on the average are used on connecting flights. No fare discount-moderate number of discount seats strategy: This strategy describes Cluster 2 where small planes seating 52 passengers on average are used to provide service and 33.9% of the seats are discounted, a percentage close to the overall average of 35.9% discount seats on connecting flights. All flights affected by this strategy are direct and airlines charge a discount fare of $815.24 that is almost the same as the overall mean discount fare of $812.69 per round trip. Because the fare is almost the same as the mean discount fare for all observations, it is described as the no fare discount-moderate discount seats strategy. Alternatively, we characterize it as the norm to which others can be compared. The results show that the probability of airlines using this strategy increases by 10.6% with each increase in the number of days in advance a ticket is purchased, and by 36.8% when the number of discount seats increases. Conversely, the probability of using it reduces by 11.0% as fares increase and by 9.6% with each additional passenger. The factors that mostly reduce this probability are
9 In the discussion following the supply of discount seats assumes fixed plane size. If aircraft size increases, the supply of discount seats shifts to the right, the reverse being also true.
K. Obeng, R. Sakano / Journal of Air Transport Management 24 (2012) 42e48
47
Table 1 Characteristics of clusters. Variable
Fare Days before flight Layover time squared Discount seats on originating flight Discount seats on connecting flight Direct flight days before flight Trip time (in-flight time þ layover time þ departure delay) Geometric mean of passengers on pffiffiffiffiffiffiffiffiffiffiffiffi originating (Q1) and connecting flights (Q2) i.e., ð Q2 Q1 Þ Direct flight (%) Capacity of originating plane Capacity of connecting plane
Mean
Mean
Mean
Mean
Cluster 1 (N ¼ 167)
Cluster 2 (N ¼ 120)
Cluster 3 (N ¼ 257)
Cluster 4 (N ¼ 60)
556.19 13.0 2.5 27.6 67.7 N/A 4.58 66.0
815.24 8.3 N/A 17.7 N/A 8.3 2.55 38.1
823.79 6.0 2.9 12.3 41.7 N/A 4.69 65.7
1474.00 6.3 16.7 9.9 21.7 0.0 8.54 67.8
0.00% 62.5 131.7
100% 52.1 N/A
0.00% 71.1 127.3
trip time and how many days in advance direct flights are available. For instance, an increase in trip time reduces this probability by 41.1%, whereas each additional day a direct flight is offered reduces the probability of using this strategy by 20.6%. Tickets for these flights are offered on the average a week in advance; trip time is 2.55 h, 38.1 passengers per plane take flights affected by this strategy and 92.5% of the affected flights depart from 6:30ame7:30am Small fare premium-few discount seats strategy: This strategy (Cluster 3) is when increased demand from airlines channeling passengers through their hubs results in flying larger planes, and offering few discount seats at a very small premium of $9.10 over the overall mean discount fare of $812.69. The main characteristics of this strategy include the absence of direct flights and offering 17.2% and 32.8% discount seats on originating and connecting flights. The marginal effects of the variables are the largest here than they are in the other
1.67% 58.1 170.2
Overall mean
812.69 8.4 3.6 17.3 38.6 1.7 4.62 52.9 20.33% 63.7 107.5
strategies discussed earlier. For example, the probability of using this strategy reduces by 16.9% with an increase in the number of days in advance a ticket is purchased, and by 58.5% when there is an increase in the number of discount seats. However, increases in fares, trip time and the number of days in advance on which direct flights are available increase the probability of using this strategy by 17.5%, 65.4% and 32.7%. And, an increase in the number of passengers increases the probability of using this strategy by 15.2%. From Table 1, the mean discount fare of $823.79 for flights in this cluster is offered on the average six days before the flight day, the flights have 2.9 h layover and as many passengers as in the first cluster. Additionally, 45.1% of the flights affected by this strategy depart from 10:30ame11:30am, while 29.2% depart from 5:30ame6:30am Large Fare premium-very few discount seats strategy: The final cluster (Cluster 4) gives the large fare premium-very few
Table 2 Maximum likelihood results of fixed effects ordered logit model. Fixed effects ordered probability model Log likelihood function AIC information criterion AIC finite sample BIC Information criterion
372.261 1.2889 1.2907 1.4129
Variable Days before the flight Fare ($) Discount seats on originating flight Discount seats on connecting flight Geometric mean of passengers on originating (Q1) pffiffiffiffiffiffiffiffiffiffiffiffi and connecting flights (Q2) i.e., ð Q2 Q1 Þ Layover time squared Direct flight days before flight Trip time (in-flight + layover + departure delay) Mu(1) Mu(2)
Coefficient 0.4578* 0.4734* 1.3284* 0.2584* 0.4129*
Marginal Effects Variable Days before the flight Fare ($) Discount seats on originating flight Discount seats on connecting flight Geometric mean of passengers on originating (Q1) pffiffiffiffiffiffiffiffiffiffiffiffi and connecting flights (Q2) i.e., ð Q2 Q1 Þ Layover time squared Direct flight days before flight Trip time (in-flight + layover + departure delay) Note: * is 1% significant.
0.1373 0.8879* 1.7731* 1.0687* 4.9065*
Y ¼ 00 0.0630 0.0652 0.1830 0.0356 0.0569
Y ¼ 01 0.1062 0.1098 0.3082 0.0599 0.0958
Y ¼ 02 0.1688 0.1746 0.4898 0.0953 0.1523
Y ¼ 03 0.0005 0.0005 0.0014 0.0003 0.0004
0.0189 0.1223 0.2442
0.0319 0.2060 0.4114
0.0506 0.3274 0.6538
0.0001 0.0009 0.0019
48
K. Obeng, R. Sakano / Journal of Air Transport Management 24 (2012) 42e48
discount seats strategy because there is indeed a large premium of $661 when its mean discount fare of $1474 is compared to the overall mean discount fare of $812.69. And, its 17.0% and 12.3% discount seats on originating and connecting flights are far lower than the mean reported earlier despite airlines flying larger planes on connecting flights which have 170.2 seats on the average. An explanation for this strategy is that both high-fare seats and discount-fare seats are substitutes in production, especially on connecting flights which fly near capacity without discounts due to less elastic high demand relative to capacity. With this less elastic demand a large fare premium over the mean is needed making few discount seats available at regular fares. Thus, if the number of high-fare seats increases to meet increased demand, the supply of discount seats decreases because with fixed capacity fewer discount seats become available at each discount-fare level. If the demand for discount seats is relatively less elastic, then this decrease in supply would result in high fares and fare premiums. However, the very small marginal effects of the variables on the probability of choosing this strategy show that they do not affect this strategy much. For example, increases in fares, trip time and the number of days in advance when direct flights are available increase the probability of using this strategy by 0.1%, 0.2% and 0.1%. Comparatively, an increase in discount seats reduces this probability by 0.2% whereas an increase in passenger load increases it by 0.04%. In Table 1 most of the flights in this strategy connect with others and only 1.7% are direct. Because of these connections travel time and layover time are long; 8.5 h and 4.1 h. Also, only 60 flights are affected by this strategy with 51.7% departing between 6:30am and 7:30am
6. Conclusion This paper classifies the fare discount-discount seats strategies which airlines use in yield management into stylized groups and identify the characteristics of each group to inform decision making. At least five such strategies are conceptualized: small fare discount-many discount seats, small fare discount-few discount seats strategy, large fare discount-few discount seats, large fare discount-many discount seats strategies and fare premium-no discount seats strategies. It was argued that these strategies are
chosen on the basis of elasticity of demand and plane capacity relative to demand. Using a constrained revenue maximization model in which switching is explicitly considered a marginal revenue equalization rule is derived and used to show that the strategies to adopt are the small fare discount-few discount seats and large fare discount-many discount seats. While the revenue maximization rule is standard, because both demands shift down and discount-fare seats demand is more elastic than high-fare seats demand when there is switching, marginal revenue equalization is reached where there are more discount seats. Additionally, alternate derivation of Littlewood’s rule are presented, which is that the discount fare is the product of the high-fare and the probability that there are more high-fare seats than there are discount-fare seats. An approximation for this probability based on price elasticities of demand, cross-elasticities of demand and the seats allocated to high- and discount-fares is estimated.
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