Rationalization of the European air net

Tmnrpn Jtm., Vol. 11, pp. 235444.

PergamonPress 1977. F’rintcd in timatBritain

RATIONALIZATION

OF THE EUROPEAN AIR NET STEVENGORDON

Simat, Helliesen and Eichner, Newton Centre, MA 02159,U.S.A.

and RICIURD DE NEUFVILLE Center for Transportation Studies, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A. (Received 30 Aptil 1976; in revised four 13 October 1976)

Absfract-This paper investigates the question of whether it might be possible to rationalize, that is to increase the quality of service for a given cost, the airlii network within Europe. Various policy analysts have suggested that sign&ant benefits might be achieved along these lines if the Common Market were to reduce the biiteral restrictions on European airlines. Our conclusionis that this is not the case. A main interest of this paper shouldbe the approaches we propose for analyzing transport nets. First, we argue that, when one considers the multidimensional output of scheduled service, we should recognize that economies of scale do exist even for transport modes which are ordinarily not thought to have this characteristic. This provides an important motivation for concentration of services, as does in fact exist. Second, we propose a measure of network connectivity which takes into account the intensitv of connections between the nodes. This measure permits a much more precise discussion of the nature of any transportation network.

The existence of the Common Market has brought Western Europe face-to-face with a fundamental policy issue in air transport: How can its air net be rationalized? Many experts believe that better or cheaper air”transport can be achieved in Europe through a common policy to reduce the number of air routes in the system or, at least, deemphasize marginal routes. The idea Is to suppress direct routes with minimal service and thus to force the users of these routes onto the remaining highdensity routes that could be served more economically. Although proposals to that effect have met considerable ol&Gtion within the European Economic Community (EEC), they have progressed through several stages of action by the EEC, and are still under consideration. Perhaps one reason that no action has been taken on these proposals is that the arguments on their behalf are mostly intuitive. As means have been lacking to estimate the potential economic benefits, the participating nations are Unwilling to make the effort to negotiate new route awards, or perhaps, to make political sacrifices to achieve these ends. As precise measures or models of the air transport system have not been readily available, considerable doubt remains as to whether concentration of the European air net would be in the public interest. We have therefore attempted to develop an analysis of the issue. To accomplish this, we have, first of all, had to establish a theoretical basis for investigating the structure of transport nets. This includes: (i) A concept of the supply of transport that describes both the capacity of transport produced (the traditional measure of output) and the level of service provided: and (ii) A measure of the structure of transport nets that incorporates not just the existence of links (the usual measure) but also some indication of their “strength”.

We have then also used recently developed methods of optimizing the supply of scheduled service on a network to explore how air nets might be structured most s&ably, for the actual distriiution of travellers in Western Europe, to meet their demands and relative preferences for Merent levels of service. Our conclusion is that the EEC has been wise to take no action on the proposals to reduce the number of air routes in the system. Our analysis gives us little reason to believe that systematic concentration of the air net by the elimination or suppression of routes would lead to sign&ant improvements in the quality or economy of service. Our study differs from previous ones, many of which support the concentration of the air net, by being more analytic and quantitative about the benefits and costs of eliminating routes. Although, given the extent of our assumptions, we cannot definitively claim that the European network is already about as good as can be desired, we can co@dently say that evidence is lacking to show that substantial change of air routes is in the best interests of the European public and air carriers.

IIACKGROUND To TEBKBLNYISSUE The pattern of air service’in Europe developed subject to a broad range of constraints arising from narrowly perceived notions of national self-interest. For example, the kind of service with multiple stops which is so common in the United States hardly exists in Europe.. It has been suppressed by cabotage regulations which prohibit foreign airlines from serving a domestic market, and by the so-called “fifth freedom” rules which typically prevent airlines from one country from carrying tic between any other two. These constraints almost 235

236

S. GOIWN and R.

certainly increase the cost of operations to the overall disadvantage of all concerned. (Indeed, it is a general economic rule that restrictions limit productivity.) As it is possible that these restrictions could be negotiated away within the context of the Common Market, it is desirable to determine what patterns of air service ‘might be most advantageous. Specific proposals to rationalize the air net have already been placed before the Council of European Communities and require attention (see European Parliament, 1972; European Economic Community, 1972, 1973a, 1973b; Council of Europe, 1973). The essence of the proposed policies is that air service could be improved by concentrating trafBc along fewer routes. This would require that service on some routes be reduced or eliminated. Traffic between these points could be rerouted toward major routes which would then receive more service. For example, direct service between London and Stuttgart might be replaced by more London to Frankfurt to Stnttgart service. The idea is that routes with sparse tra6ic operate inefficiently and that, if their trafhc could be channeled onto routes with higher volume of service, economies could be achieved by using large aircraft which cost less per seat-mile. This view has been current for over twenty years and has been expressed and popularized extensively by Rosenberg (1970), Sealy (1966, 1957), Wheatcroft (1956) and others. Much of the motivation for the proposals to concentrate the European air net also stems from the perception that air service in Europe is both more expensive and more connected than in the United States. The fares for travelling any given distance have certainly been higher in Europe at any given time. As regards connectivity, the airlines’ own Research Bureau recently reported: “The European carriers operate a.. . . . network of 841,000 kilometers, serving 752 stations . , . . . compared with a total U.S. . . . . . network of 506,000 kilometers serving 1,087 stations.‘* (European Airlines Research Bureau, 1970). The implication is that if more miles of network connect fewer points, then the European air net must be more connected than the American net. The above quotation, which is widely paraphrased and repeated, is typical of the fuzzy &inking that surrounds the discussions of network policy. The measure of comectivity itself is not only superhcial, but also misleading. As pointed out elsewhere by the Research Bureau, the measure of route mileage is dilferent in both cases. In the United States one counts the “certificated” routes, while in Europe one counts the sectors operated, both coming and going, and therefore arrives at a number twice as large (Air Research Bureau, 1957). Second, the comparison of costs at any time is probably not especially relevant. Fares in Europe may be higher because of the cartel practices of the airlines operating in pool. They may have also been higher at any time because Europe has been less aliment and has generated comparatively less tragic so that European airlines have not been able to use the larger aircraft with lower costs per passenger. The comection between costs and

DE NEUFVILLE

network structures are far from as evident as some might like to think. All the available arguments concerning the proposed policies have, in fact, been quite intuitive. Actually, it could not have been otherwise. The European air net is so extremely complex, involving more than a thousand Aits a day over hundreds of sectors, that it has been impractical to carry out any detailed examination of alternative policies. And failing the discipline of mathematics, there has been little incentive to develop exact definitions of the parameters of the problem: the measures of network structure are crude and the concepts of performance and improvement for the system are little more than imprecise references to economy and, sometimes, fare reductions. Recent developments with computers now, however, permit us to analyze networks with considerable precision. We can calculate, in detail, the quality of service provided by any network, can determine efficient ways to provide the service and can, in short, investigate the real costs and benefits of different network structures. CONCEPTSFQR ANALYZINGTRANWOW NETS

Rigorous analysis of any problem requires that the parameters of interest be well-defined. Previous analyses of air nets have been deficient in this respect, as we suggested earlier. Although certain economies are thought to exist when trafhc is concentrated into fewer routes, means are lacking to describe such economies and to measure the extent to which trallic is concentrated. In order to address the issue of what kind of air net is best for Europe (or anywhere else), we have had to develop the concepts of network concentration and their resultant economies in transport systems. Scale economies in transport systems The standard economic models for the performance of a system relate the quantity of a product, Q1, to the inputs or resources required, I& such as labor, machines, etc.

Q1= q(&, &, . . .,&I.

(1)

Given prices for inputs R,, Pi = pj(Ri), which may be functions of 4, the cost function, C = c(Q,, PI, P*, * * *tPA

(2)

which gives the least cost of producing a given product, can be derived (Shephard, 1953, 1970; Walters, 1963). If input price functions remain constant, economies of scale are said to exist when the average cost per unit produced decreases as output is increased-that is, when

Let us now define VT as the total value of the product to users, and Vu as the value of each unit of product, Vu = VJQ,. If we assume that Vu is fixed, then the

Rationalizationof the Europesnairnet

existence of economies of scale also implies that the average cost of generating this amount of value decreases as output increases:

a(cl_

aQ1

1 wlQl),o. a01

vu

That is, we obtain more value for money as we bring smaller activities together into larger units. Economies of scale are then a powerful argument for concentration of service. Conventional analytic wisdom says that economies of scale are essentially nonexistent in the operation of major airlines, such as those in Europe. The argument is that, since airlines do not have to bear large fixed charges for rights-of-way or other facilities, the average cost of providing an extra aircraft is essentially the same for all companies beyond a minimal size (see Eads (1972) for a recent discussion of this). Viewed through the prism of the traditional economic model, for example, Murphy (1974) found that the cost function for U.S. airlines was: C = K,Q,‘.m = KQ,

(5)

where output is in terms of seat-miles produced (a usual measure), and controlling for fleet size, stage length, type of aircraft and factor prices. An entirely parallel argument is made for the trucking industry, another common carrier which does not own its right-of-way. (See Meyer et al., 1959.) The policy conclusion that results from this conventional theory is that there is no compelling reason to merge companies or otherwise concentrate the provision of airline or trucking service. Actual operators of such transport services feel quite convinced, however, that there is a sign&ant advantage to being larger within a given market (e.g. providing more capacity by scheduling more lIights). They observe, for example, that airlines which are larger in any market obtain a disproportionately larger share of the market and thus have lower average per-passenger unit costsand higher profits! (Fruhan, 1972; Gelerman and de Neufville, 1973; and de Neufville, 1976). To resolve this paradox, we believe it is ne&ssary to distinguish between two types of economies of scale: returns to market size and returns to firm size. As opposed to other industries in which a single product is distributed throughout a region, transportation companies typically serve many different markets simultaneously. Practically every linkage between any origin and destination, in fact, represents a different market. Economies may be associated with the size of the market and, specifically, with the intensity of tic along a link. Although this distinction has been identified before (for example, see Keeler, 1974), returns to market intensity have not been modeled or quantified as such, nor have the implications of their existence been explored. We have, therefore, attempted to quantify the impacts of market size, in terms of tra& intensity on an airline route, on operating cost. We 6rst observe that the standard models of performance are insuflicient because they assume that output has only one dimension. h-BVol.II,

No. 4-B

237

Actually, transport and other systems produce many products at any time. At least they produce a product which can have many di.&ent levels of quality. An airline, for instance, can generate a specified number of seat-miles on a route either by scheduling a single tlight with a Boeing 747 or many tlights with Boeing 727’s. The 727 scheme would provide much higher frequency of service, ;.s correspondingly more convenient for the user, and is really a differentiated product. Whether we choose to think of the output of a system in terms of multiple products, or of a single product with several qualities, the formal result is the same: the model of the performance of the system should include many variables to describe the product. The comprehensive model of the transport system should thus be: C=

c(Q,, Qz, . . ., Qm;PI, PD.. ., P.)

(6)

where Q, is output measured in the conventional way (quantity), and Qz,. . ., Q. denote other qualities of the output such as frequency of service, Qz; etc. Total value of the output, V,, would be given by the quantity of output times its unit value, Vu,as before, but now this value of the unit of quantity depends upon its quality: V, = VrAQzr. ..,

Q.).

Once we recognize that the output has many dimensions, we may also see that most of the previous discussions of economies of scale in transport are quite ambiguous (if not meaningless). Indeed, if we stick with our traditional test for economies of scale, decreasing average cost per unit produced as quantity increases,

WlQI)<()

aQ1

(or with any permutation of this concept) we see that it implies-since it is a partial derivative-that all other dimensions of output should be held constant. But this is rarely, if ever, done; the usual treatmeut of the subject is oblivious to the fact that the output of transport, say the number of seat-units along an airline route, can be increased either by increasing aircraft capacity while holding frequency constant, by increasing frequency while holding aircraft capacity constant, or by changing frequency and aircraft capacity together, as is most often done in reality. Increasing aircraft capacity alone reduces unit costs and results in economies of scale along traditional lines (as defined by eqn 3); but these economies are limited and decrease as aircraft size increases. Increasing frequency of service reduces schedule delay (defined as the absolute difference in time between when a passenger desires to depart and when the most convenient available flight departs), and generally alters the quality of output along many dimensions. Insofar as the previous analyses of economies of scale in air transport fail to specify or control how each of the dimensions of output varies, their results are inconclusive.

S. GORDONand R. DE

238

We can rectify this situation, and resolve the divetpence between the implications of conventional theory and reality, by car&d de&&ion of what we mean by economies of scale. One approach would be to persevere with a strict application of eqn (3). But this would be quite deficient from a policy point of view, since it would nullify the pragmatic usefulness of the concept. In practice, we want to know if we can Ret more value for money by increasing the scale of operations and, thus, if we should encourage a policy of industrial concentration. If the deiinition of economies of scale only incorporates one dimension of economy or value, if it excludes all notions of quality, it will be unsuited for this purpose. For policy purposes it may therefore be most helpful to focus on the change in average cost as we alter the vector of several dimensions of output, instead of the single dimension of the quantity of output. To compare these changes meaningfully, we will collapse the several dimensions into one by considering the overall value of output. To distinguish this concept from the more usual one, we may refer to cconottries of scale for uector output, where value is the common denominator. We will say that they exist if: , (4) This expression reduces to the usual measure (eqn 3) for a production process with a single dimension of output, as indicated previously. It is not a radical departure but an extension of previous notions to situations with multiple outputs, such as transport. This restatement helps resolve the conflict in policy conclusions between previous theory and practice. Consider, for example, the two-dimensional case of an airline providing service in a market with specified aircraft: increasing the quantity of output, Q,, also increases the quality of output as measured by frequency, Qz. By eqn (7). the vahre of the output is VT = Q,{V.(Qd). We thus have ~[V,,(Q31/dQ1>O. Assumirg economies of scale in a market are nonexistent in the traditional sense, we also have C = KQ, (cqn 5). The average cost of ptoducing a unit of value is then: C/V, = K[V,(QJ]-‘>O

NEUFVEU

sions, the economies of scale (quality controlled) would be calculated by deflating the average costs by a measure of the increase in quality, speci6caUy by dividing by the increase in value, for example. (This is the ‘hedonic index’ approach, now being explored by some economists.) Fiie 1 illustrates this phenomenon. All transport services which feature discrete departure times exhibit economies of scale for vector output-due to returns to market sixe-with regard to frequency of service. The example represented by eqns (8) and (9) ilhrstrates this effect. In this regard there is a strong motivation to concentrate service. Air transport is also seen to have economies of scale in the conventional sense, again due to returns to market siie, provided we control for quality of service. Indeed, if we increase capacity but keep frequency of service fixed, we must use lsrger aircraft for which it is well-known that their costs per seat-mile are lower than for smaller aircraft. (See Simpson (1974), for a further discussion of this in the context of a production function with multiple products.) This elfect increases the motivation for concentration. Conversely, these effects may be counteracted for transport and other systems by variations in other dimensions of quality. Placing more. aircraft along a route may create congestion and reduce the level and value of service, for example. Concentration of trailic itself necessarily has the negative side-effect of requiring some trafhc to be rerouted and to travel further over circuitous paths. Measuring network stwtun

for transport policy

A Rood measure should reflect the aspects of the system that concern its user. For example, as a professor might measure the value of a classroom by the number of seats it contains, a junkman might measure its value by the weight of the scrap metal it contains. We are concerned with measuring that aspect of network structure that relates to the cost and performance of the network. We expect, ~1priori, that this may relate further to the extent to which economies of scale (for vector output) can be, or are, achieved in a market. Consequently, we seek a measure of network structure that might capture the degree to which tralflc is concentrated

(8)

and thus:

.a(clVT)= _K[V(QJ]-2 W'dQ31 aQ1

IT

a01


(9) *

We can therefore., in a market, have economies of scale for vector output-which imply a policy of concentration-even when constant returns to scale exist in the narrow sense of eqns (3) and (5). An alternative and entirely equivalent approach is to look at the effect of controlling the quality of the output. This amounts to using the standard test for economies of scale, eqn (3), but carrying out the implications of the partial derivative (that is, that all else remains fixed) as is not usually done. For any product with several dimen-

L

B

\ Ouality ‘)----_____ Controlted

__

OD

c

Ouantity Produced in a Market Fig. 1. The existence of Jkonomies of Scale (Qualitycontrolled) or (for vector output)in situationswhere, as for airline service, averagecosts per unit producedare constant.

Rationalizationof the Buropeansirnet

intomark&s in ammutts great enough to achieve such econQmies. Measures of network structure exist for all kinds of geographical and sociological tiyses (see &gers (1971), for a partial description). One of the most useful indices of those available is the Gamma ratio of the a&ml number of two-way links, L, that exist in a non-planar network, to the total number that could conceivably exist: L

Gamma =N(N -

1)/2

where N is the number of points or nodes that can be

connected. Unfortunately, the Gamma ratio and other similar measures of network structure all imply the rather inadequate view that the existence of ‘links is an “all or nothing” proposition, rather than a matter of degree. This viewpoint is inconsistent with our objectives; clearly, the cost and performance of an air transport system is diIferent if tratlic moves in a given market (over a link) one time or twenty-one times per week. Our measure of network structure should reflect the “degree”, “ strength”, or “‘robustness” of the links in the network. We have consequently mod&d the Gamma ratio to include this feature. Let us lirst define the .robustness of a given link abstractly. Call this quality q for link i. (What r, should actually represent will depend upon the kind of transport system we are dealing with.) We than exploit the facts that, for any given “system robustness” Q 4 = constant) Q fif is greatest, and equal to the number of links, when all links are equally robust, r, = r, - r3, etc.; and is least when the robustness is concentrated on one link, all fi = 0 except one. We can normalize (X fi# for the total system level by dividing by Z q; and for the number of nodes, N, in the network by dividing by N(N - 1)/2, or N(N- 1) if we are concerned with directional sectors. The ratio thus formed takes on values between zero and one, approaching zero when one link predominates and unity when all links are equal. So that the index is greatest when the network is most concentrated, (one or two links predominate) we subtract this ratio from unity to form the Chi index of concentration, chi = 1 - (z fiJZ/(N(N

- 1)I: n).

(11)

1The Chi index reduces to one minus the Gamma ratio for thetrivialcasewherer,=lwhenalinkexistsandr,=O otherwise. Thus we see network concentration is somewhat related, complementarily, to network connectivity. The choice of the measure of link robustness q depends upon the nature of the transport net. For air transport, flight-miles may be a convenient measure, especially to the extent that major airlines use aircraft of comparable size and performance, as they often do. It reflects quality of service in a maiket, being proportional to frequency, and reflects the cost of such service among ,markets, being sensitive to both frequency and distance.

239

Through our choice of a the Chi index of concentration enables us to disti@sh between the structure of the network of vehicles (supply) and that of passengers (demand). The robustness of links in the supply network is conveniently measured in terms of available capacity, e.g. tlight-miles provided. The robustness of links in the demand network can conversely be measumd in terms of the capacity used, e.g. lIight4nile.s provided. The robustness of links in the demaad network can convemely be measured in terms of the capacity used, e.g. passengermiles. As shown below, optimal co&u&on of a given transport network requires that the supply-(% be less than the demand-(X-the network of supply be less concentrated than that of demand. This fact provides an immediate criterion for testing whether a proposed scheme for operating an existing air net is desirable. MoDBIsF0RANALY!4mGTEAKRmrNEIS Now that we have developed the new concepts of concentration in network structure and scale economies (for vector output)‘in a market, we can address the issue of what kind of air net is best for Europe, and we can express our conclusions in meani@ul terms (measures of network concentration). To address the issue, we have developed new models that accurately reflect the complex relationships between scale economies and network structure. Although we do not expect these preliminary efforts to be definitive, we trust that they will stimulate further, improved analysis. Meanwhile, they should at least allow us to investigate much more incisively the desirability of alternative policies. A performance modelfor a single air ma&et

We l&t present a crude performance model to illustrate the normative implications of economies of scale for vector output in a single air transport market. We later reline and apply the model to an entire network in order to derive more quantitative conclusions for Europe as a whole. We assume that only one aircraft type is used in the market. This assumption greatly simplities the analysis. The more complex analysis explicitly considers travel time as a function of aircraft type and cost as a function of aircraft mix. It also requires that expected changes in aircraft mix with changes in market intensity be quantified. The more complex analysis is theoretically more correct. But as regards Burope especially, the distances are such that there are probably no sign&ant differences depending on aircraft type; all major routes are served by jet aircraft wlth similar performance characteristics. In addition, it would appear that even the cost per seat-mile offered varies little among the jet equipment currently in use. In any particnlar market, the conventional output quantity, Q,, is the numb&r .of passengers served. The valueof the service, Vu = V,(Q, Q3, .. ., 0.) is di&rent for each market, as reflected by the demand schedule, but is a function of service quality variables, including frequency, aircraft comfort, trip time, weather delays, and service niceties. With a tixed aircraft type, aircraft comfort, trip time, and weather delays are beyond the

S. GOREON and R.

240

control of the operator. Recognizing that. frequency is the most impottant remaining service variable, we postulate that

where K, is the average iuhetent value of the ttip at inlinite frequency, F is the frequency, and f is a decreasing function. Mote speci6caUy, since the effect of frequency is to determine time between flights, and since time has value, we assume f(F) = aF-‘g@)

(13)

where the empirical constant “a” incorporates the value of time, p is the average load factor or fraction of seats occupied, and g is au increasing function approaching infinity as p approaches unity. The load factor is included in eqn (13) explicitly to account for those delays incurred when insu@cient frequency results iu load factors so high that additional schedule delays ate incurred by passengers unable to make reservations on the tlight of theit choice. Noting that p = QJkF, where k is the aitctaft capacity, VT becomes, (14) Letting Kz be the operating cost of one flight pet day, C=KJ?

(15)

Consequently, if we assume that Vu is held constant, as we did eatliet with reference to eqn (4):

(16) Two normative conclusions follow from eqn (16): (1) As Q1 increases, a(C/V,)/aQ, approaches zero, a state where constant returns to scale for vector output exist iu a market; and (2) As k increases, economies of scale for vector output in a market become mote ptonouuced, as a(C/vT)/aQ, becomes mote negative. These normative conclusions have implications for network sttuctute. As ttaEic intensity in a market increases, tetutns to market size become less pronounced, and the airlines, haviug less incentive to concentrate additional tta& on the high-volume routes, would be mote likely to operate on a network with a lower index of concentration. Also, as aircraft size increases, economies of scale iu a market become mote pronounced, and the airlines, to achieve these economies, would be mote likely to operate on a network with a higher index of concentration. These reactions by the aitlines can be observed by studyiug aitline networks of the past (see Gordon, 1974). A petformance model for air nets

Due to the complexity of a continental ait transport

DE

Neuwru~

system, any. initial model for its multiple products has to be relatively crude. Gut model nonetheless appears to capture some of the most salient aspects of the problem, petmitting us to discuss, with some precision, the relative merits of various sttuctutes for the European network. The model is predicated on the assumption that for any quantity of setvice provided, traditionally measured iu seat-miles, the public interest is best served by maximizing the quality of service. We have measured the quality of service for any passenger along three dimensions-line-haul ttip time, number of intermediate stops or transfer, and schedule delay. We have used schedule delay as a suttogate for frequency of service because frequency is a meaningless measute for trips containing mote than one flight leg. Schedule delay is complementary to frequency; just as passengers prefer mote frequent setvice, they will prefer the lesser delay it provides. Normally, maxim&g the quality of setvice for any given quantity of effort expended, (of aircraft hours flown, for instance) would be in the cattiers’, as well as in the public’s best interest; quality of setvice influences traffic and revenues, while costs remain relatively constant with the number of seat-miles provided (assuming a lixed fleet). Nevertheless, cattiets ate constrained by cabotage and fifth-freedom restrictions and bilateral capacity limitations from achieving socially and economically efficient schedules. Consequently, the questions we want the model to answer ate these basic ones: what imptoyements in service can be achieved at cuttent costs if the cattiers could operate on any network and could allocate capacity as they choose: and how different would this “optimal” network be from the current one, i.e. could it be achieved through the limited medium of bilateral negotiation? Formally, we wish a model of the fotm: Quality of setvice = h (Fleet Size, Allocation of Aircraft, Structure of Ait Net) (17) which, in keeping with out notion of the production function, will be techuically e5cient at all points. This is obtained most easily by solving fitst for the distribution of setvice on the existing sttuctute of routes which minimizes delays for a given fleet size while meeting passenger desires. Then we repeat the analysis for as many different fleet sizes and combinations of additions or elimination of routes that form the existing ait net as we might choose. Basically, we generate the production function by detetministic simulation of as many points as necessary, aloug the lines described by de Neufville and Marks (1974). For a fixed ait net and fleet size, the total delay is the sum of the delay on .each liuk, which in tum equals the number of passengers ou that link, Us,times theit ilight time, t,, plus the delay occasioned by infrequent flights. Since, for a fixed network, the passengers’ line-haul flight time and the number of in&mediate stops or transfers is essentially fixed, we need only won-y about the latter delay, and this is inversely proportional to the number of

Rationakation of the European air net

flights and a function of the average load factor, p,, on the link. The greater the load factor, the more diflhztilt it will be to make a. reservation, and the greater the likelihood that the traveller will have to take a later llight. The crux of the analysis is then: MiuimizeDelay, D = PI2 (u,/t;;)(1 - P;)-“~ I

For any Fleet Size, S = x u,tdpl i where s and II are empirical constants and fl is the number of flights along a link i. This formulation is consistent with the single-market model presented above; the objective function is equivalent to the maxim&&on of passengers’ value of service, as given by eqns (12) and (13) (where g(pl) is expressed by the rightmost factor in objective Function IQ, summed over all passengers and all markets. The formulation of eqn (18) assumes, of course, that schedule delay is inversely proportional to tlight frequency, at least to a tirst approximation. Befinements by route considering local peaking and passenger behavior would ultimately be considered, but not for this 6rst analysis. Solutions to Problem 18 are found by the Lagrangian multiplier method and a search process. The computations are extremely tedious and tiresome, but are readily solved by computer. (Gordon (1974) gives a full description of the procedure.) The computer routine also calculates the average travel time and number of transfers per trip in order to provide some measure of the negative effects of the rerouting caused by the elimination of particular links. Some interesting policy conclusions for operation of air nets flow directly from this formulation. First, let us consider the operation of a fleet of aircraft of similar capacity, c. By definition of the Lagrangian multiplier, A, the net which mimmizes delay must satisfy the condition: pr2(l-&‘)-*‘s =

U&i(A/aC)*

(19)

Since A, a, and c are 6xedi the load factor should vary as u,t, (passenger-hours) along a route. If we consider cities equally far apart, t, = Cl, then the routes with the most tratEc, u, > uz, should have higher load factors. (Logically, the reason for this is that the productivity of an extraflight-in terms of reducing delay-is less on routes where there are more flights: consequently, there ought to be relatively more flights, implying lower load factors, on the routes with less tra5c). Conversely, if we consider routes with equal tra!Ec, the longer routes, t, > tz, should have higher load factors. (See Gordon, 1973, and Douglas, 1971 for a further discussion of this.) This rational policy is just the opposite of the one that had been implicitly pursued by the U.S. Civil Aeronautics Board which-through its generous policy on long distance fares-encouraged airlines to schedule relatively more aircraft and lower their load factors on the longer links, and thus to decrease the concentration of the U.S. air net.

241

For networks over which air transport is provided by aircraft of sign&a&~ different sire, the situation is somewhat different. One should then expect that the .larger aircraft, which are cheaper to operate per seat-mile would be used on the routes with the most tratIlc. This effect would lead the load factors on different routes to be more equal. These criteria for optimal service also establish a lower bound on the level of concentration. Since optimal service requires in all cases that low-volume routes have more flights per passenger than high-volume routes, the ratio of tlights on any two routes of the air net should be closer to unity than the ratio of passengers. Consequently, for the optimum network supply, the supplyChi (the measure of concentration determined by flows of aircraft), should be less than the demand-Chi, the measure of concentration determined by flows of passengers.

CONCENl%ATlONOFTEEEUEOPWNAlRNSl-

We are now in a position to examine the actual concentration of the air net in Europe and to consider how far it may differ from what might be most desirable. We can also compare its structure and performance to the U.S. air net to see to what extent the usual comparisons between U.S. and European airline operations are well founded. We do not plan to examine whether individual European carriers could achieve economies by route rationalization. Parallel research by Grieg (1975), partially based on some of the concepts presented here, indicates that individual carriers might benefit from the elimination of cabotage restrictions, which currently effectively make multiple stop routed uneconomical in Europe. These results do not bear, however, on the question of whether the system as a whole should be rationalized.

Analysisprocedure The analysis has two parts. First, we calculate, for both the European and U.S. air nets, the concentration represented by the flow of travellers (the demand-Chi), the concentration supplied by the carriers as a group (the supply-%) and the pattern of concentration which would, for the existing fleet and structure of routes, minimixe the schedule delay (the minimum-delay-Chi). The comparison of these results gives us a precise idea of the actual structure of the air nets. Next, we investigate the implications of alternative European air nets, in particular those with fewer links between cities along the lines widely advocated and already mentioned. In this analysis we calculate not only the cost and minimumdelay produced by each configuration, but also the average length of trip and the average number of transfers per trip-both of which can be expected to increase as various routes are eliminated. Finally, we weigh these factors to estimate what kind of network appears to be in the best interests of the European community as a whole.

242

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lhta

As it is neither possible nor meani&tl to analyxe all

air services in Western Europe, we limitedour attention to the air net conuectingthe twenty largest generators of (international) scheduled IIights. Consequently, our analysis and conclusious pertain only to this basic network of interuational air services in Europe. While this may sound like a serious limitation, we have nevertheless consideredthe network that is most open to ratiomlixation-the set of points between which almost mdimited possible combinatious of co~ections may exist. The next twenty largest tratEc generators iu Europe are considerably smaller, generating approximately 15% as many i@ernationalaircraft movements,and 11%as many iutemational passengers as the first twenty. Due to the smallamount of t.ralRcgenerated at points other than the largest twenty, carrier economics dictate that such points be comtected with only one of two other points on the network, there are few degrees of freedom in designing the munodeled part of the network. The dam are much too extensive to be listed here, but can be obtained from Gordon (1974) or the sources described below. In Western Europe the twenty largest generatorsof air tragic were obtaiued from the ICAO Digest of Statistics, No: 182 (1972). They are, in alphabetic order: Amsterdam, Athens, Barcelona, Brussels, ‘Copenhagen, Dublin,Dusseldorf,Frankfurt, Geneva, Lisbon, London, Madrid, Milan, Munich, Oslo, Paris, Rome, Stockholm, Vienna and Zurich. According to the International OtIicial Airline Guide, these cities had 278 sectors between them (one each way between two cities) in May 1973 covered by an average of 1,216 flights per day (Donnelly, 1973).As indicated by the ICAO Digest of Statistics No. 179 (ICAO, 1972), supplemented by subsidiaryestimates for domestic tratIic on links such as Dusseldorf-Munichand Milan-Rome, this net carried about 30 million passenger-miles a day. The ICAO Digest of Statistics provided the necessary detailed information on the numberof flights,availableseats,and passengerson all links. It is deficientin that it only covers international trafilc and excludes non-member(or non-reporting)airlines. These are miuimaldefects. TratEc data for the United States are reported quarterly by the Civil AeronauticsBoard. For any year, the existing supply network for U.S. air transport can be determined from the North American Airline Guide.

Table 1. Comparison of actual European and U.S. air nets between top 20 cities

Situation

Chi concentrationfor Estimated Actual Actual Minimum pax/week (in millions) demand supply delay

Europe1973 USA 1973 1969 1%5 tNot available.

0.69 1.70 1.49 0.89

0.418 t 0.397

t

0.384 0.295 0.374 0.537

0.334 t 0.275

t

(This time, howeva, the number of flights had to be counted a&the seat-miles estimated for each link, as these data are not provided) In 1%9, the top twenty gemramm of scheduled air tra@c in the United States were, alphabetically, Atlauta, Boston, Chicago, Cleveland, Dallas, Denver, Detroit, Houston, Las Vegas, Los Angeles,Miami,Minneapolis,New York, Philadelphia, Pittsburgh, Saint Louis, San Francisco, Seattle, Tampa and Washington.This net included 312 sectors with 3,038llights a day and carried approximately 100 millionpassenger-milesa day. Results The comparisonof the European and U.S. air nets is

displayedin Table 1. NormahzedChi i&ices of concentration are shown for the existiq demand and supply, and for the.network that would mi&nixe delay over the existing links. The table contaius a few surprises. If we compare the nets at any time, as the European Air Research Bureau and others have, it is not at all obvious that the European net is less concentrated (lower Chi). It certainly does not appear to be so on an absolute sense as of the most recent data. In 1973,for example, the European air net is actually more coucentrated if we consider the degree of connectivity between pciuts and, specitIc.ally,the number of European sectors which have only a few flights/week.But, of course, there has been much less air tra& in Europe than in the United States at any time. Can we suppose that, since less tratRcis associatedwith higher concentration in the U.S., that the appropriate comparison between the two regions is betweea the air nets with similardensities of trafllc, say between Europe 1973and U.S. 1%5, or with similardemand-C&say between Europe 1973and U.S. 1%9? Possibly, but we would then have to worry about what effect the introductionof widebody aircraft would have had for Europe by 1973.I&finitive answers are d&u&-if not impossiil+to extract when such differences exist. The one thing that we can say with confidence is that simplistic comparisons between the U.S. and Europe are a poor basis for motivatingpolicy decisions. The second surprise is that airline operations in Europe are closer to mi&&ing overall delay on their structure of routes than .theAmericanoperations.To see this, we compare U.S. and European networks with similarpatterns of actual tra&c, that is, Europe 1973and the U.S. 1969,when the demandChi are approximately equal.The supply-& for Europe is then almost half way between the demand-Chiand the minimumdelay-Chi; the U.S. supplyChi is only about a sixth of the way toward :miuimi&goverall delay. (As expected, a rational policy implies that the demand-&i must exceed the supply-Chifor a given structure of routes.) This means that American carriers tend to match the patterns of individual demands whereas European carriers collectively pursue policies that achieve a structure which is closer to some objective for their entire air transport system. This is what one would expect, of course, knowingthat American carriers compete individuallyin markets, whereas European carriers collaboratethrough

243

Rstionslizihn of the European air net

airline pools governing fares, frequency of service and capacity along routes. From some point of view, at least, the European air net is thus already more rational than the U.S. air net. This observation needs to be interpreted carefully, however. So far, we have considered only the existing structure of routes for both regions: no links or sectors have been dropped. Since economies of scale for vector output do exist in the markets constituted by the airline links, it may be desirable to concentrate trallic on fewer links and thus increase the index of concentration. Meanwhile, it is actually quite remarkable that the allocation of air transport services which minimkzs overall delay to the passengers actually implies lower concentration on the existing routes: the frequency of departures ought to be more equal, that direct llights ought to be promoted. Specilically, for example, the calculations indicate that there ought to be relatively more Stockholm-Zurich and Amsterdam-Madrid llights if there are going to be any at all. Possible results of eliminating routes on the European air net are shown in Table 2. Starting from the existing structure of routes, more and more of the sectors with little trathc on them were eliminated. As the fleet was kept constant, both passengers and aircraft had to be reallocated to the remaining sectors. As the number of sectors was reduced, frequency of service on the important links increased and the schedule delay, caused by waiting for a flight, dropped almost as fast. This improvement of service for travellers along favored routes would be compensated by increased circuity for others, as represented by both additional transfers and longer routes. The preferred design for the air net depends upon the relative values one assigns to each dimension of the quality of service. These values ought to reflect the preferences of the consumers. Indeed, the level of trathc for which one designs the transport system varies with quality of service provided. Gptimality cannot be delined in terms of the supply of transport alone, it must consider the interaction of supply and demand. Consequently, we must plan networks in consideration of the determinants of the consumers’ demand, that is, in consideration of their relative preference for dilferent qualities of service. If one assumes that travellers dislike each kind of delay equally, then it appears that the best network for Europe is much more concentrated than the existing

network. This premise leads one to drop about one-third of all sectors (going from 278 to 162 between the top 20 generators of air tratKc in Europe) and to reduce to total delay by about 10%. This kind of result has been con&med by Greig’s analysis of Swissair’s European route structure (Greig, 1975). Another assumption could be that travellers are relatively less sensitive to schedule delay: Indeed, many can arrange their activities to conform to the airline schedules: They sleep longer in the morning, meet longer with associates, and so on. If we thus assume that schedule delays should only be weighted by one-third, one obtains the weighted total delay shown in Table 2. The analysis indicates that the most socially desirable contlguration of the European air net is essentially as connected as the actual net. (The optimal Chi is about 0.418 or fairly close to the actual Chi of 0.384.) By conventional measures of connectivity the change might be quite drastic, since up to 10% of the sectors might be eliminated (going from 278 to 238). But this reduction in connectivity would be superlicial in terms of performance: the sectors eliminated would include such links as Dublin-Paris and Amsterdam-Madrid, which already provide little service and add little to the real co~cctivity

of the system. As wholesale elimination of these sectors does not appear to benetlt the overall system perceptibly, and would probably be quite diliicult to implement for political reasons; this policy does not seem to have much to recommend it.

SUMMMYOF-ON5 The

following points have emerged from our detailed analysis: (1) Comparisons between the European and U.S. air nets are far from conclusive. While the Europe network may in some sense be more connected and less concentrated than the U.S. network, taking into account the relative concentration provided along each sector, the evidence is far from compelling and offers no basis for policy conclusions. (2) The European air net actually appears to be about as well-connected as could be desired, at least as could be determined within the limitations of this analysis. (3) Marginal improvements in overall air transport service in Europe could be obtained by eliminating some sectors and by improving the frequency of service upon some of the sectors of intermediate importance. (4) A wholesale policy of eliminating sectors would not seem to provide the kind

Table 2. Comparison of altexnative European air nets between top 20 cities in 1973 Route structure Sectors Miiumassumed delayChi 278t 238 218 162 116 102

Qua$ty

0.334 0.418 0.468 0.603 0.713 0.747

tActual situation, May 1973.

service

Schedule delay

Same seat miles for all choices

1.16 1.05 0.98 0.78 0.62 0.56

Quality of service (hours of day/trip) due to Transfers circuitous Raw travel total needed 0.00 0.01 0.03 0.11 0.25 0.30

1.15 1.16 1.17 1.21 1.28 1.30

2.31 2.22 2.18 2.10 2.15 2.16

Weighted total 1.54 1.52 1.53 1.58 1.74 1.79

244

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GORDONand

R.

DE

NEUWILLE

of sign&ant improvements that would make the efforts European Ecooomic Community, Transport Committee (1973b) On the Proposal fmm the Commission of the Eumpean worthwhile. Communitiesto theCouncil(Dot 134/72)for a Decision on rhe We therefore conchide that the current proposals for First Measures of a Common Approach to Air Transport rationalking the European air net by concentrating trafEc (Dot. 195/72)(L. No& rapporteur). BNSS~S. may be misguided. Other policies for rationalizing EuropeanParliament, Transport Committee (1972)Draft report relating to air transport problems in Europe (L. No&, European air transport, such as proposals to permit rapporteur), August 22. multi-sector frights; might yet be advantageous and Fruhan W. E., Jr. (1972) The Fight for CompeUiue Advantage. deserve close examination. So far, however, we see no Harvard Business School, Boston, Mass. compelling reasons. for spending much effort on the Gelerman W. and de Neufville R. (1973) Planning for satellite airports. ASCE Transpor. Engng J. 537-551, August. proposals that have been presented to the Council of Gordon S. R and de Neufville R. (1973) Design of air European Communities.

transportatioo networks, Tmnspn Res. 7,207~222. Acknowkdgcmtv&-We are grateful to the advice, helpful Gordon S. R. (1974)Rektionships Between Economies of Scale and the Shape of Tmnsportarion Networks. Ph.D. Discriticisms and eocoumgemeot of Michael Beesley, Ann sertatioo, MIT Department of Civil Engineering, Cambridge, Friedlaeoder, William &rrisoo, John Grieg, John Heath, Nathan Sit, Edward Smick and several referets in developing this Mass. study. Particular thanks for financial support also go to the Greig J. A. (1975)The Rationalisotion of AirlineNetworks within Institute of Transportation and Tr&Ic Engineeriug (now the Western Europe with Special Reference fo Swissair. Ph.D. Dissertation, London School of Ecooomics and Political Institute for Tran&rtatioo Studies), University California, Science, London. Berkeley; the U.S. Department of Transportation, under Grant DOT-OS-5023947;and the T,echnology and Policy Program at International Civil Aviatioo Organ&ion (1972a) ZXgest of SraMcs No. 179: Trajic Flow 1972.Series TF, No. 59. the Massachusetts I&&ute of Technology. Iotematiooal Civil Aviatioo Omanizatioo (1972b) Digest of Statistics No, 182: Airport Tr&. Series AT, No. 13._ Air Research Bureau (1957) Comparison Between the ZkueIop- Keeler T. E. (1974)Railroad costs, returns to scale, and excess ment of Air Tmnspoti in Europe and the United Stakx capacity, Rev. Econ. Statistics 201-208, May. BN&s. Meyer J., et al. (1959) The Economics of Competition in Council of Europe, Consultative Assembly, Committee on Tmnsport Zndusttis. Harvard University Press, Cambridge, Economic Affairs and Development (1973) On Civil A&ion h&S. in Europe. Documeot 3275 (Rivi&e, rapporteur). MurphyN. (1974)Sources of productivityincreases in the U.S. de Neufville R. and Marks D. H. (1974) Systems Planning and passenger airlioe industry,in de Neufville aod Marks (1974). Design: Case tiudies in Mod&g, Optimization and Evalu- Reuben H. Doooelly Publications (1973) O&M Airline Guides, ation. Prentice-Hall, Englewood Cliffs, New Jersey. Ioternatiooal and North American Editions, Chicago, May. de Neufville R. (1976) Airporf Systems Planning: A C&xl Rogers A. (1971) Miatrix Methods in Urban and Regional Examination of the Models and Experience. Macmillan, Analysis. Holdeo-Day, San Franc&o and London. London and MIT Press, Cambridge, Mass. Rosenberg A. (1970) Air Tmuel W&in Eumpe. Kungl. BokDouglas G. W. (1971) Excess capacity, service quality and the tryckeriet, P. A. Norstedt & Sooer, Stockholm. structure of airline fares, Proceedings, 12th Annual Meetingof Sealy K. R. (1%6) Geography of Air Transport. Hutchiosoo the Transportation Research Forum. Richard B. Cross, U&e&y Library, London (i&t edition, 1957). Oxford, Iod. Sheuhard R W. (1970) Theorv of Cost and Production FuncEads G. (1972) 7@eLocal Service Airline Experiment. Brookings r&s. P&&oh U&ersiG Press, Princeton, New Jersey, Institution, Washington, D.C. (revised edition of Cosf and Production Functions, 1953). European Airfines Research Bureau (1970) Compomfiue E.x- Simpson R. W. (1974)A theory for domestic airline ecooomics, amination of EARB and United Stares Airlines. EARB 403, Proceedings, 15th Annual Meeting of the Transportation Brussels. Research Forum. Richard B. Cross Co., Oxford, Iod. European Economic Compumity (1972)Draft decision (EEC) of US Civil Aeronautics Board (Quarterly) Origin-Destinarion the Council on the lirst measures of a common approach for air Survey of Airline Passenger T&k. Domestic, U.S. Govemtransport, September 27. meot Printing O&e, Washingtoo, D.C. European Economic Community (19736 Draft Report of the Walters A. A. (1963) Production and cost functions: An Section for Transport and Communication on the Draft econometric survey, Econome0ica 31, l-66. Decision (EEC) of Ihe Council on the First Measrps of Wheatcroft S. (19%) m Lkonomics of European Air Tmnsport. Common Approach for Air Tmnsport. bussels. Manchester University Press, Manchester, England.

of