57
e e
Uncles and Andrew S.C. Ehrenberg Centre for Marketing and Communication, London Business School, Sussex Place, Regent’s Park, London NWI 4SA, United Kingdom
Contracts for oil companies to supply airlines with aviation fuel at different European airports follow regular patterns. For example, the loyalty of airlines tends to be highly divided among different oil companies, and there is no sign of any marked segmentation. The patterns resemble those found for fast-moving consumer goods (fmcg) markets and the same theoretical Dirichlet model holds. Underlying analogies with fmcg markets and managerial implications are drawn out.
on
One input to marketing decisions is to understand the structure of one’s market. How loyal are one’s customers? compare with one’s co mented is the market? and what threats are there? Comprehensive purchasing data about the competition are often not available, other than for certain fast-moving consumer goods (fmcg) markets. An exception in industrial or business-to-business marketing is the market for aviation fuel. Here there are 1- to S-year contracts at individual airports between oil companies and airlines, awarded on the basis ly individual aircraft of sealed bids, to of all these contracts with fuel. The exist is generally known - who supplies whom but not the details (e.g., size of contract and er we report how t ice)e
is structured, in terms of the contracts which leading oil companies had with the different airlines operating at a selection of airports in Europe. In Section 2 we first look at the data narrowly, from just one supplier’s point of view, here Shell. The picture is one of divided customer loyalty, with Shell having many airline customers but mostly rather few contracts with each across the different airports. This seems unsatisfactory or even threatening - are Shell’s customers dissatisfied? Is its bidding for the contracts wrong? Or do the results imply opportunities for doing better? In Section 3 we then reach a very different conclusion by comparing the observed patterns for Shell with those for its competitors, and also with those for fmcg markets as represented by the I&i&let model. The picture for Shell now looks normal - no special threats, but also no special opportunities. We discuss the analogies with fmcg markets and the broader managerial and theoretical implications in the final two sections. The data The data examined here concern 1962 con-
tracts between six leading oil companies such as Shell, BP, etc. plus an “all others” grouping, and 249 airlines such as Air France, British Airways, KLM, and Swissair, at 16 large international airports in Europe with an average of almost 100000 international cornmercial aircraft movements in 1988. The airports were a selection, supplied by Shell International, with no airports without a Shell
Intern. J. of Research in Marketing 7 (1990) 57-68
167~8116/90/$03.50 8 1990 - Elsevier Science Publishers B.V. (North-Holland)
58
M.D.
Uncles, A.S. C. Ehrenberg / Industrial buying behavior
will see, large numbers of small customers, Double Jeopardy and Duplication of Purchase Law patterns) was found to resemble closely findings of an earlier study of aviation fuel contracts, in another region of the world (Africa) and before the 1973 oil crisis (Ehrenberg, 1975; Ehrenberg and Goodhardt, 1977). The results also resemble widely-established findings in fmcg markets ranging from breakfast cereals and detergents to petrol and et al., 1984; motor oil (e.g., Goodhardt Ehrenberg, 1972, 1988). This has been confirmed in detail in Section 3 by testing the data against the theoretical Dirichlet model (here the empirical-Ditichlet version) which has already been found to describe such fmcg markets. The construction of the Dirichlet model as a stochastic representation of buyer behavior is outlined in Appendix A. The aim of the study was not to prove that the Dirichlet model held for such industrial markets. Instead, it was exploratory - to see Y.-hatthe structure of this particular industrial market was like. Except for the one set of previous empirical results almost 20 years earlier there was no prior reason for expecting any particular outcome. There are some similarities with fmcg markets, for example that an airline can have contracts with the same oil company at different airports, just as a consumer can buy the same brand over time at different retail outlets. But there are also differences, for example in the sheer numbers of customers and of retail outlets. We consider these possible analogies and differences further in the final discussion in Section 4.
2.
Looking at the market from Shell’s point of view, it has a third of all contracts (653 of the 1962 contracts at the I6 ai base). The question lates into custo
(4 How many of the airlines does Shell have (b) (4
(4 (e)
(0
as customers? How many contracts does Shell have with its customers at the different airports? How large are Shell’s customers in terms of the number of contracts which its customers have with any of the oil companies across the 16 different airports? How much of their business across these airports does Shell have (the ratio of (b) and (c))? How many of its customers buy exclusively from Shell? Which of the other oil companies are most directly competitive with Shell?
For the industrial marketing manager it matters whether Shell’s 653 contracts are with just a few major customers, or spread across most of the airlines. And it matters whether an airline’s contracts with Shell constitute most of that airline’s aviation fuel business or only a small share. Such issues affect how Shell deals with its customers, whether it searches for new customers or for more business from existing customers, how it fixes prices for new tenders, and how its operational services at each airport can be managed. What, then, is the record for Shell? The answers from the data are:
(4 Shell has obtained a penetration
as high as 73%, far higher than its market share of 33% - as many as 182 of all 249 airlines are customers of Shell.
(W But it generally has few contracts
with each customer, on average only 3.5 contracts among the different airports, and with half of its customers merely 1 or 2.
Cc) This is far less than the 9 contracts which Shell’s average airline customer has across the I6 airports (not all airlines operate at all 16 airports).
(4
therefore has only a min of its customers’ aviation fu (i.e., 3.5 by 9).
M. D. Umles, A. S. C. Ehrenherg / Industriu: hying behavior
(e) Some 37% of Shell’s customers do however buy exclusively from Shell across the different airports.
Table 1 Summary measures of contracts Suppliers
All in all, the picture seems one of Shell having some loyalty but not a great deal. It has many buyers, but not much business with each across the different airports in Europe, although the potential for more business was there. In fact, it looks as if whether an airline at a certain airport awards a contract to Shell hardly depends on whether or not that airline has awarded Shell a contract at another airport. There may be some links between the two events, but the outcome appears to be irregular and unsystematic from one case to another. Does this then imply airlines are dissatisfied, or that there are opportunities here for Shell to increase its business with its existing customers, or are these results inevitable - an inherent feat re of the market?
The advantage of having information about the whole market is that one can compare one’s own position with that of one’s competitors. In this section we compare Shell’s performance with that of the other oil companies. Are the results for Shell high or low for example, ov~dy37% exclusive buyers (as in (e) above), or as many as 37%? We also compare these results with the
Market shares
between suppliers and airlines
Percentage of airlines who are customers a
Average number of constracts per customer a
0
T
0
T
loo
100
100
7.8
7.8
Shell ” Others” BP Total Mobil Esso Chevron
33 23 14 9 9 8 4
73 51 44 28 28 28 19
72 60 44 31 29 27 16
3.5 3.5 2.5 2.5 2.3 2.1 1.7
3.7 3.1 2.6 2.3 2.3 2.3 2.1
Average
14
39
40
2.6
2.6
(0 About 40% of its customers also have contracts with BP, about 30% with Total, 26% with Mobil, and fewer with each of the remaining oil companies.
59
(W
Any
a 0: observed
figures; T: theoretical
Dirichlet predictions.
The overall outcome is that Shell’s own market results generally look normal, instead of implying an unusually low degree of loyalty. (Since our data base is confined to airports at which Shell is active, some of the figures for Shell will in fact stand out as exceptionally high, beyond what its market share would warrant, but certainly not low.) Set out in Table 1 is each oil company’s market share (in terms of contracts), the percentage of airlines who are that oil company’s customers at one or more of the airports (“penetration”), and the average number of contracts with these airline customers across the 16 airports. This is shown for the six leading oil companies and the “Bthers” grouping of lesser ones like Elf, Fina, and Agip. Table 1 gives both the observed results and the predictions of the empirical-Dirichlet model (see Appendix A). Table 1 puts the Shell results from Section 2 into a wider perspective, empirical as well as theoretical. Thus, Shell had many custom= ~=.~r~~~nf 2 5 contracts with ers but only an rrvblueu o(l _._ e now see that Shell had in fact each. larges also t ~~~~~~~~~~~(73%).
M.D. Uncles, A. S. C. Ehrenberg / Industrial buying behavior
60 Table 2 The distribution
of contracts
(by customers) Number
Suppliers
of contracts
(W customers)
1
2
3
4
5
6
?
8
9+
Shell
0% I-%
30 32
22 18
12 13
10 10
6 7
3 5
4 4
4 3
8 8
“ Others”
0% -I-%
30 38
16 20
19 13
1 9
10 6
5 4
2 3
2 2
9 5
BP
0% T%
42 46
24 21
14 12
7 7
5 5
2 3
2 2
1 1
3 3
Total
0% T%
36 52
33 21
11 11
7 6
4 4
1 2
6 1
0 1
1 2
Mobil
0% -l-%
47 52
19 21
19 11
6 6
3 4
1 2
0 1
1 I
3 2
Esso
0% T%
51 53
18 21
17 10
8 6
4 3
0 2
0 1
0 1
1 2
Chevron
0% T%
54 58
29 20
8 9
8 5
0 3
0 2
0 1
0 1
0 1
Average
0% T4&
42 47
23 20
14
8 7
5 4
2 3
2 2
1 1
3 3
11
The other oil companies also had much higher penetrations than their market shares and they too had relatively few contracts with each of their customers. But they had even fewer contracts than Shell’s 3.5 (e.g., averages of only 2.5 for BP and Total, and 1.7 for Chevron). This downward trend with market shart ‘%%s Familiar. It is an instance of a widei;,) observed statistical phenomenon, that smaller brands have :ewer buyers who also buy them iess ofte:l on average, This has been called the Doubie Jeopardy effect (see, e.g., McPhse, 196.‘; Ehrenberg et al., 1990). The picture for Shell looks normal so far, given its market share at the airports in question, an is in fact closely matched by the theoretical e noted in Section 2 that about half of Shell’s customers had only or 2 contracts with Shell. Table 2 sets t s out in more detail, together again vith the corn results for the other oil co
1 or 2 contracts is endemic to the market and is also closely predictable. Most suppliers in fact have an even higher proportion of occasional customers than does Shell, another manifestation of the Double Jeopardy effect (i.e., smaller brands have more light customers). Earlier we also saw that Shell had only 40% of its customers’ business; that means Shell’s customers have more contracts with other oil companies collectively than with Shell itself. Table 3 now shows that the other smaller oil companies fared even worse, and that this is again closely predictable, in line with their market shares. Customers of P, for instance, had on average 2.5 contracts with BP, 8.5 with other oil co nies, and therefore 11 contracts in all itself met less than a quarter of its customers’ requirements. Thus, each oil company’s customers placed much of
M.D. Uncles, A.S. C. Ehrenberg / Industrial buying behavior Table 3 The average number of contracts per supplier
Suppliers
Average number of contracts per customer With each supplier
With any supplier
As a share of any supplier
OTOTOT 1
Any
7.8
7.8
8
8
100
Shell “Others’* BP Total Mobil Esso Chevron
3.5 3.5 2.5 2.5 2.3 2.1 1.7
3.7 3.1 2.6 23 2.3 2.3 2.1
9 11 11 14 14 14 14
18 IO 11 11 11 12 12
40 31 23 18 17 15 12
38 30 24 20 20 19 17
Average
2.6
2.6
12
11
22
24
The
fin8~~
t,hat 37% sf
Shell’s customers
were adzdue, customers of Shell (i.e., airlines which had no contracts with other oil companies at the 16 airports) is more unusual. Table 4 shows that this is in fact an exceptionally high incidence of exclusive buyers. The high figure for Shell is, we believe, due to the fact that our data base included only &r-ports where Shell was operative. More generally, Table 4 shows that the incidence of sole buyers is otherwise very low, yet closely in line with predictions from the Dirichlet model. (Leaving the Shell figures out from the column averages in Table 4 Table 4 Exclusive contracts between suppliers and airlines Suppliers
Percentage of customers who are exclusive
Average number of contracts per customer
0
0
T
T 7.8
Total Mobil Esso Chevron
1 6 0 4
Average
IO
” For exceptions, see text.
61
would not affect the conclusion that oil companies generally have predictably few 100% loyal customers.) Table 4 also shows that such exclusive or 100%loyal buyers generally have few contracts - just 1.6 on average - rather fewer in fact than an oil company’s average customer, who had 2.6 contracts (Table 1). Moreover, we note that the 100%loyal buyers are “light buyers” of aviation fuel overall, in that the few contracts they have with their exclusive supplier are, by definition, equal to the total number of contracts which they have with anybody at the airports in question. This is low compared with the average of 12 or so contracts in Table 3 for all airline customers. Overall, the conclusion is therefore that exclusive 100%loyal buyers are relatively unimportant in terms of sales - they are few in number and are light buyers, with a lowerthan-average number of contracts. Finally, we consider the extent to which the non-loyal customers of an oil company also have contracts with each of the separate competing suppliers. Table 5 shows the extent of customers for the of the “duplication” various pairs of oil companies, together with theoretical predictions along the bottom row. The extent of &is for Shell’s own customers (shown in the first row) turns out to be lower than normal - again, we believe this arises from the Shell bias in the selection of airports for which we have competitive information. Otherwise, Table 5 shows a pattern which can be easily summarised by the so-called Duplication of Purchase Law. This typically tends to hold for fmcg markets (see, e.g., Ehrenberg, 1972, 1988) and is itself an approximation of the Dirichaet model It says that the percentage of buyers of brand enetration
of brand A.
also have con-
M.D.
62
Uncles. A. S. C. Ehrenherg / Industrial buying hehaoior
Table 5 The incidence of dupliczie contracting Customers of
Who also have contracts with (Z) Shell
Shell
“Others” BP Total Mobil Fsso Chevron Average duplication Predicted duplication
--
BP
“Others” 4(1 ,’
____I
Total
Mobil
ESSO
Chevron
38 a
2x -’
‘6 *
30 a
20 a
58
44 43
45 41 60
47 47 53 57 56
3c 28 43 39 38 -
47 40
33 27
71 63 76 67 78 77
68 81 81 85 81
69 63 72 65
58 51 63
57 58
72 loo il
74 72
61 62
48 39
48 (Jo
a For exceptions. see texl.
tracts with Shell, the fourth that about 48% do so with Total, and the last column that roughly 33% do so with Chevron. Despite the physical complexities of the market (different airports in different countries, with separate and costly fuel installations), the competitive picture is very simple: there is virtually no special clustering of particular oil companies (i.e., “ brands”) as exceptionally competitive. The levels of these duplications are predicted by the Duplication of Purchase Law as being 1.4 times the penetration, i.e., the percentage of all airlines who have at least one contract with that oil company. (The proportionality factor 1.4 is estimated as the ratio 55/39 of the average duplications in Table 5 to the average of the percentage of customers shown in Table 1.) Except for Shell, the fit is on the whole close. This means that the degree of competitive overlap between pairs of suppliers in this market shows no major clusters but is mainly linked to market share.
Industrial marketing is often rightly portrayed as complex, with suppliers having to meet ever-changing technical specifications, and buyers on gathcring new data in or e risks associated with each
19771 Webster, 1978; Jackson and Cooper, 1988; Smith and Bard, 1989). The process of organizational buying, of tlegotiating or tendering for contracts, also tends to be complex. However, similarities between the pwrchasing of some fairly undifferentiated industrial products and fmcg’s have been acknowledged in the past (see Robinson et al. (1967) on straight rebuys of industrial components, Ghingold (1987) on the importance of purchasing-related activities for routine reorders of office furniture, and Easton (1975, 1980) on sales of chemical additives, paper and packaging). Given the close resemblance of the observed results for aviation fuel contracts to those for fmcg markets, we now draw cut similarities and differences with the industrial markets. These are the sort of considerations that have to be borne in mind &hen similarly considering other industrial markets in future. They relate to the nature and size of the purchase decisions (e.g., contracts), the numbers of customers and of retail outlets, the roles of product differentiation and exogenous variables, and the availability of data. Thr purhse decisions In our darn. the airline buyer - KLM, Air rance, Swissair’ etc. -- general1 one e&ion wit
A4.D. Uncles, A. S. C. Ehrenherg / lndustrtul buying hehacpinr
r say a year’s particular airport (a contract supply). But the airline can also have contracts Gth the same oil company at o airports. The analogy in the case of f markets is not with individual purchases but with penetration, i.e., a consumer buying a brand at least mce over a period such as a year, at a given retail outlet and at others. The purchase process The purchasing process for contracts is one of competitive bidding, where the outcome is generally regarded as probabilistic (see, e.g., Simmonds, 1965). In contrast, buyer behavior in fmcg markets is basically deterministic (individuals have reasons for when and what they buy), even though the patterns across different consumers appear so irregular that with very large numbers of consumers the decisions can be regarded as-if-random, as required by stochastic models such as the Dirichlet. The size of contracts
‘Zhe size of the individual contracts varies markedly with the number and capacity of the aircraft to be fuelled. But the average size of the different contracts obtained by each oil any differed relatively little, being about 2 to 3 million gallons per year (with one outlier at 6 million). It follows that the total sales of the oil companies varied mainly with the number of contracts each had. This is the variable we have analysed here. By the same token, how many purchases of a brand of an fmcg product individual consumers make in a year at a given retailer also varies greatly from consumer to consumer, e average rates across different consumers differ little from br e.g., Gso 88). Customers er of actual or
ll(250 airlines
63
in our data base), and with a fairly direct supplier-buyer relationship, in contrast to consumer products where the numbers are in the millions. Distribution
Physical constraints matter crucially, such as having a storage installation at an airport and whether an airline actually flies there. This resembles the retailer’s presence in a neighbourhood and the poicr&al customers’ access to the shopping location. The number of retail outlets is fairly small (16 in our sample, and at most a hundred or two in the whole of a major region like Europe or the United States), compared with thousands in the case of grocery outlets. Branding
With different oil companies providing a commodity (aviation fuel), brand differentiation has to be on the basis of factors such as bid prices, ground services at the airport, or organizational selling. Some fmcg markets are similarly undifferentiated, but others are highly differentiated (e.g., breakfast cereals, biscuits, or confectionary), although the same (Dirichlet- type) pat terns of buyer behavior apply in each case.
A methodological feature of the results is that predictable patterns could be established without any detailed knowledge of costs and revenues, the size of the contracts, the price, or of the organizational buying processes that were involved. TJ.Gs is also the case in stationary fmcg markets and is made very explicit by the Dirichlet model which contains no exogenous variables.
Data
on competitive purchasing in inarkets is likely to remain scarce
64
M.D. Uncles, A. S. C. Ehrenberg / Industrial buying behavior
data, such as diary or scanner-based panels). gut once one knows what to look for - mainly whetltler or not the patterns are like those reported here - one can tes this for other markets even with incomplete information (such as using only data for one’s own customers and their dealings with competitors. as illustrated for Shell in Section 2).
5. Discussion We have seen in this paper that the structure of the market for aviation fuel contracts between oil companies and airlines can be simple. This simplicity arises at several levels: (a) The numerical patterns in Tables 1 to 5 are regular rather than chaotic. In particular, the patterns are much the same for different oil companies, except for a market-share effect. (b) What the patterns show is also straightforward. Thus, across the European airports, an oil company generally has few contracts with any one airline (typically only one or two contracts with about haif its customers). It has very few 100%loyal customers, and on average supplies only some 20% of its customers’ needs. There are no clusters 0f two or more oil companies who are especially competitive with each other, so implying very little distinct segmentation. (c) These patterns, basically of divided customer loyalty, are not a haphazard occurrence in this market. Instead they are like the contractual patterns that were found for aviation fuel in another region of the world, Africa, before the oil crisis in the early 197Os, despite all the intervening changes (such as volsrtile prices, over-supply and intensive competition, shorter contracts, and more split contracts at individual airports). ore generally, the patterns are not (d) unique in that they closely rese found for a very wi
Many industrial markets are very different from that for aviation fuel. Some have highly differentiated products, or more or less exclusive contractual relationships with one supplier, or oevy small numbers of players. But we believe that in those industrial markets where it is common to have a raltge of suppliers, similar patterns to the ones here might be observed; for example, they might also show divided but nonetheless positive loyalty to each of several suppliers, and little distinct segmentation between fairly close &stitutes. On the other hand the patterns could turn out to be very different. What is needed now is for market analysts to look at a variety of other industrial markets (if there is data). Knowing that there are patterns - in the market for aviation fuel contracts as well as in fmcg markets, and that these are predictable from the theoretical Dirichlet model should help analysts recognise any patterns that exist in their own industrial markets. In conclusion, two issues need to be considered. One is why the patterns are as they are. In par&ular, why is there divided loyalty? The other is what the managerial implications are. In particular, to what extent should a manager take the patterns as “normal” or seek to “buck the trend”? 5.1. Why do the patterns occur? Airlines mostly have few fuel contracts with the same oil supplier. One reason could be a deliberate policy of multi-sourcing, to reduce risk or to increase competition (‘“divide and rule”). Some split-contracts do in fact occur at the same airport, with KIN, say, offering for competitive tender two or more contracts to different oil companies at that airport. Nevertheless, the data here mostly c0ncern contracts given to suppliers at different airports, usually in different countries, negotiated at different pon-ns in ti
M.D. Lkcles, A.S.C. Ehrenberg / Industrial buying behavior
to manage from the centre. It would in any case provide scope for negotiating price cuts for bulk orders (i.e., for exclusive contracts across many or all of the airports). An alternative and, we think, more plausible explanation is that the pattern is facilitated by the sealed-bid tendering process. If suppliers operate to similar cost functions, and tenders are negotiated locally, and more or less independently at different airports, the likely outcome is an as-if-random chance of success and this automatically spreads contracts across different suppliers. This formulation fits in with the stochastic specification of the Dirichlet model, as noted in Section 1. Indeed, a stochastic model would be more directly justified here than for fmcg markets. There the individual purchase decisions (whether, when, what, and where) are essentially deterministic, as already noted. They appear irregular across different consumers, and with very large numbers of consumers, a stochastic specification of as-if-random behavior with fixed (zero-order) probabilities tends to describe equilibrium markets well. 5.2. What can a manager do? A common question when faced with a regular market structure such as here is what a manager can do. Consider BP, with a “middling” market share of 14% at the European airports in question (Table 1). It has only 1 or 2 contracts with two-thirds of its airline customers (Table 2) and an average of 2.5 contracts overall (out of the average of 11 which its customers put out to tender, Table 3. er of contracts, one option would be to aim for more airline customers, still with a few conhat would be going with the oil companies have done this ave Q et so too
65
The alternative option for BP would be to 11 contracts, instead of only an average of 2.5. But this would be going against the grain of the market, i.e., aiming at something which nobody else has ever accomplished to any substantial extent, whether in selling aviation fuel or fmcgs. Knowing the descriptive structure of one’s market therefore provides strong indications of what strategies or tactics might lead to unusual outcomes and hence be unlikely to succeed, unless one has explicit reasons for being uniquely different. get more of its existing customers’
otes on the
et model
The Dirichlet model is a stochastic model of bu;:er behavior which has been developed in the context of fast-moving consumer goods (Chatfield and Goodhardt, 1975; Goodhardt et al., 1984; Ehrenberg, 1988; and references given there). For aviation fuel contracts we have used the empirical-Dirichlet version of the model which makes fewer assumptions about the product-class level of purchasing. The main justification for using the Dirichlet model lies in the way it successfully describes the detailed structure of the market, as we have seen in the main text (Tables 1 to 5). We have also noted that there are broad conceptual parallels with fmcg markets, but also some differences. Thus, a contract between an airline customer and an oil company to supply fuel on suitable occasions at a particular airport is seen as equivalent to a consumer voluntarily patronising a particular retail outlet over a period of time to buy the product once or more often. The Dirichlet is used to predict regular measures of buying ication reflects that at 1 customers purchase very irregular; for example, which oil companies airlines choose at
M.D. Uncles, A.S.C. Ehrenberg / Industrial buying behavior
66
different airfields will vary a lot. The model assumes that individual contracts arise “as-ifwith specified probabilities. at-random” Potentially, with sealed-bid tendering for fuel contracts, that is a reasonable representation. The Dirichlet model describes purchase incidence and brand-choice. For the latter, i.e., the choice of an oil company, the model assumes a mixture of two probability distributions, to give the number of contracts r which an airline makes with a particular oil company, given that it has n contracts in all. The distributions are that (i) each airline’s probability p of choosing a given oil company is constant across airports and follows a multinomial distribution M( r 1 p, n), and (ii) that the distribution of such probabilities p across airlines follows a particular “Dirichlet” type of multivariate BetaBinomial distribution D(plc~). (Here, D(p[c~)=Cp~~-‘,..., 4 ag-’ for g oil companies, where the a’s are proportional to the oil companies’ market shares and add to the parameter S, as noted below, and C is a scaling coefficient which is a function of the a.) F a or purchase incidence, the empiricalDirichlet uses the observed frequency of n = 1, 2, 3, **. contracts as input, as shown in Table A.l, hence its name “empirical” (i.e., that 19% of airlines had n = 1 contracts at the I6 airports, 8% had n = 2 contracts, and so on, with more than 16 contracts occurring in a few cases because some airlines had split contracts at some of the 16 airports). The model is for an unsegmented market, i.e., it assumes that the above statistical distributions are independent of each other. Thus, Table A.1 The observed
frequency
distribution
of the number of contracts
the distributions of (i) and (ii) above are assumed the same for airlines with many contracts and ones with few. The empirical-Dirichlet has one parameter, S, the sum of the values of the (II in the model. It reflects how diverse consumers’ are in their brand choices. The parameter can be estimated from the penetration and average purchase frequency of the product and of each or any of the itemized brands. There are no closed algebraic formulae and the estimation of the model’s parameters and predictions requires heavy arithmetic (Ehrenberg, 1988, Appendix C). This is grealty helped by suitable software (see, e.g., Nelson, 1986; Uncles, 1989). A central feature of the Dir-i&let model is that, for its various predictions, the only brand-specific inputs needed are the brands’ (i.e., oil companies’) market shares. A wide range of predictions are then given by the model. These include both single-brand measures as in Tables 1 and 2 (the percentage of airlines who are customers, the average number of contracts per customer, and the distribution of contracts which airlines have with each oil supplier), and measures of multibrand buying as in Tables 3 to 5 (the number of contracts with any oil supplier, the number of exclusive deals, and the extent of multiplecontracting across suppliers at different airports). The empirical-Dirichlet model is a less restrictive version of the main “NBD Dirichlet” model (see also Ehrenberg. 1988, Chapter 13). The latter specifies the incidence of purchase of the product-class as a mixture of Poisson per airline
Number of contracts % of airlines
1 19
2 8
3 8
4 6
5 6
6 3
7 8
8 7
9 3
10 2
Number of contracts 5”oof airlines
11 3
12 4
13 4
14 2
15 5
16 4
17 2
18 1
19 1
20 0
Number of contracts R of airlines
21 0.8
22 0
23
24 0
25 0.4
26 0
21 0.8
28 0
29 0.4
30 + 0.4
0.8
M.D. Uncles, A.S. C. Ehrenberg / Industrial buying behavior
distributions (for each customer) and a Gamma distribution (for the means of the Poissons across customers). This leads to a Negative-Binomial distribution (NBD) for the number of purchases (contracts) as in Table A.l. Where it fits (as for many fmcg markets), the advantage of the NBD-Dir&let model is that it enables predictions to be made for different length time-periods (e.g., for purchasing patterns like those in Tables 1 to 5 for a year, or a quarter, or a month). This does not apply with aviation fuel contracts. There are several reasons for using the empirical-Dirichlet here. One is that the probability of an airline having a contract at any one of the airports cannot be Poisson, since airports are of different sizes. (In contrast, a consumer’s probability of purchasing the product-class would be constant for equal successive time-periods in a stationary market.) Problems in the overall definition of a market, and in particular the selection of 16 airports in our current European data base, also mean that the distribution of the number of contracts awarded by airlines in the study is likely to be ad hoc rather than follow a closely predictable statistical pattern. A further technical factor is that with a fixed number of airports (e.g., up to 16 here) the overall frequency distribution should be a Beta-Binomial or the like, rather than a semiinfinite Negative-Binomial (although the observed distribution in Table A.1 extends further because of the occurrence of some splitcontracts). In fmcg markets, the NBD assumption usually gives a good fit to the observed data. Hence inputting the observed product-class distribution gives very much the same Dirichlet predictions. This accounts for e patterns for fmcg’s with those for aviation fuel in Tables 1 to 5.
co nternational
Trading
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Company, for which we are most grateful. We also value the helpful suggestions from the anonymous referees. This paper is part of an on-going programme of work at the Centre for Marketing & Communication, London Business School, supported by some 30 leading companies.
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