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A robust methodology for setting tariffs
¹elecommunications Policy, Vol. 22, No. 10, pp. 863—874, 1998 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0308-5961/98 $19.00#0.00
PII: S0308-5961(98)00066-4
A robust methodology for setting tariffs
J T Buchanan Pricing new or existing services is a challenge in the current state of the communications industry, with new industrial structures, fast technical change and varying degrees of competition and regulation. Basically the industry is newly immature, with few good models for, and little data on, the behaviour of consumers or competitors. In this paper we describe the development of a robust methodology for the determination of prices, able to cater for some of the sources of uncertainty in the real world, such as market behaviour. By robust, we mean the ability to re-use the basic model with relatively little change if, for example, the underlying sub-model of consumer behaviour is changed from cost minimising to risk averse, or the basis of pricing is changed from value to cost. 1998 Elsevier Science Ltd. All rights reserved
J. T. Buchanan is with the Department of Computer Science, University of Strathclyde, Livingstone Tower, 26 Richmond Street, Glasgow G1 1XH, UK. He is also a Royal Society Industrial Fellow and works for Analysys Ltd, St Giles’ Court, 24 Castle Street, Cambridge CB3 0AJ, UK. Tel: 0 141 548 3424; fax: 0 141 553 4101; e-mail: [email protected]. 1
There is also considerable interest in the pricing of (transport layer) entities which are more readily associated with the mechanisms enabling services or their associated qualities, e.g. bandwidth and burstiness ratios. See Walker, D., Kelly, F., and Solomon, J., Tariffing in the new IP/ATM environment. Telecommunications Policy, 1997, 21(4), 283–295. Eventually these two exercises will relate, probably through
continued on page 864
In telecommunications, operational pricing considerations used to be limited to the determination of initial connection, periodic rental and usage charges. For some services this is still the case, but the boundaries have become blurred with tariffs now bundling usage with rental and even allowing a trade-off between rental and usage. Other components, such as the number of instruments, and further service bundling, are also increasingly common. With new technology, for example in broadband, experience with pricing is just beginning and is further complicated by new traffic types and quality of service considerations. Note that our interest is in pricing services, i.e. the communications feature or facility as observed by the customer. To add to these complications, relatively little is known about consumer (and competitor) behaviour. Most empirical studies have been longitudinal and econometric in nature, with analysis based on historical data2—4 or indeed offering a record of practice.5—7 In a more prescriptive vein there have been attempts to forecast consumer demand for new services taking into account cross effects. In looking at what is available to assist in the tariff-setting problem, there are three main types of study to be found in the literature and the industry. Firstly, there is the formal economic and econometric work. This may take the form of a normative theory of tariffs, where the concern is to establish a theory of pricing (natural monopoly) services with an emphasis on increasing economic efficiency and achieving acceptable distributive results. Inter alia this will involve establishing a description of market behaviour (usually in terms of elasticities) and also address social/political aspects of service provision, including regulation. While nominally prescriptive it is not clear how these theories can be turned directly into operational tools of use to decision-makers in today’s industry. In the interests of progress the theories tend to make simplifying assumptions about many of the problem features described below, or indeed are not able to incorporate them at all. An alternative approach uses insights from economic theory to give a descriptive trace of the development of competition between 2, later 4, mobile operators in the UK. Prominent in this study are considerations of evolving technology and regulation, and how these relate to industry structure and growth.
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continued from page 863 the usual economic intermediary devices, but that is not an issue pursued in this study. 2 Hackl, P. and Westlund, A. H., Demand for international telecommunication timevarying price elasticity, Journal of Econometrics, 1996, 70(1), 25–39. 3 Cracknell, D., and Knott, M., The measurement of price elasticities—the BT experience, International Journal of Forecasting, 1995, 11(4), 321–329. 4 Bousquet, A., and Ivaldi, M., Optimal pricing of telephone usage: an econometric implementation. Information Economics and Policy, 1997, 9(3), 219–239. 5 Ypsilanti, D., International telecommunication pricing practices and principles: a progress review, OECD Information Computer Communications Policy (Paris), 1995, 36. 6 Paltridge, S., Mobile cellular communication pricing strategies and competition. OECD Information Computer Communications Policy (Paris), 1996, 39. 7 Waverman, L. and Ypsilanti, D., International telecommunication tariffs: charging practices and procedures. OECD Information Computer Communications Policy (Paris), 1994, 34. 8 Weerahandi, S., Hisiger, R. S. and Chien, V., A framework for forecasting demand for new services and their cross effects on existing services. Information Economics and Policy, 1994, 6(2), 143—162. Weerahandi et al. model the substitutive and complementary effects often found in the introduction of new services with parameters estimated from historical consumer choice behaviour. 9 Mitchell, B. M. and Vogelsang, I., Telecommunications Pricing: Theory and Practice. Cambridge University Press, Cambridge, 1991. 10 Valletti, T. M. and Cave, M., Competition in UK mobile communications. Telecommunications Policy, 1998, 22(2), 109–131. 11 Roy, A. and Henry, W., Introduction: special issue on pricing strategy and marketing mix. Journal of Business Research, 1995, 33(3), 183—186. 12 Nagle, T. T. and Holden, R. K., The Strategy and Tactics of Pricing, 2nd Edn. Prentice-Hall, Englewood Cliffs, NJ, 1995. 13 There is already a qualitative understanding of this phenomena (see Hills, T. and Hopkins, M., Tariffing ATM: Maximising the Business Opportunity. Analysys Publications, Cambridge, 1997) but there is a need for this to be augmented by a more analytic and quantitative approach.
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Secondly, many discussions in the industry, certainly away from the academic cotext, concentrate on describing the problem, perhaps with some analysis but usually with little prescription, i.e. focusing on how prices may be set. Presentations putatively on pricing are often more about business strategy, market segmentation and product development—important in themselves, and related to pricing—but not the decisions themselves. Finally, in examining the literature of academic marketing research, some pertinent observations may be made. A recent research collation attempted to assess pricing as a issue of marketing strategy covering a wide range of methodologies, experimental design, econometric analysis and the conceptualisation of the pricing decision as a game. The contributions themselves were subject to analysis in terms of their place in a twoway table, which considered studies as either normative or descriptive and dealing with individual or aggregate behaviour. Of the eight studies, six were descriptive/individual and the remaining two normative/aggregate. This is representative of the marketing literature which is not redolent with analytic prescriptive work of possible use to pricing managers or strategists. Rather the concern is with the description of key problem elements and the use of some accounting data to inform the pricing process.
Elements of the problem Many of the elements, which are potentially part of the tariffing problem, are illustrated in Figure 1. In any particular problem context, the significance of particular problem elements, and the extent to which they are treated implicitly or explicitly, may vary considerably. For example, as a function of regulation, or perhaps through maturity of the service offering and competition, tariffs may be required to be closely related to costs and an operator’s scope for setting tariffs is thus partly determined by cost allocation. Alternatively the tariff determination may be taking place in a context of little or no regulation and limited competition, in which case the basis for tariffing may be more closely related to ‘what the market can bear’—pricing by value. In both cases we choose to treat the context as implicit, but explicitly model the operator’s scope which has been determined by that context. Tariff setting may be seen (or rather approximated) as a one-off or single stage decision. Thus an operator is posing the question—given my scope for setting values to key tariff parameters, a description of consumer (and possibly competitor) behaviour, what parameter values do I chose to achieve my business objective—for example maximising revenue? Alternatively, tariff determination may be seen as a sequence of related settings, taking place over a sequence of points in time. In this context, there is considerable additional variety in the model, such as the extent and the method by which future uncertainties or unknowns are described, capturing consumer and competitor behaviour and determining suitable business objectives. Note too that in considering a service offering over time, it may be appropriate to consider the concept of service life cycle, where early in the life of a product/service there may be an opportunity to price by value (charge what the market will bear) until competition and possibly regulation brings about a regime where price is more closely related to cost.
A robust methodology for setting tariffs: J T Buchanan
Figure 1. Problem context.
Capturing consumer behaviour can give rise to a number of distinct modelling outcomes. It may be the case that classical elasticity data is available or it may be judged appropriate to model consumers as rational cost minimisers or indeed as risk averse. Deconstructing current tariff offerings in the UK mobile market suggests that the operators believe the domestic consumer to be very risk averse. The nature of the model for consumer behaviour can thus vary considerably, and could even take the form of (numerical) market intelligence or estimates, rules that codify behaviour, or a mixture of behaviours where the consumers are not homogeneous in behaviour.
Objectives In this study the primary objective is to determine a robust, extensible basis from which to explore the determination of tariffs for services and products. The approach should be able to support variety in any or all of the above features and have substantial re-usable components. It should be reasonable in terms of computational demands and support exploration of management scenarios, using as much or as little formal data and structure as is available. Hence it should support different bases for pricing (e.g. cost-based or demand-led), different models of market, consumer and competitor behaviour, different time-scales, different ways of describing the uncertain or unknown, and different business objectives. In the following sections we give an overview of the methodology and follow this with a simple example. This will serve to demonstrate the approach. More technical material is available elsewhere.
Approach 14 Buchanan, J. T., Pricing Communications Services by Sequential Optimisation. Technical Note, Department of Computer Science, University of Strathclyde, Glasgow G1 1XH, 1998.
Most forms of model building—and this is at the core of our approach to the tariff setting problem—involve a number of stages. These can be thought of as specification, formulation, solution and analysis, leading to refinement or rework, and further iterations in some of these processes by
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way of exploring scenarios. In the interests of descriptive simplicity, the method appears to be linear, but in reality there is considerable backtracking among the stages, revisiting assumptions and reworking aspects of the model. We will work through the principles of these stages, as found in our approach. In the tariff setting problem, the specification stage involves determining the relevant problem context, the features of the problem, and the relationships among them. This could include specifying E business objectives, e.g. maximising revenue or market share, E key tariff elements, e.g. bundled talk-time and peak rate charges, E the structure and scope of market offerings, e.g. five or six price plans for different service levels, E the tariff envelopes of interest, e.g. ranges for element values such as peak rate, determined by cost or value considerations, E market demand, e.g. need we represent sensitivity of demand to tariffs, E consumer behaviour, e.g. the use of demand elasticities, risk aversion, cost minimisation, or some mixture of these, E market structure, e.g. the nature of competition or cannibalisation of the customer base, and E the time horizon for the study, e.g. static (one time period) or dynamic (setting tariffs over several time periods). For the pricing problem this general specification stage thus specialises to the first few steps of Figure 2. Given the output from the specification phase, formulation is the process that translates that into a more formal model. This will be of some mathematical, logical or structured form. It could be a set of spreadsheets each of which is an evaluation of one possible pricing policy or it could be a structured expression of the space of alternative policies, creating an envelope within which the operator is interested in finding those best matching business objectives. Depending on the nature of the specification there may be several possible formulations—indeed this is quite common in some decision support work. Making judgements among the formulations as the best to develop is a skilled process and will involve consideration of number of issues, such as ‘best fit’ to the specification, data availability/credibility, ease of software development and support for scenario exploration. Given a formal codification of the problem of interest, there is then the requirement to cast this in a machine-readable form to which some solution algorithm can be applied. For simple enough models, this will be straightforward, but other perhaps more realistic models will involve the technical analyst in making choices among possible solution procedures and control parameters, to achieve quality solutions using acceptable computational resources. All of this corresponds to the ‘Set up computational framework’ step of Figure 2. There are several important elements to the analysis phase. Primary among these is the extent to which the solution can be understood by the domain specialists, in this case network operators or service providers. Does the solution make sense? Are there unsatisfactory elements, which reflect real world features not specified in the formulation, perhaps because they are unsaid or too difficult to codify? Has the exercise so far shown up any features or data which were omitted and which now ought to be included, and vice versa? An example of the real world constraints may be a marketing requirement that price break points have visual or cognitive
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Figure 2. Steps of procedure.
appeal, e.g. a talk time of 60 min rather than the proposed optimum of 63.2. Depending on the underlying mathematics, this may be easy or difficult to incorporate a priori. In the scenario exploration phase the primary concern is in using the developed model to explore a range of options. These will usually reflect concerns about sensitivities or unknowns in the assumptions and data, and will normally be used in a judgmental manner by management. Expectations engendered by modern computer environments require that this process be as fluent as possible, ideally at a pace which supports real-time interaction and analysis.
Modelling consumer behaviour A key element in this work is the underlying model of consumer behaviour, that is, the rates at which consumers join a service or leave it, either to a competitor, another service from the same operator or by dropping out of the market. In addition customers may change the extent to which they
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use a service, perhaps influenced by tariff levels or their own personal/business needs. The range of possible models described in this section reflects different views about this behaviour and its impact on the pricing problem. A priori, there appear to be three possibly related views of consumer behaviour. In a mature market, considerable statistical information will be available, and this could be used to generate input for a pricing model, either as individual data points or through some formulaic summary (best-fit?) of the statistical data. Alternatively, a micro-level understanding of, or hypothesis about, consumer behaviour may be captured in formulaic terms; consumers may be found or deemed to be cost minimisers or demonstrating some form of risk aversion. Finally, consumer behaviour may be specified in a judgmental manner, determined by operator experience and/or market intelligence. This may take the form of a set of independent judgements or it may be able to be assimilated in some approximate or formulaic manner. Note that this variety means that the approach can address problems where an entirely new service is being proposed, as well as circumstances where the interest is in seeking improved returns from existing offerings. How such models of consumer behaviour are actually used is a key element in the pricing methodology, and we proceed to a detailed examination of that below.
An example To illustrate aspects of our approach, we take a problem with tariff features similar to those found, for example, in the UK mobile market. Consider the problem of an operator with the market for a service as described in Figure 3 and with some model of consumer behaviour. The business objective is to maximise revenues by setting tariffs in the light of the market model and consumer behaviour. The relevant tariff parameters in any one package have been determined to be (1) the monthly rental/usage fee ( fG for package i), (2) the ‘free’ talk time associated with the fee (ttG for package i), (3) the marginal costs for peak and off-peak calls for a total talk time in excess of the ‘free’ amount (pkG and opkG respectively for package i). The operator thus has to choose the number of such tariff packages to offer and the values for the parameters within each package. For this illustration we assume that the market for talk time is described by a distribution such as shown in Figure 3, but note that the methodology can cope with tariff-sensitive demand and arbitrary distributions. A possible solution to the problem is shown in Figure 4 where values for all the variables (rental, talk time etc.) have been determined, though only talk time shows in this presentation. In the first analysis, assume that Figure 3 is indeed the market for operator i, i.e. in the first instance we are not concerned with interoperator competition where the market will partition as a function of competitors’ offerings or where it is tariff-sensitive. This generalisation follows at a later stage within the same methodological framework. This is not to say that there are no mathematical, software and interpretation issues to be addressed in particular implementations.
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Figure 3. Talk time distribution.
Figure 4. A solution.
A simultaneous approach to tariff setting One method which could be applied to this example, and by generalisation to others, is to see the operator’s problem as that of determining simultaneously the set of talk times, monthly rentals, peak and off-peak rates for say 4 (or 5 or 6. 2 ) tariff offerings. A programme could be implemented to search across all ‘interesting’ options and find that combination which best meets business objectives, such as revenue maximisation. At some stage this will naturally involve application of the consumer demand model to the market data. While such a brute force enumeration strategy may be workable for some applications it could become much more difficult as the problem complexity increases, for example through more detailed models of consumer or competitor behaviour, or by consideration of the tariff-setting problem over time rather than as a one-off decision. In fact it is also
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unnecessary and more structured heuristics of the form we advocate will bring bonuses such as an improved capability for scenario analysis as well as reduced computational demands. The structured approach will also have more reusable components, as discussed below.
A sequential or serial approach to tariff setting Consider instead an approach which sees the setting of, say, a 5 tariff offering as a sequence of increasingly more general problems, starting with capturing the effect of setting one tariff, and following that with the inclusion of a second, a third and so on. Such a recursive or incremental procedure is at the core of a set of general modelling techniques known as dynamic programming or sequential optimisation.15—16 For suitable problems this approach can be structured to achieve the same effect as simultaneous enumeration but with much less computational effort and with some positive benefits in respect of scenario exploration.
Application of the consumer model
15 Bertsekas, D. P., Dynamic Programming: Deterministic and Stochastic Models. Prentice-Hall, Englewood Chiffs, NJ, 1987. 16 Smith, D. K., Dynamic Programming: A Practical Introduction. Ellis Horwood, New York, 1991. 17 See Bersekes, op cit. Ref 15 or Smith, op cit. Ref 16.
Figure 5. Two tariff packages.
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We will briefly illustrate something of the mechanics of the simultaneous and serial approaches but omit technical detail. To apply a consumer choice model there must naturally be at least two packages on offer. Consider the situation of Figure 5 where two packages are to be placed. This can be viewed in two distinct ways. Firstly, it can be considered as the problem of determining the outcome when tt and tt (and the unseen variables) have been set. Alternatively it can be seen as adding the second package at tt to a situation where the outcome has already been determined when tt was the only offering, as above. The value for both computational processes will be the same but the route by which it is achieved is different. Note that the effects of the distinction in terms of computational effort only really emerge when problems with 3 or more packages are tackled. Given there is now consumer choice—package 1 or package 2—a model for consumer behaviour is now significant, i.e. what criterion/criteria do
A robust methodology for setting tariffs: J T Buchanan
consumers have and what information is applied? Suppose customers are cost minimisers and have perfect information about their monthly talk time, in terms of total and distribution between peak and off-peak. In practical applications, market relativities usually apply to the parameters for each package, for example package 2 offers cheaper per minute rates than package 1, i.e. f/tt(f /tt ,
pk(pk and opk(opk .
For customers with a monthly use less than or equal to tt , it will be optimal to take tariff package 1 while for customers with talk time greater than or equal to tt it will be optimal (cost minimising) to take tariff package 2 subject to certain assumptions. For a customer with talk time between these two monthly offerings, a simple calculation involving peak and off peak rates together with the excess calls (over tt) which are peak and off-peak will readily determine whether package 1 or 2 should be taken. For any given setting of the peak and off-peak rates and proportions there is a simple break point between tt and tt where customers to the left will opt for package 1 and those to the right will opt for package 2. Customers at the break point are indifferent between the two packages. If customers are other than cost minimisers, for example they are risk averse and have some uncertainty about their total talk time and/or proportions of peak and off-peak, a similar analysis will lead to a (different) break point where decisions about best tariff will go one way or the other. Clearly this type of argument can be applied as further tariff packages are added to the set of offerings, with the net effect for the operator being determined by the underlying nature of consumer behaviour. This use of the consumer model is at the core of the simultaneous and serial approaches. It is important to note that the arithmetic outcomes are identical but the process and its properties are distinct.
The incremental calculation Consider again the case of Figure 5 where we view it as adding package 2 to a situation where previously only package 1 was available. The return to the operator with tt added is then the return from tt alone plus some perturbation engendered by bringing in tt. The details of this will depend on the model for consumer behaviour. For the cost minimising case (and actually for many others) the perturbation consists of 2 main parts namely a deduction from the package 1 only value because of customers lost to package 2 and a contribution from package 2 because of those customers who sign up for it in lieu of package 1. The first part is the modification of a previously calculated value; the second is a new piece of data. This general distinction between the simultaneous and serial approaches continues as more tariff packages are considered. Thus for the 3 package problem the simultaneous approach will evaluate the revenue outcome by partitioning the market over the available packages, while the serial approach will apply a perturbation to a 2 package solution. The latter reuses data; the former generates from scratch ignoring earlier calculations.
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Setting optimal tariffs Suppose we move on to be concerned with good combinations of packages, not just evaluating particular combinations. Solving this problem can be related to either the simultaneous or serial approach. The operator seeks an answer to the question ‘Given I wish to use, say, five tariff packages where do I place these offerings to maximise revenue?’ The mechanics of the simultaneous and serial approaches can both be used, in principle, to answer this question. The difference in mechanism, of calculating from scratch versus perturbing previously calculated data, carries over to this phase. The details of this are not important for this exposition, but may be found in standard works on serial optimisation, as referenced above. Implementing the model is tantamount to organising a search over various tariff elements. For the mobile example this means determining fG , ttG , pkG and opkG for each i. In the serial approach it is possible to arrange that this search take place in such a way that any reference to the underlying model of consumer behaviour is postponed until the innermost part of the computation. The effect of this is seen when the search procedure is transformed into software. The consumer model is then isolated into one self-contained module and if it is desirable to explore several potential models then this can be achieved with minimum disruption to the programme, since the bulk of it will remain unchanged apart from the consumer module. This important property is part of the claim to robustness. By comparison, a simultaneous approach may well involve the solution of quite different mathematical models when assumptions about consumer behaviour are modified.
Computational experience A programme was written to undertake such an optimal tariff-setting task for an operator using tariff elements similar to those described above, i.e. rather like some of the UK mobile offerings. A range of options was explored, using 4, 5 and 6 tariff packages where each component package was allowed to take values for its key parameters (such as talk time) within some prescribed range. For example, the first (cheapest) range could be anything from 10 to 30 min per month, set at multiples of 5. Alternatively, the operator can specify constraints on some aspects of the offerings, such as the monthly talk time over 4 packages should be such that it doubles as we go up the range and the unit cost of time purchased should decrease by 25% from package to package. Using a structured heuristic, such as serial optimisation, gives considerable flexibility to the modeller to incorporate the operator’s ideas. Models of this scale can be solved to optimality in a few seconds of PC compute time.
Generalisations For presentation purposes many of the technical details of the incremental approach have been suppressed. However the procedure described above can be used to illustrate the potential for generalisation. At the point where the consumer model is being used to determine the reaction to the tariff offerings, the analysis above only considered those offerings from one
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operator. The same basic mechanics can be used to disambiguate consumer behaviour when there are offerings from more than one operator—as long as this is suitably codified in the problem specification. Again aspects of consumers joining/leaving service are susceptible to the same treatment. Because we are using a structured heuristic and not some simultaneous mathematical model, it is possible to accommodate a considerable variety of codifications of consumer behaviour. This could be formula-driven, statistical, or rule-based—as long as there is some description of the step that takes us from the market description to the appropriate service offering. This is talk time to tariff package in the example above. The same framework can thus be used for modelling a competitive situation. The description above relates to an operator setting tariffs to which a market responds. It therefore corresponds to a one-off decision and says nothing about the problem where a sequence of tariff decisions are taken, perhaps in reaction to competitors’ behaviour or related to a change of basis for pricing—the service life cycle issue. Such a serial decision problem is a ‘natural’ for the sequential or incremental approach described above where we relate decisions at one stage with the consequences and options at a later stage. Above, the stage increment corresponded to adding in another tariff package. For the problem of rolling out tariffs over time, the stage is just time itself, used in whatever increments (quarters, years) is appropriate for the application. To apply this approach obviously requires information over and above that of the simple model above, most notably some model of competitor behaviour. This could take one of very many forms. For example, one operator may generally price at a discount to another and hence the tariff time line of the latter determines that of the former. Alternatively, one operator in considering competitors’ possible behaviour may describe a set of reactions and the likelihood of each of them being pursued. Depending on the descriptive mechanisms used, the problem over time can take one of three main forms. It can be deterministic, with no explicit representation of uncertainty, for example where it is assumed that one operator’s pricing strategy is to discount those of the incumbent. It can be stochastic where events such as competitors’ tactics are enumerated and ascribed likelihoods. Finally it can be adaptive, a generalisation of stochastic where some of the uncertainties are modified over time in the light of experience—a kind of learning behaviour. All of these generalisations can be accommodated within the serial optimisation framework, though the more complex variants may have more substantial computational requirements since the search space, or envelope of interest, may expand in size and be more complex. These and other technical considerations are discussed elsewhere.18
Conclusions
18
Buchanan, op cit. Ref 14.
The methodology is designed to support management analysis of service pricing decisions. It is a flexible and robust framework, able to accommodate considerable variety in the domain features that can be captured, including different models of consumer and competitor behaviour. By virtue of the use of a structured heuristic approach, quite different problems can be addressed. For example a broadband pricing application may require a different set of management control variables, such as bandwidth
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and QoS. As long as the appropriate codifications can be determined, the same approach is valid in principle. Deterministic models, for example of the UK mobile market, have modest computational requirements and through the use of the serial approach fluent scenario analysis is possible. While the approach is nominally about determining optimal tariffs to meet some business objective, note that it is straightforward to constrain the nature of the solution, for example requiring that the mobile solution have talk times of say, 15 min and 60 min, amongst others. Indeed this actually makes the problem simpler from a computational perspective. The approach may thus fairly be described as exploring solutions, as well as prescribing them. The ability to incorporate a wide variety of behavioural models also means that the approach is as applicable to tariff setting in new services as it is to the revision of tariffs in existing services.
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PII: S0308-5961(98)00066-4
A robust methodology for setting tariffs
J T Buchanan Pricing new or existing services is a challenge in the current state of the communications industry, with new industrial structures, fast technical change and varying degrees of competition and regulation. Basically the industry is newly immature, with few good models for, and little data on, the behaviour of consumers or competitors. In this paper we describe the development of a robust methodology for the determination of prices, able to cater for some of the sources of uncertainty in the real world, such as market behaviour. By robust, we mean the ability to re-use the basic model with relatively little change if, for example, the underlying sub-model of consumer behaviour is changed from cost minimising to risk averse, or the basis of pricing is changed from value to cost. 1998 Elsevier Science Ltd. All rights reserved
J. T. Buchanan is with the Department of Computer Science, University of Strathclyde, Livingstone Tower, 26 Richmond Street, Glasgow G1 1XH, UK. He is also a Royal Society Industrial Fellow and works for Analysys Ltd, St Giles’ Court, 24 Castle Street, Cambridge CB3 0AJ, UK. Tel: 0 141 548 3424; fax: 0 141 553 4101; e-mail: [email protected]. 1
There is also considerable interest in the pricing of (transport layer) entities which are more readily associated with the mechanisms enabling services or their associated qualities, e.g. bandwidth and burstiness ratios. See Walker, D., Kelly, F., and Solomon, J., Tariffing in the new IP/ATM environment. Telecommunications Policy, 1997, 21(4), 283–295. Eventually these two exercises will relate, probably through
continued on page 864
In telecommunications, operational pricing considerations used to be limited to the determination of initial connection, periodic rental and usage charges. For some services this is still the case, but the boundaries have become blurred with tariffs now bundling usage with rental and even allowing a trade-off between rental and usage. Other components, such as the number of instruments, and further service bundling, are also increasingly common. With new technology, for example in broadband, experience with pricing is just beginning and is further complicated by new traffic types and quality of service considerations. Note that our interest is in pricing services, i.e. the communications feature or facility as observed by the customer. To add to these complications, relatively little is known about consumer (and competitor) behaviour. Most empirical studies have been longitudinal and econometric in nature, with analysis based on historical data2—4 or indeed offering a record of practice.5—7 In a more prescriptive vein there have been attempts to forecast consumer demand for new services taking into account cross effects. In looking at what is available to assist in the tariff-setting problem, there are three main types of study to be found in the literature and the industry. Firstly, there is the formal economic and econometric work. This may take the form of a normative theory of tariffs, where the concern is to establish a theory of pricing (natural monopoly) services with an emphasis on increasing economic efficiency and achieving acceptable distributive results. Inter alia this will involve establishing a description of market behaviour (usually in terms of elasticities) and also address social/political aspects of service provision, including regulation. While nominally prescriptive it is not clear how these theories can be turned directly into operational tools of use to decision-makers in today’s industry. In the interests of progress the theories tend to make simplifying assumptions about many of the problem features described below, or indeed are not able to incorporate them at all. An alternative approach uses insights from economic theory to give a descriptive trace of the development of competition between 2, later 4, mobile operators in the UK. Prominent in this study are considerations of evolving technology and regulation, and how these relate to industry structure and growth.
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continued from page 863 the usual economic intermediary devices, but that is not an issue pursued in this study. 2 Hackl, P. and Westlund, A. H., Demand for international telecommunication timevarying price elasticity, Journal of Econometrics, 1996, 70(1), 25–39. 3 Cracknell, D., and Knott, M., The measurement of price elasticities—the BT experience, International Journal of Forecasting, 1995, 11(4), 321–329. 4 Bousquet, A., and Ivaldi, M., Optimal pricing of telephone usage: an econometric implementation. Information Economics and Policy, 1997, 9(3), 219–239. 5 Ypsilanti, D., International telecommunication pricing practices and principles: a progress review, OECD Information Computer Communications Policy (Paris), 1995, 36. 6 Paltridge, S., Mobile cellular communication pricing strategies and competition. OECD Information Computer Communications Policy (Paris), 1996, 39. 7 Waverman, L. and Ypsilanti, D., International telecommunication tariffs: charging practices and procedures. OECD Information Computer Communications Policy (Paris), 1994, 34. 8 Weerahandi, S., Hisiger, R. S. and Chien, V., A framework for forecasting demand for new services and their cross effects on existing services. Information Economics and Policy, 1994, 6(2), 143—162. Weerahandi et al. model the substitutive and complementary effects often found in the introduction of new services with parameters estimated from historical consumer choice behaviour. 9 Mitchell, B. M. and Vogelsang, I., Telecommunications Pricing: Theory and Practice. Cambridge University Press, Cambridge, 1991. 10 Valletti, T. M. and Cave, M., Competition in UK mobile communications. Telecommunications Policy, 1998, 22(2), 109–131. 11 Roy, A. and Henry, W., Introduction: special issue on pricing strategy and marketing mix. Journal of Business Research, 1995, 33(3), 183—186. 12 Nagle, T. T. and Holden, R. K., The Strategy and Tactics of Pricing, 2nd Edn. Prentice-Hall, Englewood Cliffs, NJ, 1995. 13 There is already a qualitative understanding of this phenomena (see Hills, T. and Hopkins, M., Tariffing ATM: Maximising the Business Opportunity. Analysys Publications, Cambridge, 1997) but there is a need for this to be augmented by a more analytic and quantitative approach.
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Secondly, many discussions in the industry, certainly away from the academic cotext, concentrate on describing the problem, perhaps with some analysis but usually with little prescription, i.e. focusing on how prices may be set. Presentations putatively on pricing are often more about business strategy, market segmentation and product development—important in themselves, and related to pricing—but not the decisions themselves. Finally, in examining the literature of academic marketing research, some pertinent observations may be made. A recent research collation attempted to assess pricing as a issue of marketing strategy covering a wide range of methodologies, experimental design, econometric analysis and the conceptualisation of the pricing decision as a game. The contributions themselves were subject to analysis in terms of their place in a twoway table, which considered studies as either normative or descriptive and dealing with individual or aggregate behaviour. Of the eight studies, six were descriptive/individual and the remaining two normative/aggregate. This is representative of the marketing literature which is not redolent with analytic prescriptive work of possible use to pricing managers or strategists. Rather the concern is with the description of key problem elements and the use of some accounting data to inform the pricing process.
Elements of the problem Many of the elements, which are potentially part of the tariffing problem, are illustrated in Figure 1. In any particular problem context, the significance of particular problem elements, and the extent to which they are treated implicitly or explicitly, may vary considerably. For example, as a function of regulation, or perhaps through maturity of the service offering and competition, tariffs may be required to be closely related to costs and an operator’s scope for setting tariffs is thus partly determined by cost allocation. Alternatively the tariff determination may be taking place in a context of little or no regulation and limited competition, in which case the basis for tariffing may be more closely related to ‘what the market can bear’—pricing by value. In both cases we choose to treat the context as implicit, but explicitly model the operator’s scope which has been determined by that context. Tariff setting may be seen (or rather approximated) as a one-off or single stage decision. Thus an operator is posing the question—given my scope for setting values to key tariff parameters, a description of consumer (and possibly competitor) behaviour, what parameter values do I chose to achieve my business objective—for example maximising revenue? Alternatively, tariff determination may be seen as a sequence of related settings, taking place over a sequence of points in time. In this context, there is considerable additional variety in the model, such as the extent and the method by which future uncertainties or unknowns are described, capturing consumer and competitor behaviour and determining suitable business objectives. Note too that in considering a service offering over time, it may be appropriate to consider the concept of service life cycle, where early in the life of a product/service there may be an opportunity to price by value (charge what the market will bear) until competition and possibly regulation brings about a regime where price is more closely related to cost.
A robust methodology for setting tariffs: J T Buchanan
Figure 1. Problem context.
Capturing consumer behaviour can give rise to a number of distinct modelling outcomes. It may be the case that classical elasticity data is available or it may be judged appropriate to model consumers as rational cost minimisers or indeed as risk averse. Deconstructing current tariff offerings in the UK mobile market suggests that the operators believe the domestic consumer to be very risk averse. The nature of the model for consumer behaviour can thus vary considerably, and could even take the form of (numerical) market intelligence or estimates, rules that codify behaviour, or a mixture of behaviours where the consumers are not homogeneous in behaviour.
Objectives In this study the primary objective is to determine a robust, extensible basis from which to explore the determination of tariffs for services and products. The approach should be able to support variety in any or all of the above features and have substantial re-usable components. It should be reasonable in terms of computational demands and support exploration of management scenarios, using as much or as little formal data and structure as is available. Hence it should support different bases for pricing (e.g. cost-based or demand-led), different models of market, consumer and competitor behaviour, different time-scales, different ways of describing the uncertain or unknown, and different business objectives. In the following sections we give an overview of the methodology and follow this with a simple example. This will serve to demonstrate the approach. More technical material is available elsewhere.
Approach 14 Buchanan, J. T., Pricing Communications Services by Sequential Optimisation. Technical Note, Department of Computer Science, University of Strathclyde, Glasgow G1 1XH, 1998.
Most forms of model building—and this is at the core of our approach to the tariff setting problem—involve a number of stages. These can be thought of as specification, formulation, solution and analysis, leading to refinement or rework, and further iterations in some of these processes by
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way of exploring scenarios. In the interests of descriptive simplicity, the method appears to be linear, but in reality there is considerable backtracking among the stages, revisiting assumptions and reworking aspects of the model. We will work through the principles of these stages, as found in our approach. In the tariff setting problem, the specification stage involves determining the relevant problem context, the features of the problem, and the relationships among them. This could include specifying E business objectives, e.g. maximising revenue or market share, E key tariff elements, e.g. bundled talk-time and peak rate charges, E the structure and scope of market offerings, e.g. five or six price plans for different service levels, E the tariff envelopes of interest, e.g. ranges for element values such as peak rate, determined by cost or value considerations, E market demand, e.g. need we represent sensitivity of demand to tariffs, E consumer behaviour, e.g. the use of demand elasticities, risk aversion, cost minimisation, or some mixture of these, E market structure, e.g. the nature of competition or cannibalisation of the customer base, and E the time horizon for the study, e.g. static (one time period) or dynamic (setting tariffs over several time periods). For the pricing problem this general specification stage thus specialises to the first few steps of Figure 2. Given the output from the specification phase, formulation is the process that translates that into a more formal model. This will be of some mathematical, logical or structured form. It could be a set of spreadsheets each of which is an evaluation of one possible pricing policy or it could be a structured expression of the space of alternative policies, creating an envelope within which the operator is interested in finding those best matching business objectives. Depending on the nature of the specification there may be several possible formulations—indeed this is quite common in some decision support work. Making judgements among the formulations as the best to develop is a skilled process and will involve consideration of number of issues, such as ‘best fit’ to the specification, data availability/credibility, ease of software development and support for scenario exploration. Given a formal codification of the problem of interest, there is then the requirement to cast this in a machine-readable form to which some solution algorithm can be applied. For simple enough models, this will be straightforward, but other perhaps more realistic models will involve the technical analyst in making choices among possible solution procedures and control parameters, to achieve quality solutions using acceptable computational resources. All of this corresponds to the ‘Set up computational framework’ step of Figure 2. There are several important elements to the analysis phase. Primary among these is the extent to which the solution can be understood by the domain specialists, in this case network operators or service providers. Does the solution make sense? Are there unsatisfactory elements, which reflect real world features not specified in the formulation, perhaps because they are unsaid or too difficult to codify? Has the exercise so far shown up any features or data which were omitted and which now ought to be included, and vice versa? An example of the real world constraints may be a marketing requirement that price break points have visual or cognitive
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Figure 2. Steps of procedure.
appeal, e.g. a talk time of 60 min rather than the proposed optimum of 63.2. Depending on the underlying mathematics, this may be easy or difficult to incorporate a priori. In the scenario exploration phase the primary concern is in using the developed model to explore a range of options. These will usually reflect concerns about sensitivities or unknowns in the assumptions and data, and will normally be used in a judgmental manner by management. Expectations engendered by modern computer environments require that this process be as fluent as possible, ideally at a pace which supports real-time interaction and analysis.
Modelling consumer behaviour A key element in this work is the underlying model of consumer behaviour, that is, the rates at which consumers join a service or leave it, either to a competitor, another service from the same operator or by dropping out of the market. In addition customers may change the extent to which they
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use a service, perhaps influenced by tariff levels or their own personal/business needs. The range of possible models described in this section reflects different views about this behaviour and its impact on the pricing problem. A priori, there appear to be three possibly related views of consumer behaviour. In a mature market, considerable statistical information will be available, and this could be used to generate input for a pricing model, either as individual data points or through some formulaic summary (best-fit?) of the statistical data. Alternatively, a micro-level understanding of, or hypothesis about, consumer behaviour may be captured in formulaic terms; consumers may be found or deemed to be cost minimisers or demonstrating some form of risk aversion. Finally, consumer behaviour may be specified in a judgmental manner, determined by operator experience and/or market intelligence. This may take the form of a set of independent judgements or it may be able to be assimilated in some approximate or formulaic manner. Note that this variety means that the approach can address problems where an entirely new service is being proposed, as well as circumstances where the interest is in seeking improved returns from existing offerings. How such models of consumer behaviour are actually used is a key element in the pricing methodology, and we proceed to a detailed examination of that below.
An example To illustrate aspects of our approach, we take a problem with tariff features similar to those found, for example, in the UK mobile market. Consider the problem of an operator with the market for a service as described in Figure 3 and with some model of consumer behaviour. The business objective is to maximise revenues by setting tariffs in the light of the market model and consumer behaviour. The relevant tariff parameters in any one package have been determined to be (1) the monthly rental/usage fee ( fG for package i), (2) the ‘free’ talk time associated with the fee (ttG for package i), (3) the marginal costs for peak and off-peak calls for a total talk time in excess of the ‘free’ amount (pkG and opkG respectively for package i). The operator thus has to choose the number of such tariff packages to offer and the values for the parameters within each package. For this illustration we assume that the market for talk time is described by a distribution such as shown in Figure 3, but note that the methodology can cope with tariff-sensitive demand and arbitrary distributions. A possible solution to the problem is shown in Figure 4 where values for all the variables (rental, talk time etc.) have been determined, though only talk time shows in this presentation. In the first analysis, assume that Figure 3 is indeed the market for operator i, i.e. in the first instance we are not concerned with interoperator competition where the market will partition as a function of competitors’ offerings or where it is tariff-sensitive. This generalisation follows at a later stage within the same methodological framework. This is not to say that there are no mathematical, software and interpretation issues to be addressed in particular implementations.
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Figure 3. Talk time distribution.
Figure 4. A solution.
A simultaneous approach to tariff setting One method which could be applied to this example, and by generalisation to others, is to see the operator’s problem as that of determining simultaneously the set of talk times, monthly rentals, peak and off-peak rates for say 4 (or 5 or 6. 2 ) tariff offerings. A programme could be implemented to search across all ‘interesting’ options and find that combination which best meets business objectives, such as revenue maximisation. At some stage this will naturally involve application of the consumer demand model to the market data. While such a brute force enumeration strategy may be workable for some applications it could become much more difficult as the problem complexity increases, for example through more detailed models of consumer or competitor behaviour, or by consideration of the tariff-setting problem over time rather than as a one-off decision. In fact it is also
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unnecessary and more structured heuristics of the form we advocate will bring bonuses such as an improved capability for scenario analysis as well as reduced computational demands. The structured approach will also have more reusable components, as discussed below.
A sequential or serial approach to tariff setting Consider instead an approach which sees the setting of, say, a 5 tariff offering as a sequence of increasingly more general problems, starting with capturing the effect of setting one tariff, and following that with the inclusion of a second, a third and so on. Such a recursive or incremental procedure is at the core of a set of general modelling techniques known as dynamic programming or sequential optimisation.15—16 For suitable problems this approach can be structured to achieve the same effect as simultaneous enumeration but with much less computational effort and with some positive benefits in respect of scenario exploration.
Application of the consumer model
15 Bertsekas, D. P., Dynamic Programming: Deterministic and Stochastic Models. Prentice-Hall, Englewood Chiffs, NJ, 1987. 16 Smith, D. K., Dynamic Programming: A Practical Introduction. Ellis Horwood, New York, 1991. 17 See Bersekes, op cit. Ref 15 or Smith, op cit. Ref 16.
Figure 5. Two tariff packages.
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We will briefly illustrate something of the mechanics of the simultaneous and serial approaches but omit technical detail. To apply a consumer choice model there must naturally be at least two packages on offer. Consider the situation of Figure 5 where two packages are to be placed. This can be viewed in two distinct ways. Firstly, it can be considered as the problem of determining the outcome when tt and tt (and the unseen variables) have been set. Alternatively it can be seen as adding the second package at tt to a situation where the outcome has already been determined when tt was the only offering, as above. The value for both computational processes will be the same but the route by which it is achieved is different. Note that the effects of the distinction in terms of computational effort only really emerge when problems with 3 or more packages are tackled. Given there is now consumer choice—package 1 or package 2—a model for consumer behaviour is now significant, i.e. what criterion/criteria do
A robust methodology for setting tariffs: J T Buchanan
consumers have and what information is applied? Suppose customers are cost minimisers and have perfect information about their monthly talk time, in terms of total and distribution between peak and off-peak. In practical applications, market relativities usually apply to the parameters for each package, for example package 2 offers cheaper per minute rates than package 1, i.e. f/tt(f /tt ,
pk(pk and opk(opk .
For customers with a monthly use less than or equal to tt , it will be optimal to take tariff package 1 while for customers with talk time greater than or equal to tt it will be optimal (cost minimising) to take tariff package 2 subject to certain assumptions. For a customer with talk time between these two monthly offerings, a simple calculation involving peak and off peak rates together with the excess calls (over tt) which are peak and off-peak will readily determine whether package 1 or 2 should be taken. For any given setting of the peak and off-peak rates and proportions there is a simple break point between tt and tt where customers to the left will opt for package 1 and those to the right will opt for package 2. Customers at the break point are indifferent between the two packages. If customers are other than cost minimisers, for example they are risk averse and have some uncertainty about their total talk time and/or proportions of peak and off-peak, a similar analysis will lead to a (different) break point where decisions about best tariff will go one way or the other. Clearly this type of argument can be applied as further tariff packages are added to the set of offerings, with the net effect for the operator being determined by the underlying nature of consumer behaviour. This use of the consumer model is at the core of the simultaneous and serial approaches. It is important to note that the arithmetic outcomes are identical but the process and its properties are distinct.
The incremental calculation Consider again the case of Figure 5 where we view it as adding package 2 to a situation where previously only package 1 was available. The return to the operator with tt added is then the return from tt alone plus some perturbation engendered by bringing in tt. The details of this will depend on the model for consumer behaviour. For the cost minimising case (and actually for many others) the perturbation consists of 2 main parts namely a deduction from the package 1 only value because of customers lost to package 2 and a contribution from package 2 because of those customers who sign up for it in lieu of package 1. The first part is the modification of a previously calculated value; the second is a new piece of data. This general distinction between the simultaneous and serial approaches continues as more tariff packages are considered. Thus for the 3 package problem the simultaneous approach will evaluate the revenue outcome by partitioning the market over the available packages, while the serial approach will apply a perturbation to a 2 package solution. The latter reuses data; the former generates from scratch ignoring earlier calculations.
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Setting optimal tariffs Suppose we move on to be concerned with good combinations of packages, not just evaluating particular combinations. Solving this problem can be related to either the simultaneous or serial approach. The operator seeks an answer to the question ‘Given I wish to use, say, five tariff packages where do I place these offerings to maximise revenue?’ The mechanics of the simultaneous and serial approaches can both be used, in principle, to answer this question. The difference in mechanism, of calculating from scratch versus perturbing previously calculated data, carries over to this phase. The details of this are not important for this exposition, but may be found in standard works on serial optimisation, as referenced above. Implementing the model is tantamount to organising a search over various tariff elements. For the mobile example this means determining fG , ttG , pkG and opkG for each i. In the serial approach it is possible to arrange that this search take place in such a way that any reference to the underlying model of consumer behaviour is postponed until the innermost part of the computation. The effect of this is seen when the search procedure is transformed into software. The consumer model is then isolated into one self-contained module and if it is desirable to explore several potential models then this can be achieved with minimum disruption to the programme, since the bulk of it will remain unchanged apart from the consumer module. This important property is part of the claim to robustness. By comparison, a simultaneous approach may well involve the solution of quite different mathematical models when assumptions about consumer behaviour are modified.
Computational experience A programme was written to undertake such an optimal tariff-setting task for an operator using tariff elements similar to those described above, i.e. rather like some of the UK mobile offerings. A range of options was explored, using 4, 5 and 6 tariff packages where each component package was allowed to take values for its key parameters (such as talk time) within some prescribed range. For example, the first (cheapest) range could be anything from 10 to 30 min per month, set at multiples of 5. Alternatively, the operator can specify constraints on some aspects of the offerings, such as the monthly talk time over 4 packages should be such that it doubles as we go up the range and the unit cost of time purchased should decrease by 25% from package to package. Using a structured heuristic, such as serial optimisation, gives considerable flexibility to the modeller to incorporate the operator’s ideas. Models of this scale can be solved to optimality in a few seconds of PC compute time.
Generalisations For presentation purposes many of the technical details of the incremental approach have been suppressed. However the procedure described above can be used to illustrate the potential for generalisation. At the point where the consumer model is being used to determine the reaction to the tariff offerings, the analysis above only considered those offerings from one
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operator. The same basic mechanics can be used to disambiguate consumer behaviour when there are offerings from more than one operator—as long as this is suitably codified in the problem specification. Again aspects of consumers joining/leaving service are susceptible to the same treatment. Because we are using a structured heuristic and not some simultaneous mathematical model, it is possible to accommodate a considerable variety of codifications of consumer behaviour. This could be formula-driven, statistical, or rule-based—as long as there is some description of the step that takes us from the market description to the appropriate service offering. This is talk time to tariff package in the example above. The same framework can thus be used for modelling a competitive situation. The description above relates to an operator setting tariffs to which a market responds. It therefore corresponds to a one-off decision and says nothing about the problem where a sequence of tariff decisions are taken, perhaps in reaction to competitors’ behaviour or related to a change of basis for pricing—the service life cycle issue. Such a serial decision problem is a ‘natural’ for the sequential or incremental approach described above where we relate decisions at one stage with the consequences and options at a later stage. Above, the stage increment corresponded to adding in another tariff package. For the problem of rolling out tariffs over time, the stage is just time itself, used in whatever increments (quarters, years) is appropriate for the application. To apply this approach obviously requires information over and above that of the simple model above, most notably some model of competitor behaviour. This could take one of very many forms. For example, one operator may generally price at a discount to another and hence the tariff time line of the latter determines that of the former. Alternatively, one operator in considering competitors’ possible behaviour may describe a set of reactions and the likelihood of each of them being pursued. Depending on the descriptive mechanisms used, the problem over time can take one of three main forms. It can be deterministic, with no explicit representation of uncertainty, for example where it is assumed that one operator’s pricing strategy is to discount those of the incumbent. It can be stochastic where events such as competitors’ tactics are enumerated and ascribed likelihoods. Finally it can be adaptive, a generalisation of stochastic where some of the uncertainties are modified over time in the light of experience—a kind of learning behaviour. All of these generalisations can be accommodated within the serial optimisation framework, though the more complex variants may have more substantial computational requirements since the search space, or envelope of interest, may expand in size and be more complex. These and other technical considerations are discussed elsewhere.18
Conclusions
18
Buchanan, op cit. Ref 14.
The methodology is designed to support management analysis of service pricing decisions. It is a flexible and robust framework, able to accommodate considerable variety in the domain features that can be captured, including different models of consumer and competitor behaviour. By virtue of the use of a structured heuristic approach, quite different problems can be addressed. For example a broadband pricing application may require a different set of management control variables, such as bandwidth
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and QoS. As long as the appropriate codifications can be determined, the same approach is valid in principle. Deterministic models, for example of the UK mobile market, have modest computational requirements and through the use of the serial approach fluent scenario analysis is possible. While the approach is nominally about determining optimal tariffs to meet some business objective, note that it is straightforward to constrain the nature of the solution, for example requiring that the mobile solution have talk times of say, 15 min and 60 min, amongst others. Indeed this actually makes the problem simpler from a computational perspective. The approach may thus fairly be described as exploring solutions, as well as prescribing them. The ability to incorporate a wide variety of behavioural models also means that the approach is as applicable to tariff setting in new services as it is to the revision of tariffs in existing services.
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