Elsevier

Decision Support Systems

Volume 50, Issue 1, December 2010, Pages 281-291
Decision Support Systems

Optimal sequence of free traffic offers in mixed fee-consumption pricing packages

https://doi.org/10.1016/j.dss.2010.08.030Get rights and content

Abstract

Customer migration, a.k.a. churn, is a relevant phenomenon in the telecommunications sector. Service providers may limit the extent of churning by winning back leaving customers through better pricing packages. The proposal of a new pricing package and the subsequent acceptance/rejection decision by the customer trigger a back-and-forth interaction till either the customer accepts the proposal or the providers stop providing a new proposal. The case of a pricing scheme based both on a fee and on a consumption-based rate (with a free traffic level included in the bundle) is analysed, assuming that the customer's demand is statistically known and described by either the exponential or the Rayleigh probability distribution. The service provider may adjust its offer after the customer's rejection by increasing the amount of free traffic. For this scenario we provide: a) the stopping conditions for the maximum amount of free traffic; b) the optimal sequence of proposals (i.e., that maximizing the expected marginal profit of the provider). The analysis is then briefly extended to the case of simultaneous updating of both the free traffic amount and the unit price.

Introduction

The liberalization of telecommunications services has allowed the entry of a number of competing operators in the market. A natural consequence of the end of the monopolistic era is that users are allowed to migrate from an operator to another. Examples of services for which migration is quite a significant phenomenon are the following:

  • Number portability;

  • Carrier selection;

  • ADSL subscription;

  • LLU (local loop unbundling).

The phenomenon of customer migration is not new, having been studied in markets different than telecommunications, e.g., to evaluate the loyalty to a brand or a product and predict the probability of repeated purchases or the value of a current customer [8], [12]. An alternative name for the phenomenon is provider switching, while the erosion of the customer base due to migration is named churn. The intensity by which customers migrate is typically represented by the churn rate, i.e., the proportion of customers that abandons their former operator within a given timeframe (typically one month or one year). Some data concerning the monthly churn rates are reported in Table 1 for a worldwide survey, confirming that operators may lose around a quarter of their customers per year [14].

Churning is quite a damaging phenomenon for the abandoned (losing) provider, due to the loss of the corresponding flow of revenues. Though the customer base may be maintained by the acquisition of new customers, service providers incur much higher expenses when attempting to win new customers than when retaining existing ones. Hence, providers prefer to reduce churn by trying to retain their prospective churners. Computer-assisted churn management systems have been devised for this purpose (see [6]). Essential features of such systems are: churn prediction and identification of potential churners; definition and realization of retention actions towards prospective churners. These features allow to delineate a preventive strategy, whereby customers' dissatisfaction is dealt with prior to the appearance of the intention to migrate. However, if a customer has already asked to leave, the provider has to resort to a reactive strategy. The most relevant tool at the disposal of the provider to win back the customer is the redefinition of the pricing package in order to make it more attractive to the migrating customer. Such redefinition has to be customized for each customer and therefore represents an instance of differentiated pricing (see [5], where an auction-based mechanism is proposed to maximize revenues for a service provider facing different classes of customers who express individual pricing requirements and service levels needs). The redefinition can go through several stages, offering better and better packages (till the economic sustainability limit), should the customer refuse. So, we can imagine a back-and-forth interaction between the service provider and the customer, with the service provider offering a pricing package and the customer deciding whether to accept it or to refuse it, with the rejection leading to a new (and better) package, till the eventual acceptance by the customer or the stoppage of offers by the provider. When redefining the pricing package, the provider has anyway to choose (possibly in an optimal way) the pricing parameters of the package.

In this paper we deal with this problem, namely the optimal redefinition of a parameter of the pricing package. We introduce a model both for the interaction between the provider and the customer, and for the customer's behaviour, and derive the optimal offer at each stage of the back-and-forth sequence of exchanges between the customer and the service provider. Optimality is to be meant as the maximization of the expected revenues. We develop our methodology in the context of the most widely deployed two-part tariffing scheme (see Section 2), whose parameters are the unit price and a free traffic value, defining two scenarios for the traffic generated by customers (see Section 3) and considering the reaction of customers, who can either accept or refuse the offer (see Section 5). In this context we first consider a strategy consisting in updating the free traffic offer only (keeping the unit price fixed), and provide: a) upper bounds for the amount of free traffic that the service provider can offer keeping positive profits, in Section 4; b) the optimal sequence of offers as that maximizing the expected profits at each stage, in Section 6. Numerical examples of such optimal sequences are then reported in Section 7 for some typical instances. In addition we consider in Section 8 a strategy that jointly optimizes both the unit price and the free traffic amount.

Section snippets

Pricing packages

A tool commonly employed by service providers to fight churn is the proper definition of a pricing package attractive for the user. Prospective churners can in fact renege to migrate to a different provider if the prices proposed by their present provider appear to be convenient. It is therefore expected that any provider puts a lot of effort into the definition of the pricing scheme, especially in reply to the declared intention of the customer to leave. In this section we describe a mixed

Customer's traffic distribution

The revenues gained under the pricing package described by expr. (1) depend on the value of the traffic developed by the customer. Since that demand is random, its characterization by a probability density function is needed. Though in principle a characterization for the single customer could be considered, the amount of available statistical data would be quite low for the required accuracy. We assume therefore that, for the purpose of characterizing the traffic demand, customers are

Service provider's profit

The decision by the service provider to retain a customer is based on the expected profitability of that customer. The service provider will put forward a new offer as long as the expected profit (to be obtained from that customer) is positive, as determined by the expected consumption level and the prospective free traffic level. The decision as to the latter is therefore driven by the customer's profitability. In this section we provide expressions for the service provider's profit when the

Estimation of acceptance probability

In addition to modelling the traffic demand by the customer, we must also consider its behaviour in response to the sequence of offers put forward by the provider. In the interaction scheme we have sketched in Section 2, the customer can reply to the provider's offer with the simple accept/reject decision. Hence, its behaviour can be summed up by the probability that it accepts the offer. In this section we propose a model for such probability.

At the k-th offer we describe the event that the

Optimization of profits

The provider's problem is to set the optimal amount of free traffic it is going to offer to the customer. Here the optimal choice is the one maximizing the expected marginal profit of the provider. The provider is then led to optimize its trade-off between potential profit and acceptance probability: the lower is the free traffic offer the larger are the revenues but the smaller is the probability that the customer is going to accept. In order to compute the expected marginal profit at the k-th

Optimal sequences of offers

In this section we provide some numerical results obtained by applying the optimization procedure described in the previous section. In order to present the results in a parametrized way, we group some of the quantities appearing as a whole both in the maximum free levels of exprs. (10), (11), and in the expected marginal profits to be maximized, by resorting to definition (12). In addition, the free traffic offer is always expressed as a percentage of the average traffic μ0 when β = 0 (the no-IC

Joint optimization of unit price and free traffic

In this section we consider the case when the unit price p and the free traffic b are updated simultaneously, at each new round of the sequence of offers. For this strategy we revise the expression of the marginal profit and provide some sample results.

The results obtained so far have been derived under specific assumptions on the consumer's behaviour: its average consumed traffic μX, as per expr. (4), and the probability that the customer will accept the new offer, as per expr. (23). In both

Conclusions

We have derived the optimal strategy for a losing provider to win back churning customers by acting on the tariffing plan. The strategy has been derived for a tariffing scheme where the service provider increases, at each offer round, the free traffic amount in response to the rejection of the previous offer by the customer. In Section 8 we briefly address the case where both the free traffic amount and the unit price are updated in response to a customer turndown. The interaction between the

Maurizio Naldi graduated cum laude in 1988 in Electronic Engineering at the University of Palermo and then received his Ph.D. in Telecommunications Engineering from the University of Rome “Tor Vergata”. After graduation he pursued an industrial career, first at Selenia as a radar designer (1989–1991), and then in the Network Planning Departments of Italcable (1991–1994), Telecom Italia (1995–1998), and WIND (1998–2000) where he was appointed Head, Traffic Forecasting & Network Cost Evaluation

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Maurizio Naldi graduated cum laude in 1988 in Electronic Engineering at the University of Palermo and then received his Ph.D. in Telecommunications Engineering from the University of Rome “Tor Vergata”. After graduation he pursued an industrial career, first at Selenia as a radar designer (1989–1991), and then in the Network Planning Departments of Italcable (1991–1994), Telecom Italia (1995–1998), and WIND (1998–2000) where he was appointed Head, Traffic Forecasting & Network Cost Evaluation Group. In the 1992–2000 period he was active in the standardization bodies (ETSI and ITU), in particular as Associate Rapporteur for Broadband Traffic Measurements and Models at ITU Study Group 2. Since 2000 he is with the University of Rome at Tor Vergata, where he is now an Aggregate Professor.

Andrea Pacifici is an Assistant Professor in operations research at the Engineering Faculty of the University of Rome Tor Vergata. He received a bachelor's degree in Information Engineering and a PhD in operations research both at the University of Rome ‘La Sapienza’. His research is mainly concerned with algorithms design and computational complexity characterisation for combinatorial optimisation problems with applications to scheduling, logistics, manufacturing, telecom and multi-agent systems.

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