Telecommunications Planning

Chapter 1 PRICING AND RESOURCE ALLOCATION FOR POINT-TO-POINT TELECOMMUNICATION SERVICES IN A COMPETITIVE MARKET: A BILEVEL OPTIMIZATION APPROACH (P. 1)

Mustapha Bouhtou, Guillaume Erbs and Michel Minoux
Abstract
With the deregulation of the telecommunication markets worldwide, network operators have to develop and offer new services to their clients in order to gain market share. In this context, yield management techniques can be used to optimize tariff computation and resource allocation so that an operator's profit can be maximized. This paper presents a problem of revenue optimization and resource allocation for point-to-point services in a competitive market. The bilevel programming paradigm is used to model the clients' behavior against the tariffs.

Hence, the competition is explicitly taken into account. A mathematical model is introduced. In the process of solving the problem, we focus on exact solution methods using currently available commercial MIP solver. Numerical results are presented illustrating the computational complexity of this approach depending on the data used and the size of the network.

Keywords: telecommunications, revenue management, pricing, resource allocation, bilevel programming, Stackelberg equilibrium

1. Introduction
Many companies in various industries are today successfully using Revenue Management as a means of optimizing their income in a highly competitive environment. These methods were introduced in the late 70's with the deregulation in the airline industry, and aim at trying to offer the right product to the right customer, at the right price, at the right time. This might consist in solving a joint problem of pricing a scarce resource while allocating it optimally. One of the main aspects of the pricing problem is the definition of a market segmentation: customers have different needs and are willing to pay the price for that.

In the airline industry, this translates for example into different perceptions of the length of a flight (one or two legs, etc.), different classes (economic, business, etc.), and seat allocation for each of the defined segments. Another important aspect is to take into account the competition but this makes the problem more difficult to tackle.

As the telecommunications industry has been deregulated, an increasing competition must be accounted for by an operator when setting tariffs for services, in order to keep or gain market share, and the application of Revenue Management is an increasing area of research. The specificities of the telecommunication industry have to be taken into account: an operator can offer different types of services (voice, Internet, mobile, leased lines, interconnection agreements, etc.) and all of these services have specific underlying protocols, network management methods and network topologies.

There is a growing interest on the field of pricing for telecommunication services. An extensive literature review on these subjects is out of the scope of this paper, but the following trends can be observed. There have been numerous papers using game theory in order to achieve an equilibrium between the users' needs and an operator's strategy, for example in the works of Altman and Wynter, 2004 or Basar and Srikant, 2002.

Also, many have proposed schemes to price network services in order to avoid congestion and regulate traffic, for example MacKie-Mason and Varian, 1993 or Kelly, 1997, Kelly et al., 1998.