A CONTINUOUS OPTIMIZATION MODEL FOR A JOINT PROBLEM OF PRICING AND RESOURCE ALLOCATION

This paper investigates the problem of maximizing therevenue of a telecommunications operator by simultaneously pricingpoint-to-point services and allocating bandwidth in its network, whilefacing competition. Customers are distributed into market segments,i.e. , groups of customers with a similar preference for the services. Thispreference is expressed using utility functions, and customers choosebetween the offers of the operator and of the competition according totheir utility. We model the problem as a leader-follower game betweenthe operator and the customers. This kind of problem has classicallybeen modeled as a bilevel program. A market segmentation is usuallydefined by a discrete distribution function of the total demand for aservice; in this case, the problem can be modeled as a combinatorialoptimization problem. In this paper, however, we motivate the use ofa continuous distribution function and investigate the nonlinear con-tinuous optimization problem obtained in this case. We analyze themathematical properties of the problem, and in particular we give anecessary and sufficient condition for its convexity. We introduce meth-ods to solve the problem and we provide encouraging numerical resultson realistic telecommunications instances of the problem, showing thatit can be solved efficiently