The stochastic single node service provision problem

Abstract

The service provision problem described in this paper comes from an application of distributed processing in telecommunications networks. The objective is to maximize a service provider's profit from offering computational based services to customers. The service provider has limited capacity and must choose from a set of software applications those he would like to offer. This can be done dynamically taking into consideration that demand for the different services is uncertain. The problem is examined in the framework of stochastic integer programming. Approximations and complexity are examined for the case when demand is described by a discrete probability distribution. For the deterministic counterpart a fully polynomial approximation scheme is known. We show that introduction of stochasticity makes the problem stongly NP-hard, implying that the existence of such a scheme for the stochastic problem is highly unlikely. For the general case a heuristic with a worst-case performance ratio that increases in the number of scenarios is presented. Restricting the class of problem instances in a way that many reasonable practical problem instances will satisfy, allows for the derivation of a heuristic with a constant worst-case performance ratio. These worst-case results are the first results for stochastic programming problems that the authors are aware of in a direction that is classical in the field of combinatorial optimization.