The Stochastic Single Node Service Provision Problem

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 proot from ooering computational based services to customers. The service provider has limited capacity of some resources and therefore must choose from a set of software applications those he would like to ooer. This can be done in a dynamic manner taking into consideration that demand for the diierent services is uncertain. This problem is examined in the framework of stochastic integer programming. We examine approximations and complexity for the case when demand is described by a discrete probability distribution and one resource limits the number of software applications that may be installed. For the general case a heuris-tic 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 rst results for stochastic problems that the authors are aware of in a direction that is classical in the eld of combinatorial optimization. The results do not follow straightforwardly from the deterministic counterparts of the problem.