The service provision problem described in this paper comes from an application of distributed processing in telecommunication networks. The objective is to maximize a service provider's profit from offering computational based services to customers. The services are built from software applications called subservices. The service provider has limited capacity of some resources and therefore must choose from a set of software subservices those he would like to offer. He maximizes profit which depends both on the number of requests met and fixed charges for installing the subservices. A fixed charge is positive when it is charged by the service provider and negative if it is an amount the service provider must pay for example to license the subservice.

Our main interest in this problem comes from it being a subproblem in a scenario decomposition of the service provision problem with stochastic demand. We assume stochasticity is represented in terms of scenarios from a discrete probability distribution. The fixed charges can be interpreted as dual prices on the linking constraints in a variable split that makes the stochastic problem separable in its demand scenarios.

The main contribution of the paper is to give a pseudo-polynomial time algorithm to solve the fixed charge problem and describe how this algorithm can be used in a fully polynomial time approximation scheme. It is also indicated how the results from this paper are used in a decomposition scheme for the stochastic service provision problem.