Stochastic integer programming is more coriplicated than stochastic linear programming, as will be explained for the case of the two-stage stochastic programming model. A survey of the results accomplished in this recent field of research is given.

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Approximation algorithms are the prevalent solution methods in the field of stochastic programming. Problems in this field are very hard to solve. Indeed, most of the research in this field has concentrated on designing solution methods that approximate the optimal solutions. However, efficiency in the complexity theoretical sense is usually not taken into account. Quality statements mostly remain restricted to convergence to an optimal solution without accompanying implications on the running time of the algorithms for attaining more and more accurate solutions.However, over the last twenty years also some studies on performance analysis of approximation algorithms for stochastic programming have appeared. In this direction we find both probabilistic analysis and worst-case analysis. There have been studies on performance ratios and on absolute divergence from optimality.Recently the complexity of stochastic programming problems has been addressed, indeed confirming that these problems are harder than most combinatorial optimization problems. Polynomial time approximation algorithms and their performance guarantees for stochastic linear and integer programming problems have seen increasing research attention only very recently.Approximation in the traditional stochastic programming sense will not be discussed in this chapter. The reader interested in this issue is referred to surveys on stochastic programming, like the Handbook on Stochastic Programming [38] or the text books [3,21,35]. We concentrate on the studies of approximation algorithms which are more similar in nature to those for combinatorial optimization.

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In memory of Åsa HallefjordThe purpose of this paper is to formally describe new optimization models for telecommunication networks with distributed processing. Modern distributed networks put more focus on the processing of information and less on the actual transportation of data than we are traditionally used to in telecommunications. This paper introduces new approaches for modelling decision support at operational, tactical and strategic levels. One of the main advantages of the technological framework we are working within is its inherent flexibility, which enables us to dynamically plan and consider uncertainty when decisions are made. When we present the models, emphasis is placed on the modelling discussions around the shift of focus towards processing, the new technological aspects, and how to utilize flexibility to cope with uncertainty.