This paper addresses a general class of two-stage stochastic programs with integer recourse and discrete distributions. We exploit the structure of the value function of the second stage integer problem to develop a novel global optimization algorithm. The proposed scheme departs from those in the current literature in that it avoids explicit enumeration of the search space while guaranteeing finite termination. Our computational results indicate superior performance of the proposed algorithm in comparison to the existing literature. Keywords: stochastic integer programming, branch and bound, finite algorithms. 1 Introduction Under the twostage stochastic programming paradigm, the decision variables of an optimization problem under uncertainty are partitioned into two sets. The first stage variables are those that have to be decided before the actual realization of the uncertain parameters. Subsequently, once the random events have presented themselves, further design or operational ...

In this paper we present a framework for solving stochastic programs with complete integer recourse and discretely distributed right-hand side vector, using Gröbner basis methods from computational algebra to solve the numerous second-stage integer programs. Using structural properties of the expected integer recourse function, we prove that under mild conditions an optimal solution is contained in a finite set. Furthermore, we present a basic scheme to enumerate this set and suggest improvements to reduce the number of function evaluations needed.

infrastructure The engineering model [17] from TINA-C is used to describe any distributed system as a set of objects interacting through an abstract infrastructure, the Distributed Processing Environment (DPE). This abstract infrastructure exists on every computer in the network and provides a layer between the computer's native computing and communication environment and the services composed of applications. The mechanisms necessary to implement the transparencies above are hidden in the implementation of the DPE. The infrastructure and functionality provided by the DPE are the same for all hardware platforms and all services. In this abstract infrastructure traders fill an important role. A trader is a repository which contains information about available interfaces and application instances. Each trader has a domain where it is working and a domain can have several traders. Traders interact with each other to make sure that requests for applications can be met independently of whe...

This paper deals with a stochastic Generalized Assignment Problem with recourse. Only a random subset of the given set of jobs will require to be actually processed. An assignment of each job to an agent is decided a priori, and once the demands are known, reassignments can be performed if there are overloaded agents. We construct a convex approximation of the objective function that is sharp at all feasible solutions. We then present three versions of an exact algorithm to solve this problem, based on branch and bound techniques, optimality cuts, and a special purpose lower bound. Numerical results are reported.

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. 1

We review convex approximations for stochastic programs with simple integer recourse. Both for the case of discrete and continuous random variables such approximations are discussed, and representations as continuous simple recourse problems are given. 1

A pension fund has to match the portfolio of long-term liabilities with the portfolio of assets. Key instruments in strategic Asset Liability Management (ALM) are the adjustments of the contribution rate of the sponsor and the reallocation of the investments in several asset classes at various points of time. We formulate a multistage mixed-integer stochastic program to model this ALM process. Special attention is paid to the use of binary variables.