Stochastic integer programming

no abstract

Exact solutions to a class of stochastic generalized assignment problems

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 subset of jobs which have to be executed is 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. (c) 2005 Elsevier B.V. All rights reserved

Simple integer recourse models : convexity and convex approximations

We consider the objective function of a simple recourse problem with fixed technology matrix and integer second-stage variables. Separability due to the simple recourse structure allows to study a one-dimensional version instead. Based on an explicit formula for the objective function, we derive a complete description of the class of probability density functions such that the objective function is convex. This result is also stated in terms of random variables. Next, we present a class of convex approximations of the objective function, which are obtained by perturbing the distributions of the right-hand side parameters. We derive a uniform bound on the absolute error of the approximation. Finally, we give a representation of convex simple integer recourse problems as continuous simple recourse problems, so that they can be solved by existing special purpose algorithms

Modelling aspects of distributed processing in telecommunication networks

The purpose of this paper is to formally describe new optimization models for telecommunication networks with distributed processing. Modem 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

Modelling aspects of distributed processing in telecommunication networks

The purpose of this paper is to formally describe new optimization models for telecommunication networks with distributed processing. Modem 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