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A multi-stage stochastic integer programming approach for capacity expansion under uncertainty

Ahmed, Shabbir; King, Alan J.; Parija, Gyana

This paper addresses a multi-period investment model for capacity expansion in an uncertain environment. Using a scenario tree approach to model the evolution of uncertain demand and cost parameters, and fixed-charge cost ...

Modeling farmers' response to uncertain rainfall in Burkina Faso

Maatman, Arno; Schweigman, Caspar; Ruijs, Arjan; Vlerk, Maarten H. van der

Farmers on the Central Plateau of Burkina Faso in West Africa cultivate under precarious con-ditions. Rainfall variability is extremely high in this area, and accounts for much of the uncertainty surrounding the farmers? ...

Decomposition algorithms for stochastic programming on a computational grid

Linderoth, Jeff; Wright, Stephen

We describe algorithms for two-stage stochastic linear programming with recourse and their implementation on a grid computing platform. In particular, we examine serial and asynchronous versions of the L-shaped method and ...

Applying the minimum risk criterion in stochastic recourse programs

Riis, Morten; Schultz, Rüdiger

In the setting of stochastic recourse programs, we consider the problem of minimizing the probability of total costs exceeding a certain threshold value. The problem is referred to as the minimum risk problem and is posed ...

Dual stochastic dominance and related mean-risk models

Ogryczak, Wlodzimierz; Ruszczynski, Andrzej

We consider the problem of constructing mean-risk models which are consistent with the second degree stochastic dominance relation. By exploiting duality relations of convex analysis we develop the quantile model of ...

Decomposition of test sets in stochastic integer programming

Hemmecke, Raymond; Schultz, Rüdiger

Graver test sets for linear two-stage stochastic integer programs are studied. It is shown that test sets can be decomposed into finitely many building blocks whose number is independent of the number of scenarios of the ...

Multistage stochastic integer programs

Römisch, Werner; Schultz, Rüdiger

We consider linear mulitstage stochastic integer programs and study their functional and dynamic programming formulations as well as conditions for optimality and stability of solutions. Furthermore, we study the application ...

Stochastic programming duality

A new duality theory is developed for a class of stochastic programs in which the probability distribution is not necessarily discrete. This provides a new framework for problems which are not necessarily bounded, are not ...

Adapting an approximate level method to the two-stage stochastic programming problem

Fábián, Csaba I.

We present a decomposition method for the solution of stwo-stage stochastic programming problems. This is an approximate method that can handle problems with large number scenarios. At the beginning, only rough approximation ...

Tree-sparse convex programs

Steinbach, Marc

Dynamic stochastic programs are prototypical for optimization problems with an inherent tree structure including characteristic sparsity patterns in the KKT systems of interior methods. We propose an integrated modeling ...

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