Multi-stage decision optimization under uncertainty depends on a careful numerical approximation of the underlying stochastic process, which describes the future uncertain values on which the decision will depend on. The quality of the scenario model severely affects the quality of the solution of the optimization model. Various approaches towards an optimal generation of discrete-state approxi...

A number of methods for solving multistage stochastic linear programs with recourse decompose the deterministic equivalent [4] to form subproblems based on scenarios (e.g., Rockafellar and Wets [6] and Mulvey and Ruszczyński [5]). Other methods use forms of Benders decomposition to form subproblems based on nodes of the scenario tree (e.g., Birge [1] and Gassmann [2]). Both types of algorithms ...

A model of multistage stochastic programming over a scenario tree is developed in which the evolution of information states, as represented by the nodes of a scenario tree, is supplemented by a dynamical system of state vectors controlled by recourse decisions. A dual problem is obtained in which multipliers associated with the primal dynamics are price vectors that are propagated backward in t...

The aim of this paper is to apply the concept of robust optimization introduced by Bel-Tal and Nemirovski to the portfolio selection problems based on multi-stage scenario trees. The objective of our portfolio selection is to maximize an expected utility function value (or equivalently, to minimize an expected disutility function value) as in a classical stochastic programming problem, except t...

We broaden the theoretical basis for generating scenario trees in multi-stage stochastic programming based on stability analysis. Numerical experience for constructing trees of demand and price scenarios in electricity portfolio management of a municipal power utility is also provided.

1 Abstract. Multiperiod nancial optimization is usually based on a stochastic model for the possible market situations. There is a rich literature about modeling and estimation of continuous-state nancial processes, but little attention has been paid how to approximate such a process by a discrete-state scenario process and how to measure the pertaining approximation error. In this paper we sho...

The solution of a multistage stochastic programming problem needs a suitable representation of uncertainty which may be obtained through a satisfactory scenario tree construction. Unfortunately there is a trade-off between the level of accuracy in the description of the stochastic component and the computational tractability of the resulting scenario-based problem. In this contribution we addre...

Event tree analysis is widely used for reliability and safety analyses as it can be used to specify how the system behaves under various failure conditions. Even though event tree analysis is automated, the construction of event trees is unfortunately manual, and thus error-prone. This paper proposes an automated technique to generate event trees from scenario specifications even before system ...