The approximation of stochastic processes by trees is an important topic in multistage stochastic programming. In this paper we focus on improving the approximation of large trees by smaller (tractable) trees. The quality of the approximation is measured by the nested distance, recently introduced in [Pflug, Pfl09]. The nested distance is derived from the Wasserstein distance. It additionally t...

Multistage stochastic linear programming (MSLP) is a powerful tool for making decisions under uncertainty. A deteministic equivalent of MSLP is a large-scale linear program with nonanticipativity constraints. Recently developed infeasible interior point methods are used to solve the resulting linear program. Technical problems arising from this approach include rank reduction and computation of...

I the context of multistage stochastic optimization problems, we propose a hybrid strategy for generalizing to nonlinear decision rules, using machine learning, a finite data set of constrained vector-valued recourse decisions optimized using scenario-tree techniques from multistage stochastic programming. The decision rules are based on a statistical model inferred from a given scenario-tree s...

Multistage stochastic mixed-integer programming is a powerful modeling paradigm appropriate for many problems involving a sequence of discrete decisions under uncertainty; however, they are difficult to solve without exploiting special structures. We present scenario-tree decomposition to establish bounds for unstructured multistage stochastic mixed-integer programs. Our method decomposes the s...

Abstract Given rapid socio-economic development, increasing food demand and decreasing available resources, the challenge of seasonal fluctuations surface water has become a major problem in agricultural sector, causing change consumption from to groundwater resources reduction farmers' income. Therefore, optimal programming cropping pattern is necessary handle such challenges. To accomplish th...

Stochastic programming models are large-scale optimization problems that are used to facilitate decisionmaking under uncertainty. Optimization algorithms for such problems need to evaluate the expected future costs of current decisions, often referred to as the recourse function. In practice, this calculation is computationally difficult as it requires the evaluation of a multidimensional integ...

Electricity swing options are Bermudan-style path-dependent derivatives on electrical energy. We consider an electricity market driven by several exogenous risk factors and formulate the pricing problem for a class of swing option contracts with energy and power limits as well as ramping constraints. Efficient numerical solution of the arising multistage stochastic program requires aggregation ...

A multistage stochastic linear program (MSLP) is a model of sequential stochastic optimization where the objective and constraints are linear. When any of the random variables used in the MSLP are continuous, the problem is infinite dimensional. In order to numerically tackle such a problem we usually replace it with a finite dimensional approximation. Even when all the random variables have fi...

We briefly discuss some history on the development of risk-averse optimization leading into coherent risk measures. For a riskaverse multistage stochastic optimization problem with a finite scenario tree, we introduce a new scenario decomposition method and prove its convergence. We then show how to apply our method to a typical operations management inventory and assembly problem. BIOGRAPHY Dr...