A new class of fuzzy stochastic optimization models—two-stage fuzzy stochastic programming with Value-at-Risk (FSP-VaR) criteria is built in this paper. Some properties of the two-stage FSP-VaR, such as value of perfect information (VPI), value of fuzzy random solution (VFRS), and bounds of the fuzzy random solution, are discussed. An Approximation Algorithm is proposed to compute the VaR by co...

In this paper, the authors solve the two stage stochastic programming with separable objective by obtaining convex polynomial approximations to the convex objective function with an arbitrary accuracy. Our proposed method will be valid for realistic applications, for example, the convex objective can be either non-differentiable or only accessible by Monte Carlo simulations. The resulting polyn...

In this paper, a stochastic two-stage model is offered for optimization of the day-ahead scheduling of the microgrid. System uncertainties including dispatchable distributed generation and energy storage contingencies are considered in the stochastic model. For handling uncertainties, Monte Carlo simulation is employed for generation several scenarios and then a reduction method is used to decr...

This paper presents a framework for the design and optimization of multi-product batch processes under uncertainty with environmental considerations. The uncertainties and environmental impacts are discussed. The profit and environmental impacts are considered as biobjectives for batch plant design. The problem, thus, is formulated as a multi-objective stochastic programming problem. It can be ...

Stochastic programming is recognized as a powerful tool to help decision making under uncertainty in financial planning. The deterministic equivalent formulations of these stochastic programs have huge dimensions even for moderate numbers of assets, time stages and scenarios per time stage. So far models treated by mathematical programming approaches have been limited to simple linear or quadra...

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.

In this paper we apply stochastic dual dynamic programming decomposition to a nonconvex multistage stochastic hydrothermal model where the nonlinear water head effects on production and the nonlinear dependence between the reservoir head and the reservoir volume are modeled. The nonconvex constraints that represent the production function of a hydro plant are approximated by McCormick envelopes...

This paper addresses a general class of capacity planning problems under uncertainty, which arises, for example, in semiconductor tool purchase planning. Using a scenario tree to model the evolution of the uncertainties, we develop a multi-stage stochastic integer programming formulation for the problem. In contrast to earlier twostage approaches, the multi-stage model allows for revision of th...

In this paper we develop a practical primal interior decomposition algorithm for two-stage stochastic programming problems. The framework of this algorithm is similar to the framework in Mehrotra and Özevin [17, 18] and Zhao [30], however their algorithm is altered in a simple yet fundamental way to achieve practical performance. In particular, this new algorithm weighs the log-barrier terms in...

This paper proposes a novel decision making framework for an electricity retailer to procure its electric demand in a bilateral-pool market in presence of charging and discharging of electric vehicles (EVs). The operational framework is a two-stage programming model in which at the first stage, the retailer and EV aggregator do their medium-term planning. Determination of retailer's optimum sel...