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 stochastic dominance for general distributions. This allows us to show that several models using quantiles and tail characteristics of the distribution are in harmony with the stoch...

In this chapter we present an approach that leverages linear programming to approximate optimal policies for controlled diffusion processes, possibly with high-dimensional state and action spaces. The approach fits a linear combination of basis functions to the dynamic programming value function; the resulting approximation guides control decisions. Linear programming is used here to compute ba...

In this paper, we consider an allocation problem in multivariate surveys with non-linear costs of enumeration as a problem of non-linear stochastic programming with multiple objective functions. The solution is obtained through Chance Constrained programming. A different formulation of the problem is also presented in which the non-linear cost function is minimised under the precision constrain...

in this paper, a new method is proposed to find the fuzzy optimal solution of fully fuzzy linear programming (abbreviated to fflp) problems. also, we employ linear programming (lp) with equality constraints to find a nonegative fuzzy number vector x which satisfies ax =b, where a is a fuzzy number matrix. then we investigate the existence of a positive solution of fully fuzzy linear system (ffls).

This paper presents a decision making approach for mid-term scheduling of large industrial consumers based on the recently introduced class of Stochastic Dominance (SD)- constrained stochastic programming. In this study, the electricity price in the pool as well as the rate of availability (unavailability) of the generating unit (forced outage rate) is considered as uncertain parameters. Th...

We propose a new modeling and solution method for probabilistically constrained optimization problems. The methodology is based on the integration of the stochastic programming and combinatorial pattern recognition fields. It permits the fast solution of stochastic optimization problems in which the random variables are represented by an extremely large number of scenarios. The method involves ...

The US air fleet is tasked with the worldwide movement of cargo and personnel. Due to a unique mixture of operating circumstances, it faces a large scale and dynamic set of cargo movement demands with sudden changes almost being the norm. Airfleet management involves periodically allocating aircraft to its myriad operations, while judiciously accounting for this uncertainty to minimize operatin...

This study presents a multimodal hub location problem which has the capability to split commodities by limited-capacity hubs and transportation systems, based on the assumption that demands are stochastic for multi-commodity network flows. In the real world cases, demands are random over the planning horizon and those which are partially fulfilled, are lost. Thus, the present study handles dema...

Congestion management in electricity markets is traditionally done using deterministic values of power system parameters considering a fixed network configuration. In this paper, a stochastic programming framework is proposed for congestion management considering the power system uncertainties. The uncertainty sources that are modeled in the proposed stochastic framework consist of contingencie...