Probabilistic or stochastic programming is a framework for modeling optimization problems that involve uncertainty.In this paper, we focus on multi-objective linear programmingproblems in which the coefficients of constraints and the righthand side vector are fuzzy random variables. There are several methodsin the literature that convert this problem to a stochastic or<b...

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...

This paper addresses a discontinuous multi-activity tour scheduling problem under demand uncertainty and when employees have identical skills. The problem is formulated as a two-stage stochastic programming model, where first-stage decisions correspond to the assignment of employees to weekly tours, while second-stage decisions are related to the allocation of work activities and breaks to dail...

Multistage stochastic integer programming (MSIP) combines the difficulty of uncertainty, dynamics, and non-convexity, and constitutes a class of extremely challenging problems. A common formulation for these problems is a dynamic programming formulation involving nested cost-to-go functions. In the linear setting, the cost-to-go functions are convex polyhedral, and decomposition algorithms, suc...

This paper addresses the class of nonlinear mixed integer stochastic programming problems. In particular, we consider two-stage problems with nonlinearities both in the objective function and constraints, pure integer first stage and mixed integer second stage variables. We exploit the specific problem structure to develop a global optimization algorithm. The basic idea is to decompose the orig...

This chapter reviews multi-stage financial planning models, with a focus on practical approaches for optimizing investors’ performance over time. We discuss two major frameworks for constructing financial planning models: 1) policy rule simulation and optimization; and 2) multi-stage stochastic programming. We advocate an integrated approach, in which a stylized stochastic program helps the inv...

In this paper, bi-level programming is proposed for designing a competitive supply chain network. A two-stage stochastic programming approach has been developed for a multi-product supply chain comprising a capacitated supplier, several distribution centers, retailers and some resellers in the market. The proposed model considers demand’s uncertainty and disruption in distribution centers and t...

In this paper we discuss time consistency of multi-stage risk averse stochastic programming problems. We approach the concept of time consistency from an optimization point of view. That is, at each state of the system optimality of a decision policy should not involve states which cannot happen in the future. We also discuss a relation of this concept of time consistency to deriving dynamic pr...