We adopt Benders’ decomposition algorithm to solve scenariobased Stochastic Constraint Programs (SCPs) with linear recourse. Rather than attempting to solve SCPs via a monolithic model, we show that one can iteratively solve a collection of smaller sub-problems and arrive at a solution to the entire problem. In this approach, decision variables corresponding to the initial stage and linear reco...

We adopt Benders’ decomposition algorithm to solve scenariobased Stochastic Constraint Programs (SCPs) with linear recourse. Rather than attempting to solve SCPs via a monolithic model, we show that one can iteratively solve a collection of smaller sub-problems and arrive at a solution to the entire problem. In this approach, decision variables corresponding to the initial stage and linear reco...

We consider risk-averse formulations of multistage stochastic linear programs. For these formulations, based on convex combinations of spectral risk measures, risk-averse dynamic programming equations can be written. As a result, the Stochastic Dual Dynamic Programming (SDDP) algorithm can be used to obtain approximations of the corresponding risk-averse recourse functions. This allows us to de...

We propose a two-stage stochastic variational inequality model to deal with random variables in variational inequalities, and formulate this model as a two-stage stochastic programming with recourse by using an expected residual minimization (ERM) solution procedure. The solvability, differentiability and convexity of the two-stage stochastic programming and the convergence of its sample averag...

We propose an algorithm for multistage stochastic linear programs with recourse where random quantities in di erent stages are independent. The algorithm successively approximates expected recourse functions by building up valid cutting planes to support these functions from below. In each iteration, for the expected recourse function in each stage, one cutting-plane is generated using the dual...

We propose an algorithm for multistage stochastic linear programs with recourse where random quantities in different stages are independent. The algorithm approximates successively expected recourse functions by building up valid cutting planes to support these functions from below. In each iteration, for the expected recourse function in each stage, one cutting plane is generated using the dua...

Motivated by the fixed routes problem, where the objective is to design a set of routes to be operated unchanged over a period of time, we study the vehicle routing problem with stochastic demands. An algorithm is developed based on a stochastic programming model with recourse. Computational experiments show that the algorithm compares favorably to existing algorithms. This research was support...