This paper is dedicated to a study of different extensions of the classical knapsack problem to the case when different elements of the problem formulation are subject to a degree of uncertainty described by random variables. This brings the knapsack problem into the realm of stochastic programming. Four different model formulations are proposed, based on the introduction of probability constra...

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...