Computational Experience with the Parallel Progressive Hedging Algorithm for Stochastic Linear Programs

Recent advances in computer architecture has started to in uence the eld of numerical optimisation. Several methods to solve large mathematical programming problems which were tried and given up in the last three decades has gained renewed interest. stochastic optimisation is such area which has a huge potential of providing successful results due to its high parallel content. In most practical mathematical programming applications the parameters are assumed to be deterministic (i.e the value of the parameters are known before hand). Due inherent randomness of many practical problems the model builder has to be satis ed with a good approximation. Stochastic optimisation tries to alleviate this type di culty. Consideration of uncertainties dramatically increases the size of resulting mathematical program. When these problems are formulated appropriately the resulting block structure could be exploited for parallization. Stochastic optimisation with recourse is the most commonly used technique to include randomness of parameters to the problem. (see Ermoliev and Wets [4]). Uncertainty is incorporated into the problem by the use of scenarios. Each realization of random quantities is referred to as a scenarios. The two stage stochastic linear programs with recourse is a class of problems which has been studied extensively. In the rst stage of two stage stochastic optimisation problems decisions have to be made which will provide a good solution without the knowledge of what scenario is going to occur in the second stage. At the second stage when the scenario becomes apparent the solution provides a recourse action which will