A Solution Procedure for a Class of Multi-Stage Linear Programming Problems under Uncertainty

摘要

In stochastic linear programming it is necessary to distinguish two major classes of problems. First, the static models for which only one decision has to be made and second the dynamic models which involve sequential decision-making. Since more and more information will be available in succeeding periods, a dynamic model entails an adaptive policy prescription which involves a choice of decision vector for the ith period under all possible alternative realizations of the random variables observed before the ith period. A general multi-stage LP(U superscript 2) model is defined and it is proven that even under quite mild assumptions regarding the stochastic nature of the parameters of the model, it is equivalent to a convex programming problem. An algorithm is developed for solving the above convex programming problem. An approximate method is provided for solving a multi-stage capital budgeting problem under uncertainty. (Author)