A synthesis of stochastic linear programming

Abstract

With the growing application of statistics to many areas of science and engineering it was inevitable that the indeterministic nature of linear programming would be recognized. The first paper in the area of stochastic linear programming was written by one of the pioneers of linear programming, G. B. Dantzig. This paper led to increased interest in the field and was followed by the works of several prominent authors in linear programming. At this point, there was considerable divergence in the problem formulations and in methods of solution. These various formulations are discussed and compared illustrating the lack of communication among the authors. Then, a problem formulation is developed which incorporates many of the formulations of the other authors and recognizes completely the stochastic nature of the problem elements.