On the Status of Multistage Linear Programming Problems

In the first part special cases are presented. Typical of the multistage problems are those encountered in dynamic problems. If the time span is divided into periods, the initial inventory provides the input for activities that occur in the first period or first stage. The output from the first stage provides the inventory input for activities in the second period or stage, etc. [Dantzig, G. B. 1951. Programming of interdependent activities: Mathematical model, chapter II. T. C. Koopmans, ed. Activity Analysis of Production and Allocation. John Wiley and Sons, 19–33. Also Econometrica17 (3–4) (1949).]. In the general case, the need to solve large scale systems is considered, followed by a discussion on solving general block triangular systems that cover a vast majority of practical problems.