On The Computational Solution of Linear Programming Problems Involving Almost-Block-Diagonal Matrices

In this paper we wish to attack a problem which arises from the study of weakly coupled economic systems, or alternatively from the study of multi-stage processes with almost-independent stages. Here the “weakness” of coupling and the “almost-independence” is measured by the number of state variables at one stage which depend on the variables of the preceding stage. By means of the functional equation technique of dynamic programming, we shall show that the computational solution can be reduced to that of the computation of a sequence of functions of one variable, in the particular problem we treat.