A General Algorithm for the Optimal Distribution of Effort

Abstract

The problem of distribution of effort is that of the optimal allocation of a given resource among various activities, that is, maximize ∑ i =1 n f i ( x i ) subject to ∑ i =1 n x i = w , x i ≥ 0. This paper presents an algorithm for obtaining the optimal allocation as a function of w , when the f i are arbitrary piecewise-linear, continuous functions. The method is recursive and appropriate for hand or machine computation. It is an extension of the well-known technique of ordering the segments of all the f i according to decreasing slope which applies in the special case when each f i has decreasing slopes (that is, is marginally decreasing).