A General Algorithm for the Optimal Distribution of Effort

The problem of distribution of effort is that of the optimal allocation of a given resource among various activities, that is, maximize ∑_i=1ⁿf_i(x_i) subject to ∑_i=1ⁿx_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).