ABSTRACT
Everyone is aware that the world is rarely perfectly linear. Yet planning analysis continues to rely heavily on linear models. Linear programming is one of the most attractive tools available for formal planning calculations. Continued reliance upon linear techniques cannot be ascribed to unavailability of good calculation algorithms for nonlinear programmes. On the contrary, powerful calculation techniques that work in the nonlinear case have been available virtually from the inception of mathematical programming. Rather, the propensity toward linearization is to be explained in terms of the difficulty of empirical estimation of nonlinear functions, at least in regions not very close to the range of current experience. In a linear world this constitutes no problem. One can determine precisely the shape of an entire hyperplane from its height and partial derivatives at a single point. But where a surface may bend and curve in a manner which the investigator knows he does not know, it is at best dangerous to draw inferences about distant portions of a surface from empirical information about its behavior in a relatively small neighborhood. Apart from that, linear estimation techniques introduce other difficulties: heavier data requirements, more complex identification criteria, and so on. All in all, therefore, even with the best of intentions, the planner generally is unable to determine the shapes of the relevant nonlinear functions. In these circumstances, recourse to linear programming techniques becomes a great temptation.
