Plan, Projection, Policy—Mathematical Programming and Planning Theory

Abstract

The purpose of planning models is to help determine how best to change the controllable variables of a system so that the system will move toward desired goals. In the case of public planning, the welfare criterion or planning objective is not likely to be the same as the objective function driving the behavior of the individual elements of the system. A rigorous definition of a theory of planning is provided through extensions to the linear-programming analysis of the decentralized firm in order to handle (1) the distinction between the planning objectives and behavioral objectives, and (2) the indirect determination of prices by a public agency through policies which modify existing prices sufficiently to achieve a prescribed allocation of resources. A set of three related mathematical programs is identified which yield respectively a target plan, a projection, and an optimal choice of policies. A combination of these programs defines the best solution in terms of the value of the target plan minus the cost of altering the system to achieve that target.