13 Subjective Programming

Programming problems are defined by a constraint set and an objective function. The role of the constraint set is to limit the courses of action— the technical word is activities—to those that are feasible, and the role of the objective function is to give the preference relation on the activities. 1 The aim is to find a feasible activity that is preferred or indi¤erent to all other feasible activities. The objective function is assumed to be given as a numerical function on the space of activities; preferred activities correspond to higher values of the function. If the objective function is linear and the constraint set is a polyhedron, the computational methods of linear programming are applicable. Computational techniques are also available for some kinds of problems in which the objective function is not linear, but in any case all such techniques do use a numerically defined objective function. There is, however, a large class of practical problems in which there is no a priori numerical objective function readily available. For example, many of the programming problems that arise in the military establishment are not concerned with the maximization of some definite and measurable quantity, such as dollar profit, but rather with the max-imization of vague concepts like ''military worth.'' Mathematical techniques for dealing with these problems are useless unless military worth is adequately defined and some method is given for measuring it. Nor are they limited to the military establishment; any organization that does not operate on a profit motive (including any government department) is in a similar situation. Even ordinary profit-making business corporations may face such problems when they must decide among activities whose e¤ect on the profit-making mechanism, though vital, is too remote and complex to be e¤ectively calculable. For example, many employee-assignment problems are of this kind; so are those that involve activities whose main e¤ect is on good will. Also, in a business operation there are often multiple motives that may conflict—for example, advancing the interests of a division or of the whole corporation of which it is a part. In such cases it may well be impossible to measure the objective simply in dollar terms.