Knowledge that Transforms

Comparative evaluation of performance, whether of personnel, products, or projects, may be necessary for purposes of selection, assignment, or improvement. Where multiple criteria are involved, it is useful to derive a single measure which will meaningfully distinguish among the competing items. In deriving such a measure, three factors are significant: 1) The specific purpose of the measure. 2) Type and amount of information available. 3) Relationship between various criteria. Neglect of these factors results in needlessly complicated “scoring” systems or in misleading results. The utility of various techniques is reviewed, and application of a Game Theory approach is discussed in detail.

The optimal composition of cattle feed, which can be formulated as a linear programming problem in the case of certainty, is considered when compositions of inputs vary. In the corresponding linear programming formulation the coefficients of the constraints are not constant but can be considered as stochastic. Reformulating the constraints as chance constraints, a nonlinear programming problem results. For an illustrative example this problem is solved using one of Zoutendijk's methods of feasible directions.

The replacement of a machine which deteriorates at a random rate is considered. We measure this deterioration in terms of a cost per unit time—i.e., a cost-density γ(t) where t is the age of the machine. Given the probability distribution of γ(t) and the replacement cost R(c, t) when γ(t) = c, we discuss optimal replacement using two different procedures: (1) replacement at a fixed age (2) replacement when the cost-density reaches a given value Expressions are derived for the resulting costs incurred in using either procedure over a long period of time. Method (2) is in general preferable.

Many large companies and governmental agencies transmit a large quantity of long distance communications between facilities. Most of these organizations reduce the expense of transmitting these communications by leasing private telephone lines instead of using commercial long distance. The monthly expense of leasing telephone lines between two facilities depends upon the number of lines leased and the air miles between facilities; it is independent of usage. For this analysis, the number of lines leased between two facilities is called a link, and the aggregate of all the links leased by an organization is called a network. This paper presents a technique to determine the optimal number of lines to be leased on each link, subject to a limit on the network expense. The technique was developed for Lockheed Missiles & Space Company at Sunnyvale, California, and its implementation has provided management with a more efficient means of controlling the leased line network.

This paper describes an algorithm for the solution of the convex programming problem using the simplex method. The algorithm is computationally very simple, requiring the solution of a single linear programming problem which can be accomplished with only slight modification of existing computer codes for the revised simplex method.

The amount of risk involved is often one of the important considerations in the evaluation of proposed investments. This paper is concerned with the derivation of the type of explicit, well-defined, and comprehensive information that is essential for an accurate appraisal of a risky investment. It is shown how, under certain assumptions, such information in the form of the probability distribution of the present worth, annual cost, or internal rate of return of the proposed investment can be derived. The derivation and use of this information is then illustrated by an example.