Several difficulties arise when multistage optimization problems with linear constraints are extended to an infinite horizon. For linear objectives the weak duality theorem fails, duality gaps exist, complementary slackness is not a sufficient condition for optimality, and the total reward may diverge. This paper presents verifiable conditions on the problem that guarantee the existence of optimal solutions and equilibrium prices for linear and nonlinear objectives. In addition, it is ascertained that the Kuhn-Tucker conditions are sufficient for optimality if additional restrictions are imposed. If the constraints are Leontief and the objective is convex (in a maximization problem), then the existence of an extreme point optimal solution can be verified. The decision taken in each period is an extreme point of the set of solutions that are feasible in that period. The Leontief case also yields a horizon theorem. All sufficiently long finite horizon problems produce a first decision that is optimal for the infinite horizon problem.

A relation < L on a set of real vectors a, b, … is a lexicographic order when a < L b if and only if a ≠ b and for every j such that b j < a j there is an i < j such that a i < b i . A simple and direct derivation is given for a multidimensional utility function whose lexicographically-ordered expected utility vectors preserve an individual's preference order on a set of probability measures. All but one of Hausner's axioms yield an equivalence on the set of preference intervals, and the resulting bet of equivalence classes is shown to account for the hierarchy in the lexicographic structure. A lexicographic utility representation is noted for the finite-dimensional case. When Hausner's other axiom is added, his theorem for lexicographic linear utility is obtained. This theorem is applied to sets of simple and discrete probability measures.

In their comments on “Models of Fact”, Charnes, Cooper, DeVoe and Learner [Charnes, A., W. W. Cooper, J. K. DeVoe, D. B. Learner. 1971. Models of fact and laws of behaviour. Management Sci. 17 367–369.] state that they will avoid a direct reply to my claims and criticisms. In following this precedent, I remark briefly on the pertinent use of references, an important matter in our work.

In a recent article [Rao, A. G., A. Shapiro. 1970. Adaptive smoothing using evolutionary spectra. Management Sci. 17(3) 208–218.] Ambar G. Rao and Arthur Shapiro have proposed a scheme for adaptive smoothing using evolutionary spectra. As the authors admit, this technique demands considerable computer storage and computer time due to the increased number of additions, multiplications and exponentiations when compared to the adaptive smoothing technique proposed by Trigg and Leach [Trigg, D. W., A. G. Leach. 1967. Exponential smoothing with an adaptive response rate. O. R. Quart. 18(1) 53–59.].

An organizational model of academic departments is developed, showing that departments consist of several coexistent structures. Commonly, curricular decisions are made democratically (i.e., by the “collegium”) and professional matters such as tenure are reserved to the senior ranks (an “oligarchy”). The organizational mode for administrative (i.e., implementive) tasks is a division of labor among peers, which varies from minimal to extensive with the degree to which the departmental members engage in service, teaching and/or research activities requiring coordination. The implications of distortions in one structure induced by the threat or use of power in another, and the implications of issues which fall neither in one area nor another but in the intersection between them, are noted.

The rows and columns of an arbitrary coefficient matrix of large numerical problems can often be permuted so that substantial time can be saved in computations. For example, if a large linear programming problem has a suitable block-angular structure, one of the time-saving decomposition algorithms can be used. This article presents a systematic method for effecting such a block-angular permutation. An example and the results of manipulations of matrices with more than 300 rows and 2500 columns are shown.

A model of a type previously used in describing intervals between industrial accidents and between consumer purchases of a product is suggested to describe psychiatric patient rehospitalization times. Two forms of the model are discussed, and estimation procedures for the parameters of each of the two forms are described. The use of the models is illustrated by applying these estimation techniques to a set of data.

In this paper a process analysis model of production in the U.S. Steel Industry is developed and tested. A technology matrix, which represents recent industry input-output structure, is estimated using engineering and metallurgical information. This matrix together with detailed cost, sales and resource capacity data is then used in a linear programming model of short-run resource allocation for the industry as a whole. Linear programming solutions are obtained and compared with available industry statistics for each year in the period 1955–1968. Theil's U statistic is computed to indicate how well the model performs. We conclude that it performs “fairly well” and that it should prove useful in various economic applications.