Knowledge that Transforms

This paper calculates some of the operating characteristics of opportunistic replacement and inspection policies. An operating characteristic of a particular policy is a function defined on the stochastic process induced when the policy is implemented. An opportunistic replacement policy makes the replacement of a single uninspected part conditional on the state (good or failed) of one or more continuously inspected (monitored) parts. An opportunistic inspection policy makes the inspection of a non-monitored part conditional on the state (good or failed) of a monitored part. Some of the operating characteristics of these policies examined in this paper are: the expected rate of opportunistic (joint) replacement of the uninspected part and one of the monitored parts; the expected rate of planned replacement of the uninspected part; the probability of at least m failures of a monitored part in the interval [0, t]; the expected rate of opportunistic inspection—inspection of the non-monitored part which is triggered by a failure of the monitored part; and the expected rate of planned inspection of the non-monitored part. These operating characteristics are precisely the information needed to establish a suitable supply policy. They should also be helpful to the maintenance manager in his efforts to predict the relative frequencies of the various maintenance actions. As an example the opportunistic replacement policy is applied to the rocket engines of a hypothetical ballistic missile. Several operating characteristics are then computed and the sensitivity of these operating characteristics to changes in the rocket engine failure rate is exhibited. This illustrative analysis indicates that both the expected rate of opportunistic (joint) replacement of the rocket engines and re-entry vehicle and the expected rate of replacement of the rocket engines due to mandatory replacement are highly sensitive to changes in the rocket engine failure rate. On the other hand, the expected rate of opportunistic (joint) replacement of the rocket engines and the guidance and control system is relatively unaffected by changes in the engine failure rate.

The linear programing algorithms available for optimizing the routing of shipments in multi-plant, multi-destination systems cannot, in the current state of knowledge, be applied directly to the more general problem of determining the number and location of regional warehouses in large-scale distribution networks. This paper outlines a heuristic computer program for locating warehouses and compares it with recently published efforts at solving the problem either by means of simulation or as a variant of linear programing. The heuristic approach outlined in this paper appears to offer significant advantages in the solution of this class of problems in that it (1) provides considerable flexibility in the specification (modeling) of the problem to be solved, (2) can be used to study large-scale problems, that is, complexes with several hundred potential warehouse sites and several thousand shipment destinations, and (3) is economical of computer time. The results obtained in applying the program to small scale problems have been equal to or better than those provided by the alternative methods considered.

Certain Properties of Connectivity Matrices are noted to be similarly applicable to Three Management Science Models which have hitherto been investigated as independent structures: (1) PERT Network Analysis; (2) Parts Explosion Techniques; and (3) Business System Data Flow Analysis. These properties suggest some computational techniques which should be helpful in the analysis of systems described by the three models.

A featured presentation at the Ninth Annual International Meeting of The Institute of Management Sciences, jointly with the Econometric Society, at Ann Arbor, Michigan, September 11, 1962. “A unified science of management.” Is it a matter of faith or of enterprise? A unified science of management conceals the self-reflective paradox. Science is an organized activity. Hence it operates according to some managerial principles. A unified science of management implies a management of science: a science of science, a self-reflective science.

Some of the more recent theoretical and computational developments in non-linear programming are surveyed. The notions of Lagrange multipliers and duality are discussed together with applications of these ideas to scientific and business problems. Moreover, several algorithms for solving quadratic programming problems are reviewed. Explicit rules are given for two of these algorithms, and a simple example is solved by both methods. A large step gradient method for the solution of convex programs is given and one of Gomory's algorithms for integer programming is described. Simple examples are solved using both of these techniques. Linear fractional programming is also discussed briefly.

A postulate common to both the structural-functional theory of social stratification and to organization theory is that hierarchical organization is functionally necessary. An alternative formulation of this postulate—which is probably more heuristic—is that different degrees of hierarchical organization have different consequences for total and partial social systems. The present inquiry into the problem of measuring organizational hierarchy begins with the selection of three central dimensions of organization: the hierarchy of skills, the hierarchy of rewards, and the hierarchy of authority. For each dimension an attempt is then made to develop and codify one or more indicators. The question of the empirical application of the indicators of the hierarchical dimensions in turn leads to a consideration of the problems of index construction, analysis of change over time, analysis of causes and consequences of variation in degree of organizational hierarchy, and of comparative research, whether cross-national, cross-organizational, or experimental in character.

Studies of industrial waiting line problems typically involve determining the proper balance between the amount of service and the amount of waiting for that service. This paper presents some basic results for the case where the study is to be based upon fundamental cost considerations and the assumption of an infinite calling population. Included are a number of economic models and accompanying procedures for determining the level of service which minimizes the total of the expected cost of service and the expected cost of waiting for that service.

An important class of mathematical programming problems is the scheduling of manufacturing and transportation systems. In many cases, the independent variables which describe the manufacturing system are interrelated in a highly nonlinear manner. The majority of the system variables are normally required to represent transportation and allocation. These variables appear linearly and must satisfy a system of equalities which is very large if considered as a single matrix. With such systems it is usually possible to select a relatively small number of the system variables so that when these selected (decision or coupling) variables are held fixed the complete nonlinear system can be partitioned into a number of relatively small independent linear sub-problems. An iterative method for the solution of such problems has been presented [Rosen, J. B. 1963. Convex partition programming. R. L. Graves, P. Wolfe, eds. Recent Advances in Mathematical Programming. McGraw Hill, 159–176.]. The method starts with initial values for the decision variables and solves the separate linear subproblems. The optimal solution to each subproblem is then used to determine that the complete system optimum has been found or to find improved values of the decision variables. This procedure is continued until the complete system optimum has been obtained. Application of the Partition Programming method to a typical large manufacturing-transportation system will be described, including computational experience. This will illustrate that the method can be successfully used for systems which do not satisfy the mathematical requirements which insure convergence of the method to a global optimum. The economic interpretation of an optimal solution will be discussed, showing how the complete system shadow prices are obtained from those of the individual subproblems.

The equilibrium joint probability distribution of queue lengths is obtained for a broad class of jobshop-like “networks of waiting lines,” where the mean arrival rate of customers depends almost arbitrarily upon the number already present, and the mean service rate at each service center depends almost arbitrarily upon the queue length there. This extension of the author's earlier work is motivated by the observation that real production systems are usually subject to influences which make for increased stability by tending, as the amount of work-in-process grows, to reduce the rate at which new work is injected or to increase the rate at which processing takes place.

The paper is divided along the following lines. First, I illustrate the inventory models having Deterministic Demand and then consider the class of Probabilistic Demand Models. Within the latter class, I consider the single period steady state case, and then the N-period dynamic inventory model. For the N-period case, I then report results covering non-zero procurement lead time, demand rate varying each period, joint solution of the inventory-control-production scheduling decision, and a multi-echelon model. Finally, since in the previous consideration of probabilistic demand models, knowledge of the demand probability distribution and its parameters were assumed, I discuss a paper dealing with the use of Bayes estimates.