Knowledge that Transforms

A person searches through a population of possible actions, looking for one with high value. He discovers these actions one after another, paying a certain cost each time. On his first encounter with a possible action, the person obtains some preliminary information about its actual value, and at this point he can take the action, he can continue looking, or, at a certain cost, he can perform a test and obtain some more information about its actual value. If he decides to test, then having obtained the additional information he can again either take the action or continue looking. The problem is to conduct this process in such a manner as to maximize expected net value, that is, the expected value of the action finally taken minus the expected total cost of searching and testing. This problem is analyzed and optimal policies are given in the case where the possible actions are regarded as independent selections from a large population. The joint distribution in this population of the actual value, the preliminary information, and the additional information gained from testing, is assumed to be known. The situation where many possibilities are to be selected, subject to a budget constraint on total search and testing cost, is also treated. For this problem asymptotically optimal results are given for large budgets.

Several queuing models are considered in which a job requires a number of different services. The services are performed in any sequence, possibly simultaneously, by a number of servers. Steady state probabilities are found for two service jobs processed by two server systems. In the first system, the two servers work on the same job if they are working. In the second system, the servers may work on different jobs. If server one is working on job k, server two may be working on job k − 1, k, or k + 1 but not on k − 2 or k + 2. In these systems, the servers are specialists. In the third system, the servers may perform either of the two required services. If one has bogged down, the other server does both parts of each job.

A method is developed for optimally selecting capital investments with uncertain returns, under conditions of limited funds and a constraint on the maximum average variance allowed in the final investment package. The concepts involved in the analysis are somewhat related to Markowitz's work on the portfolio problem. Dynamic programming is used to compute solutions.

This paper is concerned with optimal allocation over time of a single resource which is either fixed in supply or only partially renewable at a point in time. Some resources which fall in this category are mineral deposits, ground water, petroleum, wildlife, and fish. A functional equation is obtained from a dynamic programming formulation of the problem. This functional equation is used to derive approximate decision rules for resource use as a function of current supply. The results are applied to ground water storage control and tested empirically by comparison with a decision rule obtained by detailed numerical methods.

A general screening inspection program is developed in which inspection levels and the locations of inspection points are treated as variables. It is shown that the function representing the total of inspection and scrap costs will be minimized by an extreme-point solution, thus the minimum-cost inspection program will lie in a relatively restricted subset of all possible allocations. Application of a computational procedure based on dynamic-programming allows the minimum-cost program to be readily determined for instances in which the requirement for inspection is the maintenance of a specified quality level or when a linear cost may be associated with outgoing defective material.

The problem of control is defined as that of choosing operating rules for members of an organization and enforcement rules for the operating rules so to maximize the organization's objective function. The control problem is sketched for three characteristic types of large organizations: large corporations, governments in their budgetary aspects, and economic systems as a whole. The essential roles of uncertainty and of differential amounts of information in different parts of an organization in the problem of control are brought out. The merits and drawbacks of the price system as a control mechanism are discussed in light of the preceding discussion, with especial reference to the effects of uncertainty.

An algorithm, based on finding a shortest route in a finite directed network, is given for the assembly line balancing problem. Arc lengths are such that it is sufficient to find any path from the origin to destination node containing a minimal number of arcs. Computational results are presented and the algorithm is compared with prior analytical methods of line balancing.

A technique is discussed for framing a reliability model in terms of variables data rather than attribute data. A particular model is developed in terms of a Gamma process; it is believed that such a model may prove applicable to items undergoing long term storage, especially where continuous observations are not feasible. Estimates of the parameters of the model, along with a discussion of prodcedures for control and verification are included.

In this paper we endeavor to show how a management scientist maintains his integrity and individuality while changing from a staff position to a consultant position and eventually to a top executive position in a large company. It is a segment of a longitudinal study and is presented in a special format, which makes it possible to present the data at all. In the introduction we utilize an historical sketch of the management field to show at what time in the development of management science this particular person's career started and, thereby, some of the factors which helped mold his personal and character values. The vicissitudes of the problem are elaborated and background material given for the understanding of the issues involved. We hope to encourage others to present similar segments of longitudinal studies which, we feel, will help people seriously engaged in this field to develop theories based on clinically-gathered data and which will, therefore, be closer to the truth of what really happens under certain conditions in which certain human beings have an impact on large-scale organizations and vice versa.

The elapsed time to complete a scheduled task is expressed as a function of the completion times of the component tasks and the path matrix of the scheddule graph. The schedule function is interpreted geometrically as a polyhedron. If the scheduled activities have random completion times, the probability distribution of the time to complete the entire task is found by integrating over the contours of the polyhedron. Composite schedule functions are represented by algebraic formulae which are applicable in both the probabilistic and non-probabilistic cases. A method for joint control of cost and schedule is presented.