Knowledge that Transforms

Among network techniques recently widely employed in program management, Pert is addressed to the problem of assessing the manager's chances of completing a project on time. Theory and monte carlo simulation have shown that the Pert method yields results which are biased high, and this paper discusses a real example involving conditions under which the bias is very large. The manager is thus grossly misled into thinking his chances are very good, when in reality they are very poor. If the manager's network has multiple parallel paths with relatively equal means and large variances, Pert calculations will be considerably biased. Simulation can be utilized to estimate the distribution of completion time in this case, and guide the manager in appraising and controlling his chances of completion.

The basic condition underlying the entire dimension of scientific research is the firm belief in the causal inevitability of natural phenomena. It is the scientist's job to seek to identify the causes of such phenomena. He is furthermore expected to discover the interrelationships of cause and effect. Accordingly we can assert that scientific research, especially as it has developed after the Renaissance, can be considered to be primarily the practical application of the principle of causation based on observation, analysis (deductive or inductive), experiment, formation of hypothesis, and the formulation of theories and models.

The purpose of this note is to point out that the proof in Appendix 1 of Feeney and Sherbrooke [Feeney, G. J., C. C. Sherbrooke. 1966. (s − 1, s) Inventory policy under compound poisson demand. Management Sci. 12(5, January) 391–411] can be adapted to generalize to arbitrary service a queueing formula known for exponential service [Saaty, T. L. 1961. Elements of Queueing Theory. McGraw-Hill, New York, 121.].

The advertising industry is likely to be three times its current size by 1985. In view of current labor force trends, it is unlikely that the advertising industry will be able to attract a sufficient number of people to service that volume of advertising. The key to servicing this large volume of advertising is likely to be the management sciences which will provide the basis for increased productivity in the advertising industry. On the basis of past technological trends in the industry, this paper attempts to make some predictions as to the kinds of activities that are likely to be required in the agency of the future and the kinds of skills and talents that will be needed to man the agency of the future.

PERT and Critical Path techniques are enjoying exceptionally broad application in industrial and military activities. These techniques and their application have without doubt contributed significantly to better planning, control, and general organization of many programs. Although some currently used PERT computations take account of the variation in the completion times of individual operations, the methods used are approximate and are known to lead to (a) optimistic project completion times and (b) misidentifications of “critical paths.” In this paper the effect of these approximations is assessed and an unbiassed statistical distribution theory for PERT developed. Both analytic theory and numerical analysis are used to achieve this but in certain situations approximate evaluations by Monte Carlo have to be made. Moreover, a new classification of PERT networks is presented along with two methods of analysis which do not have the deficiencies noted above. The classification system delineates clearly between “uncrosaed,” “crossed,” and “mixed networks.”

The methods of R. E. Gomory for the iterative solution of the mixed-integer linear programming problem are extended directly to the case where some or all of the variables are nonuniformly discrete, i.e., they are restricted to assume values from certain specified sets of unequally-spaced constants. The algorithm presented is shown to converge in a finite number of steps for a discrete-valued objective function.

A wide variety of branch and bound algorithms have recently been described in the literature. This paper provides a generalized description of such algorithms. An objective is to demonstrate the wide applicability of branch and bound to combinatorial problems in general. Two existing algorithms are used as illustrations and a discussion of computational efficiency is included.

Systems analyses frequently require estimates of the average time that it takes to perform repetitive tasks. These time estimates may be easy to obtain; for example, if one man is performing a single operation, then a simple division of his total working time by the frequency of the task repetition, gives an estimate of the average performance time. However, in many instances, work consolidation requires that individuals be called upon to perform several different operations. For example, crews may be sent into the field to carry out a number of different tasks, for which the relative rate of occurrence may change from day to day. This introduction of multiple operations implies that the required separate time estimates can no longer be obtained by a simple division. This paper discusses linear model estimation of the average time taken to perform specific tasks; the estimation is possible even when a number of different tasks are performed by an individual or group. The models are based on the conceptual relation that the time taken to perform a task multiplied by the rate of occurrence in the considered time period, and summed over all possible tasks, should equal the total time taken by all tasks. Estimation is also possible when direct observations are difficult to obtain (as in stopwatch procedures) because the proposed models do not require direct time observations but rather utilize linear combinations of the individual time parameters. An actual application is discussed.

A discussion of the importance of a direct method in obtaining all the solutions of a transportation problem, and in obtaining solutions of more general problems, is followed by a discussion of methods of reduced matrices in which the transportation matrix is reduced, by a series of subtractions from rows and columns, to a transformed matrix to which the orthogonality condition is applicable. The direct method proceeds in a series of simple steps to the determination of zero terms having associated x ij values which eventually satisfy the row and column equations. Formal and informal versions are presented and application is made to several general problems.

The seismic reflection method employed in petroleum exploration is described, after which the problem of selecting the optimum cell size for a uniform rectangular seismic reconnaissance search pattern is stated in terms of elementary search theory. The search effectiveness for each pattern is estimated by a Monte Carlo approach due to the probabilistic nature of target geometry. The problem of allocating a limited amount of search effort to a number of regions to be searched simultaneously is formulated as a dynamic programming problem in which the decision variables are the search pattern parameters and the inter-shot point spacing along the survey lines. The approach is easily generalized so that pattern morphology and orientation also become decision variables.