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The scientific exploration of the moon requires that a number of experiments be conducted for the purpose of investigating the many questions and hypotheses posed by nearly every discipline in the scientific community. The broad interest in this effort, the limitations of time and resources for conducting the program, and the complex engineering constraints imposed by the logistics systems justify the development of an effective method of making optimum selection of experiments according to the most meaningful criteria. The developed method provides a determination of alternate optimum solutions from which scientific authority may choose. Basic lunar scientific objectives, as determined by NASA interdisciplinary panels, serve as inputs to the system. The relative worth of each objective according to scientific merit is determined by a stratified, intradisciplinary sample of the scientific community using a modified majority-rule technique. The experiments are then ordered according to their contribution to the ordered objectives. A subjective programming method provides alternate payload choices that optimize the scientific merit of the experiments within the engineering constraints of a lunar payload. An example is presented that simulates the use of an algorithm for selecting an optimism experiment payload. [ABSTRACT FROM AUTHOR]

The article presents a solution to a large-scale traveling-salesman problem which shows that a certain tour of 49 cities, one in each of the 48 states and Washington, D.C., has the shortest road distance. A brief history of the problem is provided. A city in each state including the District of Columbia was selected to try the optimal path method on a large problem. The devices in obtaining solutions include the use of undirected tours, the imposition of linear conditions to characterize the tours, the speeding up of the iterative process and the use of a combinatorial approach.

The article discusses the use of linear programming in U.S. industry. Three aspects of the application of linear programming are presented, including model building, mathematics, and computation. Many real-world industry cases have been related to finding the most economical way of transporting materials between various sources and destinations, and have been solved by special algorithms. In the mathematics of linear programming there are four main areas of research, including computational techniques that take advantage of special features of problems, methods of performing sensitivity analyses for the coefficients of the problem, methods that relate to dynamic problems, and stochastic techniques for handling uncertainty.