Search

The article presents an algorithm for solving a linear integer programming problem and describes the theoretical foundations for a new approach to integer programming. According to the authors, the approach may be described as an extension of the methods using enumeration, but by using a new, more powerful approach based on population statistics. The optimal solution to the integer programming problem in this paper is viewed as one of selecting the optimal function among a certain class of functions which map elements of one set into another. With this method in mind, the authors intend to view the different problems by characterizing the statistical structure of the associated finite class of maps.

Copyright of INFOR is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Consider two isarithmic maps of continuous actual or abstract phenomena in the same area. Research into the character of the relationship may be pursued in various ways depending upon the interests of the investigator and the level of generalization he hopes to obtain. This paper treats some of the cartographic problems inherent in such an investigation and presents the results of an inquiry into the relation between two statistical surfaces in the Great Plains area. If a correlation analysis were undertaken employing data derived from these two maps the resulting index of simple correlation would reveal that the two distributions are in general highly correlated positively, which is not a surprising fact.

A method is presented for estimating the quantitative reliability of isoline maps constructed from observations that vary in space and time. The reliability of isolines is expressed as a variance and equations are developed which relate this variance to observational errors, time errors, positional errors, synopticity errors, primary and secondary interpolation errors, and the space-time rates-of-change and the directions of the gradients of the mapped variable. Equations are also developed for designing a survey whose end product is to be an isoline map of specified variance. These relate the variance to the speeds of travel of the observers, the number of observers the dimensions of the surveyed area, and the type of survey pattern. Four types of survey patterns are illustrated: continuous observations along equi-spaced parallel transects and point observations in aligned rectangular, aligned triangular, and unaligned rectangular patterns.