On a Class of Minimum-Cost Problems - Karush, William (Management Science, 1958)
The following type of problem has arisen in various contexts in applications of management science: to determine a program of future levels of activity (e.g., production or employment) subject to known future requirements, which will minimize the total cost of the projected program over the entire planning interval of time. Mathematical methods have been developed for treating variants of this problem, and the purpose of this paper is to present an outline of methods appropriate to problems which share a certain common mathematical form.