Duality gaps which may occur in semi-infinite programs are shown to be interpretable as a phenomenon of an improper representation of the constraint set, u^TP_i \geqq c_i, i \varepsilon I. Thus, any semi-infinite system of linear inequalities has a canonically closed equivalent (with interior...

When a system is described in terms of a linear programming problem max c^Tx with Ax \leqq b, x \geqq 0, study of its properties, e.g., sensitivity analyses, etc., focuses on effects of alterations in the triple (A, b, c) on the properties of the system. These effects are non-linear and generally...

In management contexts, mathematical programming is usually used to evaluate a collection of possible alternative courses of action en route to selecting one which is best. In this capacity, mathematical programming serves as a planning aid to management. Data Envelopment Analysis reverses this...

The July, I960, issue of Management Science contains an English translation of an important original article by L. V. Kantorovich [Kantorovich, L. V. Mathematical Methods of Organizing and Planning Production. Leningrad University, 1939, with a Foreword by A. R. Marchenko (Russian). An English...

Scheduling heating oil production is an important management problem. It is also a complex one. Weather and demand uncertainties, allocation of production between different refineries, joint- and by-product relations, storage limitations, maintenance of minimal supplies and many other factors...

Discussion that was omitted from page 210 of the authors' article "Duality in Semi-Infinite Programs and Some Works of Haar and Caratheódory," Management Science, Vol. 9, No. 2 (January 1963).

An accelerating increase in linear programming applications to industrial problems has made it virtually impossible to keep abreast of them, not only because of their number (and diversity) but also because of the conditions under which many are carried out. Industrial (and governmental) secrecy...

This paper was prepared for presentation on October 15, 1965, as a luncheon address at The Institute of Management Sciences Eastern Meeting held at the Sheraton Hotel, Rochester, New York. Some of our thoughts on this subject were stimulated by a TIMS sponsored methodology symposium on...

In linear programming under uncertainty the two-stage problem is handled by assuming that one chooses a first set of constrained decision variables; this is followed by observations of certain random variables after which another set of decisions must be made to adjust for any constraint...

Recent scientific research has made available a variety of tools which can be brought to bear on managerial problems. One of these tools, which has already proved its worth in practical applications, is linear programming. It is not the purpose of this article to explore the full ramifications...