In all cases where the substitution between inputs is subject to jumps and discontinuities, and where the firm faces bottlenecks in the capacity to produce, the appropriate technique of analysis is linear programming, which is essentially a computational method for solving problems that are somehow consigned to engineers in conventional production theory. This technique was largely developed during World War II by US mathematicians and was then rapidly imported after the war into economics, principally by Koopmans, at which time it was discovered that the technique was already known to Soviet planners, who had not however recognized its connections with the long history of marginal analysis in Western production theory.

In his best-known book, Three Essays on the State of Economic Science (1957), Koopmans related linear programming to developments in general equilibrium theory, demonstrating that many of the results of standard economics could be restated with advantage in the language of activity analysis. Since then he has gone on to apply activity analysis to the problem of allocating resources over time, seeking to improve our criteria for evaluating investment projects.

Koopmans received his BA and MA in physics and mathematics from the University of Utrecht in 1932 and 1933. He went on to complete a PhD, again in physics and mathematics, at the University of Leiden in 1936, but his interest had already turned towards economics and particularly econometrics. From 1936 to 1940, he worked at the League of Nations in Geneva, Switzerland. He emigrated to the USA in 1940 and spent the war years as statistician at the Combined Shipping Adjustment Board in Washington, DC. In 1944 he joined an impressive team of young econometricians at the Cowles Commission, attached to the University of Chicago. In 1950 he co-edited Statistical Inference in Dynamic Economic Models, an important milestone in econometric theory, which popularized the use of simultaneous-equation estimates to replace the old single-equation methods of pre-war econometrics. In 1955, when the Cowles Foundation moved to Yale University, he became a professor of economics at Yale, a post from which he retired in 1981. He was president of the Econometric Society in 1950 and the American Economic Association in 1978.

His publications include Activity Analysis of Production and Allocation (1951, co-editor), Studies in Econometric Method (1953, co-editor), and Scientific Papers of Tjalling C Koopmans (1970).