Leonid Kantorovich was born in Saint Petersburg, Russia in 1912. His distinguished career can be divided into three main phases. The first involved his university education and subsequent period teaching and his research work in Leningrad4 until 1960. At the age of only 14 years he entered Leningrad State University to study mathematics and obtained his degree in 1930 and his doctorate in 1935. Kantorovich’s doctoral thesis on partially ordered function spaces led to the name ‘K-spaces’ in his honour. In the 1930s he taught mathematics at the Leningrad Institute of Construction Engineering and Leningrad State University, where he became a professor in 1934. Between 1948 and 1960 he was head of the department of mathematics at the Academy of Sciences in Leningrad. The second phase of Kantorovich’s career involved his work in Novosibirsk, where from 1960 to 1971 he was deputy director of the Siberian Institute of Mathematics. The final part of his career was spent working in Moscow. From 1971 to 1976, he was head of the Institute of National Economic Management, and from 1976 to 1986 head of the Institute of Systems Analysis of the Academy of Sciences in Moscow.

Kantorovich’s many offices and honours included: full membership of the Academy of Sciences of the USSR in 1964; and the award of the Stalin prize in mathematics in 1949. Together with Nemchinov and Novozhilov, he received the Lenin prize in economics in 1965. Kantorovich was awarded numerous honorary degrees from universities around the world and was a fellow of the Econometric Society from 1973 until his death in 1986. In 1975 he was awarded, jointly with the Dutch-born econometrician–economist Tjalling Koopmans, the Nobel Memorial Prize in Economics ‘for their contributions to the theory of optimum allocation of resources’ (Nobel Foundation, 2004).

Kantorovich was initially trained as a mathematician and during his career as a mathematician–economist made a number of important contributions to various branches of mathematical analysis, including functional analysis (see Kantorovich and Akilov, 1982). His outstanding contribution to economics entailed the development of linear programming and its application to a wide range of practical problems. Linear programming is an analytical technique which involves the formulation and solution of constrained optimisation problems by maximising or minimising a linear function subject to a number of linear and inequality constraints.

Kantorovich first developed a mathematical method for organising and planning production in a plywood factory in a working paper published in Russian by Leningrad State University Press in 1939. This paper was not, however, published in English until 1960 (Kantorovich, 1960). His 1939 paper, with minor alterations, was republished in English in 1964 (Kantorovich, 1964a). This early micro research paved the way for the application of the technique not only to production planning in individual enterprises, but also to a range of problems including transport optimisation (Kantorovich, 1958). However, his most influential and famous work is his 1965 book The Best Use of Economic Resources, which was first published in Russian in 1959. In the book, Kantorovich analysed the problem of the optimum allocation of resources for a socialist economy as a whole. The optimal solution is based on an iterative method of what Kantorovich called ‘resolving multipliers’, or what are essentially shadow prices. His work, which highlighted the importance of a price system, including investment criteria, formed the basis of proposals to decentralise production decisions and improve economic planning in the Soviet economy. In other published work he developed both static and dynamic models of economic planning (for example, Kantorovich, 1964b; 1976b).

Above all else Kantorovich will be remembered for his contribution to the development of linear programming and the application of the technique to the problem of the optimum allocation of resources. Over the course of his career he applied optimisation methods to a range of problems including, in the last phase of his career, the problem of technical progress (Kantorovich, 1976a). His views on the problems of a planned economy, most notably the Soviet economy, can be found in his Nobel Memorial Lecture (Kantorovich, 1989).

(1958), ‘On the Translocation of Masses’, Management Science, 5, October, pp. 1–4; first published in Russian in 1942.

(1960), ‘Mathematical Methods of Organizing and Planning Production’, Management Science, 6, July, pp. 363–422; first published in Russian in 1939.

(1964a), ‘Mathematical Methods of Production Planning and Organization’, in A. Nove (ed.), The Use of Mathematics in Economics, Edinburgh and London: Oliver & Boyd, pp. 225– 80; Kantorovich’s 1939 paper (see above), with minor alterations, first published in Russian in 1959.

(1964b), ‘Further Development of Mathematical Methods and Prospects of Their Application in Economic Planning’, in A. Nove (ed.), The Use of Mathematics in Economics, Edinburgh and London: Oliver & Boyd, pp. 281–321; first published in Russian in 1959.

(1965), The Best Use of Resources, Oxford: Pergamon Press; first published in Russian in 1959. (1976a), ‘Economic Problems of Scientific and Technical Progress’, Scandinavian Journal of Economics, 78 (4), pp. 521–41.

(1976b), Essays in Optimal Planning (ed. L. Smolinski), White Plains, NY: International Arts and Sciences Press.

(1982), Functional Analysis (with G.P. Akilov), 2nd edn, Oxford: Pergamon Press; first published in Russian in 1977.

(1989), ‘Mathematics in Economics: Achievements, Difficulties, Perspectives – Nobel Memorial Lecture, December 11, 1975’, American Economic Review, 79, December, pp. 18–22.

Kantorovich’s many offices and honours included: full membership of the Academy of Sciences of the USSR in 1964; and the award of the Stalin prize in mathematics in 1949. Together with Nemchinov and Novozhilov, he received the Lenin prize in economics in 1965. Kantorovich was awarded numerous honorary degrees from universities around the world and was a fellow of the Econometric Society from 1973 until his death in 1986. In 1975 he was awarded, jointly with the Dutch-born econometrician–economist Tjalling Koopmans, the Nobel Memorial Prize in Economics ‘for their contributions to the theory of optimum allocation of resources’ (Nobel Foundation, 2004).

Kantorovich was initially trained as a mathematician and during his career as a mathematician–economist made a number of important contributions to various branches of mathematical analysis, including functional analysis (see Kantorovich and Akilov, 1982). His outstanding contribution to economics entailed the development of linear programming and its application to a wide range of practical problems. Linear programming is an analytical technique which involves the formulation and solution of constrained optimisation problems by maximising or minimising a linear function subject to a number of linear and inequality constraints.

Kantorovich first developed a mathematical method for organising and planning production in a plywood factory in a working paper published in Russian by Leningrad State University Press in 1939. This paper was not, however, published in English until 1960 (Kantorovich, 1960). His 1939 paper, with minor alterations, was republished in English in 1964 (Kantorovich, 1964a). This early micro research paved the way for the application of the technique not only to production planning in individual enterprises, but also to a range of problems including transport optimisation (Kantorovich, 1958). However, his most influential and famous work is his 1965 book The Best Use of Economic Resources, which was first published in Russian in 1959. In the book, Kantorovich analysed the problem of the optimum allocation of resources for a socialist economy as a whole. The optimal solution is based on an iterative method of what Kantorovich called ‘resolving multipliers’, or what are essentially shadow prices. His work, which highlighted the importance of a price system, including investment criteria, formed the basis of proposals to decentralise production decisions and improve economic planning in the Soviet economy. In other published work he developed both static and dynamic models of economic planning (for example, Kantorovich, 1964b; 1976b).

Above all else Kantorovich will be remembered for his contribution to the development of linear programming and the application of the technique to the problem of the optimum allocation of resources. Over the course of his career he applied optimisation methods to a range of problems including, in the last phase of his career, the problem of technical progress (Kantorovich, 1976a). His views on the problems of a planned economy, most notably the Soviet economy, can be found in his Nobel Memorial Lecture (Kantorovich, 1989).

**Main Published Works**(1958), ‘On the Translocation of Masses’, Management Science, 5, October, pp. 1–4; first published in Russian in 1942.

(1960), ‘Mathematical Methods of Organizing and Planning Production’, Management Science, 6, July, pp. 363–422; first published in Russian in 1939.

(1964a), ‘Mathematical Methods of Production Planning and Organization’, in A. Nove (ed.), The Use of Mathematics in Economics, Edinburgh and London: Oliver & Boyd, pp. 225– 80; Kantorovich’s 1939 paper (see above), with minor alterations, first published in Russian in 1959.

(1964b), ‘Further Development of Mathematical Methods and Prospects of Their Application in Economic Planning’, in A. Nove (ed.), The Use of Mathematics in Economics, Edinburgh and London: Oliver & Boyd, pp. 281–321; first published in Russian in 1959.

(1965), The Best Use of Resources, Oxford: Pergamon Press; first published in Russian in 1959. (1976a), ‘Economic Problems of Scientific and Technical Progress’, Scandinavian Journal of Economics, 78 (4), pp. 521–41.

(1976b), Essays in Optimal Planning (ed. L. Smolinski), White Plains, NY: International Arts and Sciences Press.

(1982), Functional Analysis (with G.P. Akilov), 2nd edn, Oxford: Pergamon Press; first published in Russian in 1977.

(1989), ‘Mathematics in Economics: Achievements, Difficulties, Perspectives – Nobel Memorial Lecture, December 11, 1975’, American Economic Review, 79, December, pp. 18–22.

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