Leonid Kantorovich

Leonid Kantorovich was a Soviet mathematician and economist who developed linear programming and applied optimization to economic planning. He shared the 1975 Nobel Memorial Prize in Economic Sciences.

Linear programming: A method for optimizing a linear objective subject to linear constraints. Kantorovich developed the method to solve production and resource-allocation problems.
Production planning: The process of deciding what, how much, and when to produce with available resources. Kantorovich used optimization to coordinate production across Soviet enterprises.
Tjalling Koopmans: A Dutch-American economist who shared the 1975 Nobel Memorial Prize in Economic Sciences with Kantorovich. Koopmans independently developed related methods for analyzing resource allocation.
The Method of Mathematical Economics: Kantorovich’s 1939 work introducing mathematical methods for improving production and resource use. It presented his early formulation of linear programming in response to an industrial problem.
Shadow price: The change in an optimization problem’s best objective value when a resource constraint is relaxed slightly. Kantorovich used these implicit valuations to show how planning models could guide resource use.
Linear inequality: A comparison between linear expressions using an inequality sign. Linear inequalities express the constraints at the heart of his optimization methods.
Cutting stock problem: An optimization problem that minimizes waste when cutting standard stock into required pieces. A 1939 paper applied his methods to reducing waste in plywood cutting.
Vasily Nemchinov: A Soviet economist and statistician who promoted mathematical methods in economic planning. Nemchinov helped advance the institutional acceptance of mathematical economics in the Soviet Union.
Gosplan: The Soviet state planning agency responsible for coordinating national economic plans. His proposals for optimal planning addressed the problems Gosplan was tasked with managing.
Simplex algorithm: An algorithm for solving linear programming problems by moving among feasible corner points. Dantzig’s practical algorithm helped make linear programming computationally usable beyond Kantorovich’s formulations.

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