- Person
- Leonid Kantorovich
- Lived
- 1912–1986
- Field
- Mathematical economics
- From
- Soviet
The story
In 1938 Leonid Kantorovich was a 26-year-old professor of mathematics at Leningrad University, already known for his work in pure mathematics. The Soviet Union was industrialising rapidly, and that year the laboratory of the local plywood trust consulted him about a puzzling production problem. It wanted to know how to schedule eight lathes to make the greatest possible output of five different kinds of plywood in fixed proportions. The trust's engineers could not find a schedule that could not be improved further.
Kantorovich saw that, mathematically, the puzzle was one of maximising a linear function on a convex polytope, a many-sided shape defined by the factory's constraints. The textbook approach of checking the value at every corner was hopeless, because even simple problems had an enormous number of corners. He then realised that the problem was typical: assigning work to equipment, choosing the best use of farmland, cutting materials with little waste, using complex resources and routing transport all had the same mathematical form.
Drawing on ideas from functional analysis, he developed a general solution method he called 'resolving multipliers'. He also gave these multipliers an economic interpretation, as measures of how valuable each scarce resource was, linking the mathematics directly to prices and planning.
In July 1939 Leningrad University Press published his booklet The Mathematical Method of Production Planning and Organization. It set out the basic economic problems, their mathematical form, a sketch of the solution method and the first discussion of its economic sense. In essence it contained the main ideas of linear programming. One of his pupils later called it a historic document, the first mathematical formulation of optimal production planning.
The work was neglected in the Soviet Union and remained unknown in the West for many years. Tjalling Koopmans and George Dantzig, who invented the simplex method in 1947 while planning for the US Air Force, developed the field independently. Only later was Kantorovich recognised as the founder of linear programming, and in 1975 he shared the Nobel Memorial Prize in Economic Sciences with Koopmans. Today linear programming is used across transportation, energy, telecommunications and manufacturing, to plan, schedule, route and assign almost anything.
Why it matters
Linear programming is now used everywhere from airline scheduling to factory planning and supply chains, saving vast amounts of time, money and materials.
About Leonid Kantorovich
Leningrad mathematician who invented linear programming in 1939 while solving a plywood factory’s puzzle, and the only Soviet economist to win the Nobel Prize, in 1975.
More about Leonid Kantorovich
- Leonid Kantorovich showed why rational prices matterKantorovich's book The Best Use of Economic Resources, drafted during the war and published in 1959, linked efficient planning to a rational system of prices.
- Leonid Kantorovich pioneered parallel computing ideasIn the late 1940s Leonid Kantorovich organised parallel calculations on punched-card machines and proposed computer designs based on large-block processing.
- Leonid Kantorovich linked pure maths to practical computingLeonid Kantorovich's paper Functional Analysis and Applied Mathematics showed how abstract mathematics could power numerical methods, earning a State Prize in 1949.
- Leonid Kantorovich reshaped the mathematics of transportLeonid Kantorovich's work on the transportation problem gave mathematics the Monge-Kantorovich problem and the Kantorovich-Rubinstein metric.
- Leonid Kantorovich's methods cut waste in steel sheetsFrom 1948 to 1950, work guided by Leonid Kantorovich at the Leningrad Carriage-Building Works used linear programming to cut steel sheets with less waste.
- Leonid Kantorovich trained a new kind of economistIn Novosibirsk from 1960, Leonid Kantorovich built a laboratory and school that trained a generation of mathematician-economists.
- Leonid Kantorovich kept the Road of Life trucks on the iceDuring the Siege of Leningrad, Leonid Kantorovich calculated safe spacing for supply trucks crossing frozen Lake Ladoga on the Road of Life.
Sources
- Leonid Vitaliyevich Kantorovich: Biographical NobelPrize.org
- Leonid Vital'evich Kantorovich MacTutor, University of St Andrews
- Linear programming Wikipedia
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