Kantorovich invented linear programming to allocate a plywood trust's machines

In 1938 the Soviet government's Laboratory of the Plywood Trust called in Leonid Kantorovich, a 26-year-old Leningrad mathematics professor, with a grinding operational question: how should limited machines and raw materials be distributed across production tasks to get the most output? Planners juggled these allocations by hand and by precedence. Kantorovich recognized that maximizing output under resource limits could be posed in mathematical terms — as maximizing a linear function subject to linear constraints.

His 1939 booklet on mathematical methods in production planning and organization showed that problems of economic allocation could all be reduced to this shape, and — the deeper discovery — that the solution came attached to multipliers, later called shadow prices, which measure what each binding constraint is worth. In 'The Best Use of Economic Resources' (1959) he generalized the point: even a planned economy needs prices based on resource scarcity, including an accounting interest rate, if decisions are to be decentralized sensibly.

The West developed the same mathematics independently — Dantzig's simplex method gave it an engine and the name linear programming — and it became the workhorse of industrial planning, from refinery blending to crew scheduling. The Nobel committee awarded Kantorovich the 1975 prize in economic sciences, shared with Tjalling Koopmans, for contributions to the theory of the optimum allocation of resources.

Allocation is an equation, not a committee

He refused to leave 'which machine gets which job' to judgment: a well-posed problem has an answer better than any committee's.

The multipliers were the real discovery — they price the bottleneck, so planners could see what scarcity was worth before spending on it.

The linear form kept the problem solvable with the computing of its era: approximations that compute beat exactness that doesn't.

Arguing that prices must reflect scarcity made the mathematics reformist at home — the equations implied markets.

Reduce the decision to its constraint structure and the scarce thing prices itself. Optimization pays twice: once for the plan, and once for knowing exactly which bottleneck to buy out.

Linear programming became the standard planning tool of industry; refineries, paper mills, airlines and farms run daily on its descendants. At home, Kantorovich's scarcity-price arguments stayed controversial with orthodox planners, but he was elected to the Academy of Sciences, won the Lenin Prize in 1965, and shared the 1975 Nobel memorial prize with Koopmans before his death in 1986.