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1975Sveriges Riksbank Prize · Foundations

Leonid Kantorovich and Tjalling Koopmans

Citation: For their contributions to the theory of optimum allocation of resources.

The key idea

Linear programming. An optimal allocation problem with linear constraints and a linear objective has a dual: shadow prices on resources that emerge from the solution.

The explanation

Kantorovich invented linear programming in 1939 to plan plywood production in the USSR. Koopmans developed activity analysis — modelling production as a choice of activities subject to resource constraints — and showed the duality between the primal optimisation and the resource-shadow-price problem. Together they laid the algorithmic foundation of operations research.

Why Africa should care

Every yield-curve fitting, optimal transport-cost solution, and Kenyan agricultural-allocation model uses LP. The shadow-price interpretation of dual variables is exactly the framework an East African Community trade negotiator should use when arguing about effective tariff equivalents.

How to use it

Whenever you face a resource-allocation problem (budget across ministries, port capacity across imports, fertilizer across counties), formulate the LP. The shadow prices that emerge are the willingness-to-pay for relaxing each constraint — a richer guide than back-of-envelope intuition.

Canonical works

  • Leonid V. Kantorovich (1939) "Mathematical Methods of Organizing and Planning Production"
  • Tjalling C. Koopmans (ed.) (1951) "Activity Analysis of Production and Allocation" Wiley
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