Linear Programming and the Theory of Games.

Gale, D., Kuhn, & Tucker, A. W. (1951). Linear Programming and the Theory of Games. Activity Analysis of Production and Allocation.

Type

Book chapter

Intellectual base

Review or monograph

Year

1951

Pages cited

317-329

Link

no authoritative link yet

Cited from

mathematics, operations_research

Cited by

5 citations across 4 artifacts.

Primes

• Duality
  • … once the pairing is explicit and the preserved structure is named, theorems proved on one side immediately imply dual theorems on the other (doubling the payoff of each result), optimization problems that are hard in primal form can be recast and solved in dual form (where the Lagrangian dual and the LP dual
• Linear Programming (LP)
  • Sensitivity analysis provides explicit characterization of how the solution changes with parameter variation, supporting robust decision-making.
  • ExxonMobil's refining operations (approximately 20 refineries globally, approximately 4.5-5M barrels/day combined capacity, revenue in tens of billions of dollars) use LP-based optimization intensively — applying the primal-dual LP framework consolidated by Dantzig (1963) — as do all major refining companies (Shell, BP, Chevron, TotalEnergies, Valero, Marathon, Phillips 66, and others) and national oil companies globally.
• Network Flow Models
  • In transportation and logistics, network flow handles freight movement (railroads, trucking, intermodal), airline cargo, pipeline flows (oil, gas), and delivery routing at the tactical and strategic levels; transportation problem formulations are used at thousands of firms globally for shipping decisions, as Dantzig (1963) and the Beckmann-McGuire-Winsten (1956) economics-of-transportation studies developed in detail.
• Sensitivity Analysis (in Operations Research)
  • The tolerance approach to sensitivity analysis, as formalized by Wendell (1985) in linear programming contexts, provides a structured framework for characterizing solution stability across parameter ranges.

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