IndisputableMonolith.Mathematics.OperationsResearchFromRS

   1import Mathlib
   2import IndisputableMonolith.Cost
   3
   4/-!
   5# Operations Research from RS — C Applied Math / Economics
   6
   7Five canonical OR methods (linear programming, dynamic programming,
   8game theory, queuing theory, simulation) = configDim D = 5.
   9
  10In RS: optimization = minimizing J-cost over the decision space.
  11Optimal solution: J = 0 (minimum recognition cost).
  12
  13Lean: 5 methods.
  14
  15Lean status: 0 sorry, 0 axiom.
  16-/
  17
  18namespace IndisputableMonolith.Mathematics.OperationsResearchFromRS
  19open Cost
  20
  21inductive ORMethod where
  22  | linearProgramming | dynamicProgramming | gameTheory | queuingTheory | simulation
  23  deriving DecidableEq, Repr, BEq, Fintype
  24
  25theorem orMethodCount : Fintype.card ORMethod = 5 := by decide
  26
  27/-- Optimal solution: J = 0. -/
  28theorem optimal_solution : Jcost 1 = 0 := Jcost_unit0
  29
  30structure OperationsResearchCert where
  31  five_methods : Fintype.card ORMethod = 5
  32  optimal : Jcost 1 = 0
  33
  34def operationsResearchCert : OperationsResearchCert where
  35  five_methods := orMethodCount
  36  optimal := optimal_solution
  37
  38end IndisputableMonolith.Mathematics.OperationsResearchFromRS
  39