Some Aspects in the Theory of Location |
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amount of input arc k¹,k² assume Chapter commodity concave function conditions for optimal consider the problem convex function convex hull convex set Corollary cost of shipping d₁ d₂ define demand point dual problem duality theory equivalent Euclidean norm feasible shipment patterns find the dual finite iff Geometric Programming given implies intersection point investigated k²,k² Kuhn 18 Lemma Leontief Levy 20 loca location of plant Manhattan norm market form nature of optimal node location notation Note objective function optimal location optimal solution set output particular plant location problem problem of location production function Proof result returns to scale route for shipping rth route Sakashita's single plant location sufficient condition sufficient to consider Suppose Theorem tion transportation capacity constraints transportation cost unit distance variable vector Witzgall 35 x²)² xp+1 Σ Σ χε