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rie w.p. P1 r2e2 w.p. P2 Rt R₁ = Tnen w.p. Pn 0 w.p. 1-1 Pj Let DER be a vector with components Dj value of the program max ry, = ER/ Show that the optimal s.t. Ayx, 0≤ y ≤D, with variable y = R is equal to JH (x). In addition, the optimal dual solution of the capacity constraints of the previous deterministic linear program is an optimal solution of the problem minμ20 (x).

rie w.p. P1 r2e2 w.p. P2 Rt R₁ = Tnen w.p. Pn 0 w.p. 1-1 Pj Let DER be a vector with components Dj value of the program max ry, = ER/ Show that the optimal s.t. Ayx, 0≤ y ≤D, with variable y = R is equal to JH (x). In addition, the optimal dual solution of the capacity constraints of the previous deterministic linear program is an optimal solution of the problem minμ20 (x).

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Consider the network revenue management model. Suppose that the fare prices are constant (deterministic), that is they are as shown in the first image below of Rt. Let D ∈ ℝ^n be a vector with components Dj = E[t=1 to T∑(Rt,j/rj)]. Show that the optimal value of the program with variable y ∈ ℝ^n is equal to J˜^µ∗T(x). In addition, the optimal dual solution of the capacity constraints of the previous deterministic linear program is an optimal solution of the problem min µ≥0 J˜µT(x). The program in question is the following:
max (r^⊺)y,
s.t. Ay ≤ x,
0 ≤ y ≤ D

rie w.p. P1 r2e2 w.p. P2 Rt R₁ = Tnen w.p. Pn 0 w.p. 1-1 Pj
Transcribed Image Text:rie w.p. P1 r2e2 w.p. P2 Rt R₁ = Tnen w.p. Pn 0 w.p. 1-1 Pj
Let DER be a vector with components Dj value of the program max ry, = ER/ Show that the optimal s.t. Ayx, 0≤ y ≤D, with variable y = R is equal to JH (x). In addition, the optimal dual solution of the capacity constraints of the previous deterministic linear program is an optimal solution of the problem minμ20 (x).
Transcribed Image Text:Let DER be a vector with components Dj value of the program max ry, = ER/ Show that the optimal s.t. Ayx, 0≤ y ≤D, with variable y = R is equal to JH (x). In addition, the optimal dual solution of the capacity constraints of the previous deterministic linear program is an optimal solution of the problem minμ20 (x).
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