Prove that this formulation has an integer optimal solution ã, that is, ã¡¡ € Z+ V(i, j) € A.
Prove that this formulation has an integer optimal solution ã, that is, ã¡¡ € Z+ V(i, j) € A.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:3)
arcs. We represent with (i, j) the arc that joins i to j. Assume that for any pair of nodes
there is at most one arc joining them. Consider the following logistics problem involving
shipments of a certain product:
Let G = (N, A) be a graph where N is the set of nodes and A is the set of
Max. Eis)ea bijaij
EKEN+ (1) "ik – Eken-(1) Tki = d;, i E V,
0 < xij < Cij, (i, j) E A,
s.t.
where:
is the amount of product that is sent from node i to node j.
• Xij
bij is the profit of sending one unit of product through arc (i, j).
• d; is the offer (if positive) or demand (if negative) of node i, an integer value.
• Cij is the maximum amount of product that can circulate through arc (i, j), a nonnegative
integer value.
• N+(i) = {k E N / (i, k) E A}.
• N-(i) = {k € N / (k, i) E A}.
. Σεn d 0.
Prove that this formulation has an integer optimal solution ã, that is, ñij E Z+ v(i,j) e A.
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