Dual Variables

The TRANS Procedure

Dual Variables

Let $\pi_i =1, . . . , n$ be the dual variable values of the source nodes, $\pi_j =1, . . . , m$ be the dual variable values of the destination nodes, and c_ij be the cost of unit flow on the arc between source i and destination j . Then

$r_{ij}=\pi_i-\pi_j-c_{ij}$

is the reduced cost of the arc between nodes i and j. This is the amount by which the total cost increases if flow through arc (ij) is increased by one unit. The total cost decreases by r_ij if the flow through arc (i,j) is decreased by one unit. Dual variables are saved in the OUT= data set.

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