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The TRANS Procedure

Dual Variables

Let \pi_i =1, . . . , n be the dual variable values of the source nodes, \pi_j =1, . . . , mbe the dual variable values of the destination nodes, and cij 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 rij 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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