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Linear Prog COP4355_Part_20

Linear Prog COP4355_Part_20 - Chapter 8 The Transportation...

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84 Chapter 8 The Transportation Model TRANSPORTATION MAXIMIZATION PROBLEMS 8.9. Since we are maximizing, the VAM values are the difference between the highest (best) and second highest in the row or column. In placing the values we choose the highest (best) cell in the row or column with the largest first difference (VAM value). The solution is degenerate, since the number of stone cells is less than R + K -1. We have assigned cell (1,1), which has no stone path, the E. To test for optimality we let K 1 = 0. Since we have three Z ij values which are positive, it appears that we can improve the solution. Examination of the stone paths for the three cells (1,4), (2,1), and (2,4), however, shows that all three paths include the E cell in a “removal” position, so that the improvements promised by the positive improvement indices cannot be realized. Selecting the +80 cell (1,4), we move the E and have the next tableau. Sports Car Sedans Subcompacts Downtown Suburban Rural Wholesale 40 70 90 0 4 80 160 110 0 120 40 100 0 7 9 20 3 5 6 6 E 4 2 5 3 6 0 100 50 -120 40 60
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