Operations Research Handbook: Standard Algorithms and by Horst A. Eiselt, Helmut von Frajer (auth.)

By Horst A. Eiselt, Helmut von Frajer (auth.)

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N = min {C42} = c42 = 50-+ s = 2; E = min {z 4;w2} = min {5;5} = 5; x42 = 5; X= i ~] [~ i ~] ;, [~ z4 = 5- 5 = 0; z = (0;0;0;0); w2 =5-5= 0; w = (0;0;0); I = ~; Stop, X = a feas;ble transportat;on plan. 3 The Column Minimum Method Hypotheses The index-sets J and T are defined as: J: = {j}; T: = ~ , for the initial tranportation plan X : x[m X n] xij = 0 v i ,j holds. Description 1: Determine s: = min {j Step Step 2: Determine Step 3: Set Step 4: Define E J} • c rs : = min xrs: = E zr: = zr WS: Ij = WS E - E , J ·.

For pivot-row. Go to step 10. Step 9: ais > 0 ? If yes: Determine the pivot-element in column s as in the Primal Simplex-Algorithm and do one iteration. Go to step 2. If no Stop, for A. * there is no feasible solution of PA. ..

For A*< -4 there is no feasible solution of P~ 2 ) . Example 3 Given the following problem P~ 3 ): P(3). A • max n = 3·x 1 2·x 1 + A·X 2

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