Improved Primal Simplex Algorithms for Shortest Path Assignment And Minimum Cos
Improved Primal Simplex Algorithms for Shortest Path Assignment And Minimum Cos
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If the blocking arc is unique, then it leaves the basis. If there are more than one blocking arcs, then the algorithm selects the leaving arc to be the last blocking arc encountered in traversing W along its orientation starting at node w. For example, in Figure 1, the entering arc is (9, 10), the blocking arcs are (2, 3) and (7, 5), and the leaving arcs is (7, 5). It can be shown (see, e. G. , Cunningham [1976]) that the above rule guarantees that the next basis is strongly feasible. We use th...e following property of a strongly feasible basis. Observation 1. Ln every degenerate pivot, the leaving arc lies in the basis path from node w to node k. This observation follows from the facts that the entering arc (k, has a positive capacity and that a positive flow can be sent from node / to node w. Hence no arc on the basis path from node / to node w can be blocked in a degenerate pivot. In case the entering arc (k, /) is at its upper bound then the criteria to select the leaving arc is the same except that the orientation of the cycle W is defined opposite to that of arc (k, /).
What to read after Improved Primal Simplex Algorithms for Shortest Path Assignment And Minimum Cos?
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To quickly assess the difficulty of the text, read a short excerpt:
If the blocking arc is unique, then it leaves the basis. If there are more than one blocking arcs, then the algorithm selects the leaving arc to be the last blocking arc encountered in traversing W along its orientation starting at node w. For example, in Figure 1, the entering arc is (9, 10), the blocking arcs are (2, 3) and (7, 5), and the leaving arcs is (7, 5). It can be shown (see, e. G. , Cunningham [1976]) that the above rule guarantees that the next basis is strongly feasible. We use th...e following property of a strongly feasible basis. Observation 1. Ln every degenerate pivot, the leaving arc lies in the basis path from node w to node k. This observation follows from the facts that the entering arc (k, has a positive capacity and that a positive flow can be sent from node / to node w. Hence no arc on the basis path from node / to node w can be blocked in a degenerate pivot. In case the entering arc (k, /) is at its upper bound then the criteria to select the leaving arc is the same except that the orientation of the cycle W is defined opposite to that of arc (k, /).
What to read after Improved Primal Simplex Algorithms for Shortest Path Assignment And Minimum Cos?
You can find similar books in the "Read Also" column, or choose other free books by Ravindra K Ahuja to read onlineMoreLess
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