Topological Aspects for Solving Generalized Transportation Problems〔邦文〕

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In classical transportation problems, North-West Cornor Method is most famous algorithm. We can express this transportation problems as compact tableau in stead of simplex tableau. In conpact tableau, each cell of the compact tableau can be considered as the node of graph. That is to say, a basic solution corresponds to some non-zero valued nodes. Therefore, we can obtain the optical solution only using some loop of the given graph. This is the reason why North-West Cornor Method may be called as loop technique. Of cource, this method may be called as stepping stone method. As an extension of this idea, the generalized tranportation problems is also able to use the loop technique. However, this extension is not necessary a straight forward modification of the famous stepping stone method for classical transportation problems. In this paper, I represent some topological aspects of basic feasible solution for the generalized transportation problems. Consequently, we can consider the algorithm solving the generalized transportation problems by using the properties of given topology corresponding to the basic solntions.
岡山理科大学の論文