本文選題：關(guān)鍵路徑 + PERT/CPM圖　； 參考：《中國科技論文》2017年17期

【摘要】：為了研究簡單圖的有關(guān)路徑問題,將簡單有向賦權(quán)圖對應(yīng)的鄰接矩陣推廣到二維元素的初始鄰接路徑矩陣和一般鄰接路徑矩陣,定義了一般鄰接路徑矩陣的"乘法"運算,通過其"乘法"運算可以同時求出簡單有向無環(huán)賦權(quán)圖中任意2點間的最大權(quán)值以及對應(yīng)的路徑,從而可以同時求出計劃評審方法(program evaluation and review technique,PERT)圖與關(guān)鍵路線方法(critical path method,CPM)圖中的關(guān)鍵路徑與對應(yīng)的最大權(quán)值,本方法的優(yōu)點是所求路徑與對應(yīng)權(quán)值同時顯示在最終的一般鄰接路徑矩陣上。本算法易于通過計算機編程實現(xiàn),對于大規(guī)模PERT/CPM圖或簡單有向無環(huán)賦權(quán)圖,更有優(yōu)勢。
[Abstract]:In order to study the path problem of simple graph, the adjacent matrix corresponding to simple directed weighted graph is extended to the initial adjacent path matrix of two-dimensional elements and the general adjacent path matrix, and the "multiplication" operation of the general adjacent path matrix is defined. By means of its multiplication operation, the maximum weight value and the corresponding path between any two points in a simple directed acyclic weighted graph can be obtained at the same time. Therefore, the critical path and the corresponding maximum weights in the program evaluation and review technique / pert diagram and the critical route method / critical path method chart can be obtained at the same time. The advantage of this method is that the calculated path and the corresponding weights are displayed simultaneously on the final general adjacent path matrix. This algorithm is easy to realize by computer programming, and has more advantages for large-scale PERT/CPM diagrams or simple directed acyclic weighted graphs.
【作者單位】： 武漢輕工大學(xué)數(shù)學(xué)與計算機學(xué)院;
【基金】：國家自然科學(xué)基金資助項目(61179032,11301405)
【分類號】：O157.5

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