Minimum Number Of Arcs In Conditional Monte Carlo Sampling Of Stochastic Networks

Abstract

Consider a stochastic activity network, such as PERT network. This paper deals with the problem of estimating the distribution function (df) of the duration of the longest path in the stochastic network. In particular, the paper concentrates on the methods of conditional Monte Carlo sampling which have been used to approximate the df of the longest path in stochastic networks. First, we show that none of the existing conditional Monte Carlo sampling procedures conditions on the minimum number of arcs. Secondly, a method in which the conditions of a minimum number of arcs is developed. The new procedure conditions on the arcs with the highest path indices, where a “path index” of an arc is the number of paths passing through the arc, A procedure to calculate the path indices of the arcs without identifying the paths is developed. Illustrative examples and comparison with the existing conditional procedures are provided.

Résumé

Considerer un réseau d’activité stochastique, comme le réseau PERT, Cet article traite le problème pour estimer la probabilité de la duretee de la plus longe trajectoire dans le réseau stochastique. En particulier, cet article se concentre sur les méthodes conditionnelles des échantillons de Monte Carlo qui ont été utilisé pour estimer la probabilité de la trajectoire la plus longe dans le réseau stochastique. Premièrement, on démontre qu’aucun des échantillons conditionnels existe du procédé Monte Carlo conditionne sur le nombre minimum d’arcs. Deuxiémement, une méthode dans laquelle les conditions d’un nombre d’arcs minimum est developée, Cette nouvelle méthode conditionne les arcs avec les trajectoires d’indice les plus hauts, ou la “trajectoire d’indice” d’un arc est le nombre de trajectoire qui passe à travers Tare, Une méthode pour calculer les indices de trajectoire des arcs sans identifier les trajectoire est developée, Des exemples illustrés et de comparison avec les méthodes conditionnelles existant sont fournir.

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Bajis Dodin

BAJIS DODIN received his MS and PH D in Operations Research from North Carolina State University at Raleigh. Before he joined the faculty of Production and Management Science ofthe School of Business Administration at the University of Wisconsin-Milwaukee, he worked for Pullman Standard of Chicago for four years. In 1984 he joined the Graduate School of Management at the University of Califomia, Riverside. He teaches Production / Operations Management and Operations Research / Management Science. His research interests include project planning and control using deterministic and stochastic networks, production scheduling, inventory control, and flexihle manufacturing. He has published in Management Science, Operations Research, International Journal of Production Research, and Computers and Operations Research, INFOR, and OMFGA, among others. He is a memher of HE, ORSA, and TIMS and many of their functional and local chapters.