Acta mathematica scientia, Series B >
MARKOV SKELETON PROCESS IN PERT NETWORKS
Received date: 2008-12-02
Online published: 2010-09-20
Supported by
This work is supported by the National Natural Science Foundation of China (10671212, 10901164, 90820302), the Graduate Research Innovation Projects in Hunan Province (CX2009B020) and the Graduate Degree Thesis Innovation Foundation of Central Sourth University (2009ybfz11).
In this article, we investigate Programming Evaluation and Review Technique networks with independently and generally distributed activity durations. For any path in this network, we select all the activities related to this path such that the completion time of the sub-network (only consisting of all the related activities) is equal to the completion time of this path. We use the elapsed time as the supplementary variables
and model this sub-network as a Markov skeleton process, the state space is related to the sub-network structure. Then use the backward equation to compute the distribution of the sub-network's completion time, which is an important rule in project management and scheduling.
Key words： PERT networks; Markov skeleton process; backward equation
KONG Xiang-Xing , ZHANG Xuan , HOU Zhen-Ting . MARKOV SKELETON PROCESS IN PERT NETWORKS[J]. Acta mathematica scientia, Series B, 2010 , 30(5) : 1440 -1448 . DOI: 10.1016/S0252-9602(10)60136-1
[1] Charnes A, Copper W, Thompson G. Critical path analysis via chance constrained and stochastic programming. Operations Research, 1964, 12: 460--470
[2] Elmaghraby S. On the expected duration of PERT type networks. Management Science, 1976, 13: 299--306
[3] Van Slyke R. Monte carlo methods and the PERT problem. Operations Research, 1963, 11: 839--860
[4] Kulkarni V, Adlakha V. Markov and Markov-Regenerative PERT networks. Operations Research, 1986, 34: 769--781
[5] Azaron A, Katagiri H, Sakawa M, et al. Multi-objective resource allocation problem in PERT networks. European Journal of Operational Research, 2006, 172: 838--854
[6] Azaron A, Tavakkoli-Moghaddam R. A multi-objective resource allocation problem in dynamic PERT networks. Applied Mathematics and
Computation, 2006, 181: 163--174
[7] Azaron A, Katagiri H, Kato K, et al. Longest path analysis in network of queues. European Journal of Operational Research, 2006, 174: 132--149
[8] Hou Z T, Liu G X. Markov Skeleton Processes and Their Applications. 2nd ed. Beijing: Science Press, Boston: International Press, 2005
[9] Loulou R, Beale T. A comparison of variance reducing techniques in PERT simulations. Canadian Journal of Operations Research and Information, 1976, 14: 259--269
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