This paper is concerned with simulation procedures for estimating the distribution function of the time to complete stochastic activity networks. A conditional Monte Carlo method using uniformly directed cutsets is considered and combined with antithetic variate sampling and quasirandom points. The efficiency of the two variance reduction techniques is compared using CPU times and mean- square errors. By using three examples the study illustrates the decreasing benefits of using quasirandom points over antithetic variate technique as the network size increases.
Adlakha, V.G. (1987). "A Monte Carlo technique with quasirandom points for the stochastic shortest path problem." American Journal of Mathematical and Management Sciences, 7(4), 325-358.
2.
Battersby, A. (1970). Network Analysis for Planning and Scheduling, Third ed., John Wiley and Sons, New York .
3.
Burt, J.M. and M.B. Garman (1971). Conditional Monte Carlo: A simulation technique for stochastic network analysis. Management Science, 18,207-217.
4.
Burt, J.M., D.P. Gaver, and M. Perlas (1970). "Simple stochastic networks: some problems and procedures." Naval Research Logistics Quarterly, 17 (4), 439-460.
5.
Carson, J.S. (1983). "On the efficiency of antithetic sampling and conditional Monte Carlo in simulation of stochastic activity networks." School of Industrial and Systems Engineering, Georgia Institute of Technology , Georgia.
6.
Chung, K.L. (1949). "An estimate concerning the Kolmogoroff limit theorem." Transactions of the American Mathematical Society , 67, 36-40.
7.
Colby, A.H. and Elmaghraby, S.E. (1984). "On the complete reduction of directed acyclic graphs." OR Report 197, North Carolina State University atRaleigh.
8.
Dodin, B.M. (1986). "Minimum number of arcs in conditional Monte Carlo sampling of stochastic networks." INFOR., Canadian Journal of Operations Research and Information Processing, 24 (1), 33-44.
9.
Elmaghraby, S.E. (1977). Activity Networks: Project Planning and Control by Network Models, John Wiley and Sons, New York.
10.
Elmaghraby, S.E. (1985). "The estimation of some network parameters in the PERT model of activity networks: review and critique." OR Report 207, North Carolina State University atRaleigh.
Grant, F.H. , III (1983). "A note on efficiency of the antithetic variate method for simulating stochastic networks." Management Science, 29 (3), 381-384.
13.
Halton, J.H. (1960). "On the efficiency of certain quasirandom sequences of points in evaluating multidimensional integrals." Numer. Math., 2,8490.
14.
Halton, J.H. and G.B. Smith, (1964). "Algorithm 247: Radical inverse quasirandom point sequence. " Communication of the ACM, 7,701-702.
15.
Kiefer, J. (1961). "On large deviations of the empiric d.f. of vector chance variables and a law of the iterated logarithm." Pacific Journal of Mathematics, 11, 649-660.
16.
Kuipers, L. and H. Niederreiter (1974). Uniform Distributions of Sequences, John Wiley and Sons, New York.
17.
Martin, J.J. (1965). "Distribution of the time through a directed acyclic network." Operations Research, 13 (1), 46-66.
18.
Niederreiter, H. (1978). "Quasi-Monte Carlo methods and pseudorandom numbers." Bulletin of the American Mathematical Society, 84, 957-1041.
19.
Provan, J.S. and V.G. Kulkami (1989). "Exact cuts in networks ." Networks, 19(3), 281-289.
20.
Sigal, C.E. , A.A.B. Pritsker and J.J. Solberg (1979). "The use of cutsets in Monte Carlo analysis of stochastic networks." Mathematics and Computers in Simulation, 21, 376-384.
21.
Sigal, C.E. , A.A.B. Pritsker and J.J. Solberg (1980). "The stochastic shortest route problem." Operations Research, 28, 1122-1129.
22.
Sullivan, R.S. , J.C. Hayya and R. Schaul (1982). "Efficiency of the antithetic variate method for simulating stochastic networks." Management Science, 28 (5), 563-572.
23.
Van Slyke, R.M. (1963). "Monte Carlo methods and the PERT problem." Operations Research, 11, 839-860.