Note—A Note on “Efficiency of the Antithetic Variate Method for Simulating Stochastic Networks” - Grant, Floyd H. (Management Science, 1983)
In a recent paper by Sullivan, Hayya, and Schaul (Sullivan, R. S., J. C. Hayya, R. Schaul. 1982. Efficiency of the antithetic variate method for simulating stochastic networks. Management Sci. 28 (5, May) 563–572.), they present a theorem which proves that negative covariance will be guaranteed, and thus a variance reduction achieved, when estimating the project completion time in PERT networks using antithetic sampling procedures. Their proof is restricted to stochastic networks in which the arc time distributions are symmetric about their means. In this note we present a proof which guarantees a variance reduction for arbitrary arc time distributions.