Strategies for Combining Antithetic Variates and Control Variates in Designed Simulation Experiments

In this paper we examine three methods for combining the variance reduction techniques of antithetic variates and control variates to estimate the mean response in a designed simulation experiment. In Combined Method I, we perform h independent pairs of simulation runs as follows---on the second run of each such pair, we use random number streams that are antithetic (complementary) to the streams used on the first run of the pair to drive the non-control-variate components of the simulation model; and we use independent random number streams to drive the control-variate components of the simulation model. In Combined Method II, we also perform h independent pairs of runs; but on each pair of runs we use independent random number streams to drive the non-control-variate model components, and we use antithetic random number streams to drive the control-variate components. In Combined Method III, all of the random number streams driving the second run of each pair of runs are antithetic to the streams driving the first run of the pair. For each of these three methods we drive the variance of the resulting estimator of the mean response to make a theoretical comparison of the efficiency of each method. We implemented these three methods, along with the classical method of control variates, in a simulation model of a resource-constrained activity network to show how each combined method is implemented in practice and to evaluate the performance of each combined method experimentally. The results indicate that: (a) Combined Method III outperformed all other methods, and (b) the effectiveness of Combined Method III as well as the choice of whether to use Combined Method I or Combined Method II depends on the degree of correlation between the control variates and the response.