Common pseudorandom numbers

The variance estimators s20j) of the estimated effects allow unequal response variances and the use of common pseudorandom numbers. This is a well-known technique used in simulation experiments to reduce the variances of the estimated factor effects (Law and Kelton, 2000). This technique uses the same pseudorandom numbers when simulating the system for different factor combinations, thus creating positive correlations between the responses. Consequently, the variances of the estimated effects are reduced. This technique is similar to blocking in real-world experiments see, for example, Dean and Voss (1999, Chapter 10). 

We give only a short description of the three supply chain configurations and their simulation models for details we refer to Persson and Olhager (2002). At the start of our sequential bifurcation, we have three simulation models programmed in the Taylor II simulation software for discrete event simulations see Incontrol (2003). We conduct our sequential bifurcation via Microsoft Excel, using the batch run mode in Taylor II. We store input-output data in Excel worksheets. This set-up facilitates the analysis of the simulation input-output data, but it constrains the setup of the experiment. For instance, we cannot control the pseudorandom numbers in the batch mode of Taylor II. Hence, we cannot apply common pseudorandom numbers nor can we guarantee absence of overlap in the pseudorandom numbers we conjecture that the probability of overlap is negligible in practice. 

Design and Analysis Principle 9. Positive correlation between the sample performance of two systems can often be induced by assigning the same "common ) random number streams or seeds to the simulation of each system (see Section 4 for a description of random number streams and seeds). The magnitude of the correlation can be increased further by synchronizing the pseudorandom numbers, as described below. 

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