9. Concluding remarks

Sun Woong Kim, Steven G. Heeringa and Peter W. Solenberger

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In this paper, we introduced the concept of optimal solutions to a controlled selection problem with two-way stratification, and proposed a new algorithm for finding such solutions. The algorithm has been easily and successfully implemented in the new SAS-based software (SOCSLP).

Since an optimal solution is a general idea, it may be adopted as one of the useful criteria for comparing the different algorithms. As shown in the above comparisons, the new algorithm results in solutions to large controlled selection problems that are very different from those derived using previously published methods. It is also likely to yield greater probabilities of selection for optimum arrays as compared to those obtained by the previous methods.

Based on the results for the two-way controlled selection problems, we expect that the suggested method would also contribute to improvements in the properties of solutions to controlled selection problems with three-way or more stratification dimensions.

Acknowledgements

This paper is in honor of I. Hess who dedicated her life to studying controlled selection. The authors wish to thank Jea-Bok Ryu in Chongju University for providing ideas and advice in the early stage of this study. We are also grateful to two anonymous referees, the Editor and the Associate Editor for their valuable comments and suggestions.

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