HIERARCHICAL GROUPING TO MAXIMIZE PAYOFF
Air Force Wright Air Development Division, Personnel Laboratory LACKLAND AFB
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This analysis describes mathematically a general procedure for forming hierarchical groups of mutually exclusive sets in a manner which yields an optimum value for the functional relation, or objective function, that reflects the criterion chosen by the investigator. The number of groups to be formed need not be specified in advance. Given k sets, this technique permits their reduction to k-1 usually exclusive sets by considering the union of all possible pairs that can be formed and the selection of that union which has the highest payoff value with respect to the criterion chosen. This procedure can be repeated until only one set remains. Hence decisions on the number of groups to be used can be based on a knowledge of the costs of grouping at each stage in the entire hierarchical structure. A computer flowchart and a numerical example of the grouping procedure are provided. An Appendix shows how to determine the number of possible ways of forming groups and the number of distinguishable unions possible.