Sequential acceptance problems are considered with the aim to select candidates from a group, with the candidates observed sequentially, either per individual or in subgroups, and with the ordering of an individual compared to previous candidates and those in the same subgroup available. For given total group size, this problem can in principle be solved by dynamic programming, but the computational effort required makes this not feasible for problems once the number of candidates to be selected and the total group size are not small. We present a new heuristic approach to such problems, based on the principles of nonparametric predictive inference, and we study its performance via simulations, which are also used to compare the method with some alternatives. The approach is easy to implement and computationally straightforward.
60A99 62G99 62P30
Acceptance decisions Dynamic programming Heuristics Marriage problem Nonparametric predictive inference Secretary problem Sequential decisions
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