A note on the rule for sequential selection

An extension of the sequential selection problem of Kwan and Yuan which is shown to be equivalent to a simple search problem is solved. In their model, candidates for a single job position are screened until one of them is accepted. An alternative proof technique, suggested by us and independently by Chun and Platt in 1992, is used to show that the Kwan-Yuan rule for sequential selection is optimal not only for their case but also for the general problem of multiple positions for m non-identical jobs. This rule, however, is not necessarily optimal when a cost of delay is incurred (instead of cost of information). Furthermore, the equivalence between the simplest search model discussed in 1962 by Blackwell and others and the sequential selection problem of Kwan and Yuan is shown. Finally, a counter example demonstrates that, for the cost of delay case, a pairwise interchange process may lead to a local extremum.