Optimal Sequential Selection Based on Relative Ranks with Renewable Call Options

Abstract Sequential sampling problems may be affected significantly by the presence of sampling costs and the ability to recall historical observations. In the context of the classical secretary problem, we incorporate these two notions into the decision maker's action set, thereby creating a stopped decision process. Whenever a desirable applicant appears, we may consider purchasing an option to recall it subsequently. The problem is solved for the best-choice criterion, either reduced or discounted by the option costs incurred.