Optimal stopping problem with controlled recall

This paper deals with the following discrete-time optimal stopping problem. For fixed search cost a a random offer, w similar to F(w), will be found for each time. This offer is either accepted, rejected, or "reserved" for recall later The reserving cost for any offer depends on its value, regardless of how long the offer is reserved. The objective is to maximize the expected discounted net profit, provided that an offer must be accepted. The major finding is that no previously reserved offer should be accepted prior to the deadline of the search process.