Optimal stopping problem with finite-period reservation

This paper presents a discrete-time optimal stopping problem with a finite planning horizon. For a search cost s, a random offer, w ∼ F(w), will be found for each time. Offers appearing subsequently are allowed to be not only accepted or passed up but also ‘reserved’ for recall later. To reserve an offer with value w, a reserving cost r(w) is incurred with each reserved offer expiring k periods after. The objective is to maximize the expected discounted net profit with the provision that an offer must be accepted. The major finding is that an offer reserved during the search process must not be accepted prior to its maturity of reservation; however, it may be accepted on the maturity.