A new algorithm for the multi-item exponentially discounted optimal selection problem

We approach the classical problem of optimal selection, where n identical units have to be sold to bidders who come in an infinite stream, and it has to be decided which bids to accept and when. Optimal strategies are defined so as to maximize the expected total discounted revenue from the n units. The present work assumes that bids are i.i.d. and that they arrive according to a general renewal process. Observing that the optimal policy may be determined using a series of threshold values which are sorted by the values of a discrete approximation of the bid-distribution, and that in the case of exponential discounting these threshold values are easily calculable, we propose an appropriate solution algorithm. The algorithm provides the value of the problem as well.