The arrival times of what we shall call offers constitute a Poisson process. The value of any offer is a nonnegative random variable with known distribution. At an arrival epoch, we may select, reject, or hold the offer. Rejected offers may not be recalled, but an offer on hold is available for future consideration. However, cost accrues during the holding period. We seek a holding and selection strategy that maximizes the expected value of the offer selected less holding costs. The discrete time version of the problem is also considered
