We consider a single machine scheduling problem with two common delivery dates and unequal release dates for the jobs. The goal is to maximize the cumulative number of jobs processed before each delivery date. The general problem (with K ≥ 2 delivery dates) results from a practical situation in book digitization. The two delivery dates case considered here is weakly NP-hard. In this paper, we show for this problem a polynomial time algorithm with an absolute guarantee of 1. By considering the two delivery dates problem, this paper lays the basis for an approximation algorithm for the general K delivery dates problem.