Single machine scheduling with delivery dates and cumulative payoffs

We address a single machine scheduling problem with a new optimization criterion and unequal release dates. This new criterion results from a practical situation in the domain of book digitization. Given a set of job‐independent delivery dates, the goal is to maximize the cumulative number of jobs processed before each delivery date. We establish the complexity of the general problem. In addition, we discuss some polynomial cases and provide a pseudopolynomial time algorithm for the two‐delivery‐dates problem based on dynamic programming and some dominance properties. Experimental results are also reported.