This paper deals with the scheduling of n jobs on a single machine to minimize the sum of weighted earliness and weighted number of tardy jobs given a delivery window. Penalties are not incurred if jobs are completed within the delivery window. The length of this delivery window (which corresponds to the time period within which the customer is willing to take deliveries) is a given constant. The authors consider two cases of the problem; one where the position of the delivery window is internally determined (unrestricted window case) and the other where the position is an externally specified parameter (restricted window case). They present some optimal properties, prove that the problem (even for the unrestricted window case) is NP-complete, and present dynamic programming algorithms for both cases.
