A set of n jobs has to be scheduled on a single machine which can handle only one job at a time. Each job requires a given positive uninterrupted processing time and has a positive weight. The problem is to find a schedule that minimizes the sum of weighted deviations of the job completion times from a given common due date d, which is smaller than the sum of the processing times. We prove that this problem is NP-hard even if all job weights are equal. In addition, we present a pseudopolynomial algorithm that requires O(n2d) time and O(nd) space.

NP-hardness, pseudopolynomial algorithm, single-machine scheduling
dx.doi.org/10.1016/0377-2217(91)90228-N, hdl.handle.net/1765/12356
ERIM Top-Core Articles
European Journal of Operational Research
Erasmus Research Institute of Management

Hoogeveen, J.A, & van de Velde, S.L. (1991). Scheduling around a small common due date. European Journal of Operational Research, 237–242. doi:10.1016/0377-2217(91)90228-N