In scheduling problems with two competing agents, each one of the agents has his own set of jobs to be processed and his own objective function, and both share a common processor. In the single-machine problem studied in this article, the goal is to find a joint schedule that minimizes the total deviation of the job completion times of the first agent from a common due-date, subject to an upper bound on the maximum deviation of job completion times of the second agent. The problem is shown to be NP-hard even for a nonrestrictive due-date, and a pseudopolynomial dynamic program is introduced and tested numerically. For the case of a restrictive due-date (a sufficiently small due-date that may restrict the number of early jobs), a faster pseudopolynomial dynamic program is presented. We also study the multiagent case, which is proved to be strongly NP-hard. A simple heuristic for this case is introduced, which is tested numerically against a lower bound, obtained by extending the dynamic programming algorithm.
- common due-date