Single machine just-in-time scheduling problems with two competing agents

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.