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**Competitive two-agent scheduling and its applications.**
*(English)*
Zbl 1233.90163

Summary: We consider a scheduling environment with \(m\) (\(m\geqslant 1\)) identical machines in parallel and two agents. Agent A is responsible for \(n_{1}\) jobs and has a given objective function with regard to these jobs; agent B is responsible for \(n_{2}\) jobs and has an objective function that may be either the same or different from the one of agent A. The problem is to find a schedule for the \(n_{1} + n_{2}\) jobs that minimizes the objective of agent A (with regard to his \(n_{1}\) jobs) while keeping the objective of agent B (with regard to his \(n_{2}\) jobs) below or at a fixed level Q. The special case with a single machine has recently been considered in the literature, and a variety of results have been obtained for two-agent models with objectives such as \(f_{max}, \sum w_{j}C_{j}\), and \(\sum U_{j}\). In this paper, we generalize these results and solve one of the problems that had remained open. Furthermore, we enlarge the framework for the two-agent scheduling problem by including the total tardiness objective, allowing for preemptions, and considering jobs with different release dates; we consider also identical machines in parallel. We furthermore establish the relationships between two-agent scheduling problems and other areas within the scheduling field, namely rescheduling and scheduling subject to availability constraints.

### MSC:

90B35 | Deterministic scheduling theory in operations research |