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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 Scheduling theory, deterministic
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