Competitive Two-Agent Scheduling and Its Applications

We consider a scheduling environment with m (m ≥ 1) identical machines in parallel and two agents. Agent A is responsible for n₁ jobs and has a given objective function with regard to these jobs; agent B is responsible for n₂ 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 n₁ + n₂ jobs that minimizes the objective of agent A (with regard to his n₁ jobs) while keeping the objective of agent B (with regard to his n₂ 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, ∑ w_jC_j, and ∑ 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.