We study a situation where jobs of unknown duration (e.g., surgical procedures) are performed sequentially in a single facility (e.g., a hospital operating room). This facility can be any resource (material or human) that is in limited supply. Due to the uncertain duration of jobs, the time at which the facility will be available for the next job is unknown. Given the existing schedule, a starting time is selected for the next job. The scheduler's task is complicated because a job necessitates the presence of (at least) one individual (e.g., the surgeon), called the agent.
We model this situation as a game between the scheduler and the agent. The scheduler trades off the cost associated with keeping the facility idle between jobs against the cost of keeping the agent waiting. The agent trades off his waiting cost against his lateness cost. We determine the conditions under which it is necessary for the scheduler to take the agent's behavior into account. We introduce moral hazard by assuming that the agent's arrival time is random and compare this to the case where the agent selects a deterministic arrival time.