The Lazy Bureaucrat scheduling problem

We introduce a new class of scheduling problems in which the optimization is performed by the worker (single "machine") who performs the tasks. The worker's objective may be to minimize the amount of work he does (he is "lazy"). He is subject to a constraint that he must be busy when there is work that he can do; we make this notion precise, particularly when preemption is allowed. The resulting class of "perverse" scheduling problems, which we term "Lazy Bureaucrat Problems," gives rise to a rich set of new questions that explore the distinction between maximization and minimization in computing optimal schedules.