Stochastic dynamic job scheduling with interruptible setup and processing times: An approach based on queueing control

We consider a stochastic, dynamic job scheduling problem, formulated as a queueing control problem, in which a single server processes jobs of different types that arrive according to independent Poisson processes. The problem is defined on a network, with jobs arriving at designated demand points and waiting in queues to be processed by the server, which travels around the network dynamically and is able to change its course at any time. In the context of machine scheduling, this enables us to consider sequence-dependent, interruptible setup and processing times, with the network structure encoding the amounts of effort needed to switch between different tasks. We formulate the problem as a Markov decision process in which the objective is to minimize long-run average holding costs and prove the existence of a stationary policy under which the system is stable, subject to a condition on the workload of the system. We then propose a class of index-based heuristic policies, show that these possess intuitively appealing structural properties and suggest how to modify these heuristics to ensure scalability to larger problem sizes. Results from extensive numerical experiments are presented in order to show that our heuristic policies perform well against suitable benchmarks.