Heuristic Scheduling of Parallel Heterogeneous Queues with Set-Ups

We consider the problem of allocating a single server to a system of queues with Poisson arrivals. Each queue represents a class of jobs and possesses a holding cost rate, general service distribution, and general set-up time distribution. The objective is to minimize the expected holding cost due to the waiting of jobs. A set-up time is required to switch from one queue to another. We provide a limited characterization of the optimal policy and a simple heuristic scheduling policy for this problem. Simulation results demonstrate the effectiveness of our heuristic over a wide range of problem instances.