Control of a Single-Server Tandem Queueing System with Setups

This paper considers the control of a single-server tandem queueing system with setups. Jobs arrive to the system according to a Poisson process and are produced to order. A single server must perform a number of different operations on each job. There is a setup time for the server to switch between different operations. We assume that there is a holding cost at each operation, which is nondecreasing in operation number (i.e., as value is added to a job, it becomes more expensive to hold). The control problem is to decide which job the server should process at each point in time.

We formulate this control problem as a Markov-Decision Process. We partially characterize the optimal policy, develop an exact analysis of exhaustive and gated polling policies, and develop an effective heuristic policy. The results of a simulation study, which tests the performance of the policies considered, are reported. These computational results indicate that our heuristic is effective for a wide variety of cases.