The Optimal Control of a Two-Stage Tandem Queueing System with Flexible Servers

Mark E. Lewis
Industrial and Operations Engineering Department
University of Michigan
1205 Beal Avenue
Ann Arbor, MI 48109-2117

Hyun-soo Ahn
Department of Industrial Engineering and Operations Research

University of California at Berkeley
4185 Etcheverry Hall, Berkeley, CA 94720-1777


Izak Duenyas
Business School, Department of Operations Management
University Of Michigan

701 Tappan Street

Ann Arbor, MI 48109-1234

We consider the optimal control of two parallel servers in a two-stage tandem queueing system with two flexible servers. New jobs arrive to station 1 after which a series of two operations must be performed before they leave the system. Holding costs are incurred at rate h1 per unit time for each job in station 1 and at rate h2 per unit time for each job at station 2.

The system is considered under two scenarios; the collaborative case and the non-collaborative case. In the prior, the servers can collaborate to work on the same job, while in the latter each server can work on a unique job though they can work on separate jobs at the same station. We provide simple conditions under which it is optimal to allocate both servers to station 1 or 2 in the collaborative case. In the non-collaborative case, we show that the same condition as in the collaborative case guarantees the existence of an optimal policy that is exhaustive at station 1. However, the condition for exhaustive service in station 2 to be optimal does not carry over. This case is examined via a numerical study.