Optimal control of two symmetric competing queues with finite capacity and non negligible setup times

In this paper we study optimal scheduling for a two part-type, symmetric manufacturing systems subject to non negligible setup times, and characterized by finite buffer capacity. The solution method relies on 1) restricting the possible control policies to those which respect some general necessary conditions of optimality, and on 2) the exploitation of such properties to introduce a two-dimensional sampled version of the original system. The symmetric assumptions allows to map the two-dimensional sampled model onto an equivalent scalar one. By means of such a scalar sampled model we give the analytical solution of the optimal control problem addressed.