Turnpike sets in stochastic manufacturing systems with finite time horizon

This paper is concerned with finite horizon optimal production planning of stochastic manufacturing systems. The main objective is to minimize an expected disounted cost of inventories and/or backlogs. Owing to the finite time horizon formulation, the dynamics of the system are time inhomogeneous. Thus the turnpike sets of the problem are time varying. Systems with random decreasing capacity and constant demand, and systems with random increasing demand and constant capacity are dealt with. We derive explicit solutions, and show that the optimal controls can be written in terms of the turnpike sets under 'traceability' conditions