Stochastic optimal control of manufacturing systems under production-dependent failure rates

A production system consisting of two parallel machines with production-dependent failure rates is investigated in this paper. The machines produce one type of final product and unmet demand is backlogged. The objective of the system is to find a productivity policy for both machines that will minimize the inventory and shortage costs over an infinite horizon. The failure rate of the main machine depends on its productivity, while the failure rate of the second machine is constant. In the proposed model, the main machine is characterized by a higher productivity. This paper proposes a stochastic dynamic programming formulation of the problem and derives the optimal policies numerically. A numerical example is included and sensitivity analyses with respect to the system parameters are examined to illustrate the importance and effectiveness of the proposed methodology.