Analytical modelling and control of a hybrid manufacturing/remanufacturing system

A production system consisting of parallel machines deteriorating with the production dependent failure rates of the machine is investigated in this paper and extended within the framework of a manufacturing/remanufacturing system within a closed loop reverse logistics system The machines produce one type of final products. The demand rate for the final commodity is constant and unmet demand is backlogged. The goal is to find the production rates of both machines so as to minimize a long term average expected cost which includes backlogging as well as inventory costs. In the proposed model, the main machine (characterized by a higher production rate) is more robust than the second machine. The failure rate of the main machine depends on its production rate, while the failure rate of the second machine is constant. This paper proposes a stochastic dynamic programming formulation of the problem and derives the optimal production policies numerically. A simulation example is included, and sensitivity analyses with respect to the system parameters are examined to illustrate the effectiveness of the proposed methodology.