This paper presents a control problem for the optimization of the production and setup activities of an industrial system operating in an uncertain environment. This system is subject to random disturbances (breakdowns and repairs). These disturbances can engender stock shortages. The considered industrial system represents a well-known production context in industry and consists of a machine producing two types of products. In order to switch production from one product type to another, a time factor and a reconfiguration cost for the machine are associated with the setup activities. The parts production rates and the setup strategies are the decision variables which influence the inventory and the capacity of the system. The objective of the study is to find the production and setup policies which minimize the setup and inventory costs, as well as those associated with shortages. A modeling approach based on stochastic optimal control theory and a numerical algorithm used to solve the obtained optimality conditions are presented. The contribution of the paper, for industrial systems not studied in the literature, is illustrated through a numerical example and a comparative study.
"Production Planning of a Failure-Prone Manufacturing System under Different Setup Scenarios." J. Appl. Math. 2016 1 - 15, 2016. https://doi.org/10.1155/2016/4930817