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Production systems with limited repair capacity

Optimizing manufacturing systems consists of generating large-quantity outputs to fulfil customer demands. But naturally machines may fail and the production process is either slowed down or completely interrupted. In order to keep production running, we are interested in assigning repair crews to currently broken-down machines. But due to the limited repair capacity and the dynamics involved in the production process, we propose a scheduling problem based on ordinary differential equations for the description of buffer levels and the actually available processing capacity. We discuss properties of the model and present a solution approach leading to a mixed-integer programming model.