Performance analysis and optimisation of stochastic flow lines with limited material supply

We consider stochastic flow lines with limited buffer sizes and limited material supply. In these systems, the configuration of the flow line parameters and the configuration of the material supply determine the system output. Shortages of material supply can limit the performance of the production system. We use flexible (mixed-integer) linear programming approaches to evaluate and optimise the performance of long stochastic flow lines with limited material supply in discrete and continuous time. The approaches are used to quantify the impact of material shortages on the system output. Further, they are applied to determine the minimum material levels that are required to prevent material shortages of a given flow line configuration. The results of the numerical study reveal insights on the approximation accuracy of the linear programs as well as on the dependence of optimal material levels on flow line characteristics such as the presence of bottleneck machines and the system variability. The contribution of this paper consists of both, integrated models for stochastic flow lines with limited material supply and new insights on the optimal material supply of stochastic flow lines.