Sensitivity analysis and decomposition of unreliable production lines with blocking

The analysis of finite-buffered, unreliable production lines is often based on the method of decomposition, where the original system is decomposed into a series of two-stage subsystems that can be modeled as quasi birth–death processes. In this paper, we present methods for computing the gradients of the equilibrium distribution vector for such processes. Then we consider a specific production line with finite buffers and machine breakdowns and develop an algorithm that incorporates gradient estimation into the framework of Gershwin's approximate decomposition. The algorithm is applied to the problem of workforce allocation to the machines of a production line to maximize throughput. It is shown that this problem is equivalent to a convex mathematical programming problem and, therefore, a globally optimal solution can be obtained.