Optimal rate allocation in unreliable, assembly/disassembly production networks with blocking

We consider an assembly/disassembly production network with finite buffers, unreliable machines, and a number of skilled operators and repairmen. Each machine is capable of performing a single, assembly and/or disassembly operation. We assume that the processing and repair times at each machine are exponentially distributed and their rates depend on the number of operators and repairmen assigned to that machine. The problem is to allocate work force to each machine so as to maximize the throughput of the system. This problem is shown to be equivalent to a convex minimization problem. The optimal allocation is found using a steepest-descent algorithm and discrete-event simulation for performance evaluation and gradient estimation