Approximate solutions for large-scale piecewise deterministic control systems arising in manufacturing flow control models

Abstract : We propose a numerical technique for approximately solving large-scale piecewise deterministic control systems that are typically related to manufacturing flow control problems in unreliable production systems. The method consists of reformulating the stochastic control problem under study into a Markov decision process. Then we exploit the associated dynamic programming conditions and we propose an “approximate” policy iteration algorithm. This will be based on an approximation of the Bellman functions by a combination of a set of base functions, using a specific decomposition technique. The numerical method is applicable whenever a turnpike property holds for some associated infinite horizon deterministic control problem. To illustrate the approach, we solve an example and compare this new approximation method with a more classical approximation-by-decomposition technique