Gradient estimate for parameter design of threshold controllers in a failure-prone production system

Abstract

A manufacturing system, with n failure-prone machines in tandem and n internal buffers, is considered. Two threshold control policies, which can be interpreted as the noted PULL and PUSH policies, are used to regulate the system. To optimize the threshold values, the key problem is to find the available gradient information of objective functional with respect to threshold values. We apply the perturbation analysis technique to this system. By defining the machine states and events in the evolution of the system, general perturbation rules are presented. Then simple algorithms are developed to derive the gradient estimates based on a single sample process, which may save a lot of computational efforts and simulation/ experiment times. The unbiasedness and consistency of the gradient estimates are proved. Simulation examples are given to demonstrate the effectiveness of the results