Perturbation analysis and optimisation of continuous flow transfer lines with delay

Abstract

This paper addresses the optimisation of failure-prone transfer lines with delays for material transfer and with a constant demand. A continuous flow model with delays is proposed. Compared with traditional continuous flow models in which materials flow from one station to another instantaneously, material flowing out a machine waits a period of time called a delay before arriving at its downstream buffer. Machines are subject to time-dependent failures. Times between failure and times to repair are random variables with a general distribution. The production of each machine is controlled by a base stock policy. We propose a simulation-based optimisation method for determining optimal base stock levels in order to minimise the long-run average cost incurred by inventory holding and demand backlogging. It is based on an infinitesimal perturbation analysis for the estimation of gradients along the simulation. The unbiasedness of the gradient estimators is established.