Perturbation Analysis for Continuous and Discrete Flow Models: a Failure-prone Manufacturing System Study

In this paper, a manufacturing system composed by a single machine, a buffer and a stochastic demand is considered. Two models are presented: continuous and discrete flow models with delivery times, machine failures and random demands. The objective is to determine the value of the optimal buffer level, for a hedging point policy to minimize the cost function. This cost function is the sum of inventory, transportation and lost sales costs. Perturbation analysis is used for performance evaluation and optimization of the failure-prone manufacturing system. Using the two proposed models, the trajectories of buffer level are studied for the continuous and discrete cases and the perturbation analysis estimators are evaluated. These estimators are shown to be unbiased and then they are implanted in an optimization algorithm which determines the optimal buffer level in the presence of delivery time. Numerical results are presented to compare the continuous and discrete flow models and to highlight our work.