Infinitesimal perturbation analysis for optimization of two-product-manufacturing system

In this paper, we study a manufacturing system composed by two machines in serial configuration, two intermediate buffers and two buffers of finished products. All buffers have infinite capacity. The machines produce two types of products. Both products are independently stored and the demand of each one is known. The machines are subject to failures and repairs, and the times to failure and to repair are general random variables. The production speed of each machine is given by a hedging point policy. In this study, we propose a simulation-based optimization method for determining the optimal buffers level in order to minimize the sum of inventory and backlog costs. In other words: to determine the value of the hedging point that minimizes the expected total average cost. Firstly, we start by formulating the problem using a stochastic fluid model that describes the system evolution and we estimate the long-run average cost. Then we apply the infinitesimal perturbation analysis method on the buffer levels and we compute the gradient estimators. We prove that these estimators are unbiased, and then they can be used in a simple simulation based-optimization algorithm to estimate the optimal value of buffers, consequently to analyze the sensitivities of a cost function with respect to the buffer capacities. Finally the numerical results based on the simulation algorithm are presented and discussed.