Infinitesimal Perturbation Analysis and Optimization for Make-to-Stock Manufacturing Systems Based on Stochastic Fluid Models

In this paper we study Make-To-Stock manufacturing systems and seek on-line algorithms for determining optimal or near optimal buffer capacities (hedging points) that balance inventory against stockout costs. Using a zStochastic Fluid Model (SFM), we derive sample derivatives (sensitivities) which, under very weak structural assumptions on the defining demand and service processes, are shown to be unbiased estimators of the sensitivities of a cost function with respect to these capacities. When evaluated based on the sample path of discrete-part systems, we show that these estimators are greatly simplified. Thus, they can be easily implemented and evaluated on line. Though the implementation on discrete-part systems does not necessarily preserve the unbiasedness property, simulation results show that stochastic approximation algorithms that use such estimates do converge to optimal or near optimal hedging points.