On an Optimal Inventory Problem for Multi-Echelon Production System

Abstract

A multi-echelon production system is represented as a queuing system with the purpose to estimate steady-state characteristics for total average cost using regenerative approach. Regenerative structure of multi-echelon manufacturing system is observed in this article. Stochastic processes describing the behaviour of such complex systems have very complicated correlation structure. The regeneration method could be acceptable in such situations for system simulation and estimation of characteristics. However the well-known classical regeneration is not useful in real-time simulation, because classical regeneration points (at such points a demand arrives in empty system) occur too rarely. It has been recently established that weak regeneration turns out to be very effective in simulation of complex inventory systems. Some numerical results of simulation are presented