Application of Semi-Markov Drift Processes to Logistical Systems Modeling and Optimization

Abstract

In our paper, a general scheme for modeling different logistical systems functioning under uncertainty is presented. It is defined in the terms of so-called semi-Markov drift processes with several continuous components (random walks in non-negative orthant of Eucleadean space). Some examples of this scheme application for modeling and optimization of logistical systems are given: optimal lot sizing taking into account the irregularity of product delivery from a vendor to wholesaler in the multi-echelon distribution system under fixed demand; optimal distribution of a manufactured product to a set of retailers under random demand.