Approximate analysis and simulation of a three-echelon inventory system with order splitting between two suppliers

Abstract

In this paper we consider a three-echelon supply chain with two suppliers, a central warehouse and an arbitrary number of retailers with continuous review policy. Retailers face independent Poisson demand and lead times are stochastic with no predetermined probability distribution. Unsatisfied demand is lost at the retailers and backlogged at the warehouse and suppliers. We restrict the reorder point to be greater than or equal to-1. Orders placed from the warehouse are divided between the two suppliers. In this paper, multi-echelon inventory control and order splitting problems are considered as an integrated model. Adding suppliers as the third echelon to the inventory system causes order crossover at the warehouse. The total cost of the three-echelon inventory system is expressed as a weighted mean of costs for one-for-one policies. To assess the accuracy of the model, the total cost of the mathematical model is compared with that of the simulation.