Cost Approximation of a Three-echelon Inventory System with Order Splitting and Information Sharing

This paper develops an approximate cost function for a three-echelon supply chain that has two suppliers, a central warehouse and an arbitrary number of retailers. It takes an integrated approach to multi-echelon inventory control and order-splitting problems. It assumes that all facilities apply continuous review policy for replenishment, demand at the retailers follows a Poisson process, and lead times are stochastic with no predetermined probability distribution. Unsatisfied demand is considered as lost sales at the retailers and backlogged at the warehouse and suppliers. Due to information sharing between the existing echelons, order quantity at each higher level is assumed to be an integer multiple of the lower level. Order placed by the warehouse gets divided between the two suppliers and re-order point is not restricted at the warehouse or suppliers. The main contribution of this paper is its integrated approach and the practical assumption that it uses for the order arrival sequence and the unsatisfied demands. It adds two suppliers as the third echelon to the traditional twoechelon supply chain and considers dynamic sequence of orders arrival to the warehouse at each cycle. The fact that inventory control and sourcing decisions are interdependent and act as the main challenge of supply chain management, considering them in an integrated model can significantly influence operating costs and supply chain’s efficiency. Such approach can even have greater impact when blended with practical assumptions that consider lead-time as unpredictable and unsatisfied demand as lost sales. Total cost of the three-echelon inventory system is approximated based on the average unit cost and its accuracy is assessed through simulation. Numerical results with relatively low errors confirms the accuracy of the model. It also shows how to further enhance its accuracy by either increasing the holding cost at all echelons or the penalty cost at the retailers.