Centralised and decentralised three echelon inventory model for optimal inventory decisions under price dependent demand

In this paper, a three echelon inventory system with a single manufacturer supplying a single kind of a product to a single distributor and then to a single retailer, is considered. Mathematical model is developed for annual total relevant costs of the coordinated and non‐coordinated supply chain. The novel idea of the proposed model is that the demand is a function of retailer's unit selling price, which in turn is a function of retailer's replenishment quantity with dependence factor. The objective of the model is to demonstrate the optimality of inventory decisions, shipment frequencies and total relevant costs with respect to dependence factor. Numerical illustration is carried out to demonstrate the optimality of replenishment decisions. Finally, managerial insights are inferred in selecting the optimal replenishment quantity and shipment frequency that minimises the total relevant cost of the supply chain.