A Single-Manufacturer Multi-Retailer Integrated Inventory Model with Price Dependent Demand and Stochastic Lead Time

This paper deals with a two-level supply chain composed of a single manufacturer and multiple retailers. Ordered quantities of the retailers are dispatched in some equal batches from the manufacturer. Customer demand linearly depends on the selling price of the item. Lead time is random and it follows a normal distribution. The proposed model is developed for both the centralized and the decentralized scenarios. In the decentralized scenario, a Stackelberg gaming approach is used to derive the optimal decisions. The developed models are illustrated by a numerical example. It is found that integration of the supply chain players gives an impressive increment in the profit of the whole supply chain. Sensitivity analysis is also performed to explore the impacts of key-model parameters on the expected average profit of the supply chain.