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

This paper considers a two-level supply chain which is composed of a single manufacturer and multiple retailers. The ordered quantities of the retailers are delivered in some equal sized batches from the manufacturer. Customer demand is linearly dependent on the retail price of the product. Lead time is random and it follows a normal distribution. The proposed models are developed for both the centralized and the decentralized scenarios. In the decentralized model, a Stackelberg gaming approach is used to find the optimal solution. The developed models are illustrated by a numerical example. It is found that integration of the supply chain players gives an impressive increment in profit of the whole supply chain. Sensitivity analysis is also carried out to explore the impacts of key parameters on the expected average profit of the supply chain system.