This study deals with a two-level supply chain consisting of one manufacturer and one retailer. We consider an integrated production inventory system where the manufacturer processes raw materials in order to deliver finished product with imperfect quality to the retailer, where number of defective product has a uniform distribution. The retailer receives product and conducts a 100% inspection. We assume that unit price charged by the retailer influences the demand of the product. Thereby, this study establishes a link between the literature on shipment, ordering, pricing policies, imperfect quality and the joint economic lot-sizing literature. The objective is to maximize the total joint annual profits incurred by the manufacturer and the retailer. The retailer inspects the product and delivers perfect-quality product to the first market and the rejected products sent back to the manufacture to be sold in the second market. Shortages are permitted for the retailer and are completely backordered. The researchers assume the policy in which the shipment quantity is delivered to the retailer is identical at each shipment.The numerical study shows that coordination between supply chain members increases when the defective percentage is reduced, and the warranty cost increases. The warranty cost has more effect on decreasing maximum total profit under individual optimization. Manuscript profile

Hub networks play a crucial role in optimizing transportation flow and reducing overall costs by efficiently connecting origins and destinations through strategically placed hub nodes. The decision of hub location carries significant long-term implications and necessitates consideration of various factors within an uncertain environment. This paper addresses the hub arc location problem in hub networks, considering setup costs, isolated hubs, and uncertain flows between nodes. To tackle this challenge, a two-stage stochastic programming model is formulated to incorporate the uncertainty in flow volumes. Additionally, a robust optimization approach is proposed to enhance the resilience of hub location decisions against uncertain scenarios. The problem is solved using a tailored Genetic algorithm, which achieves optimal solutions with high quality and reasonable computational time. The results demonstrate the effectiveness of the proposed methodology in handling the uncertain nature of the hub location problem, contributing to the advancement of transportation planning and logistics optimization. The findings provide valuable insights for practical applications in real-world scenarios, offering a framework for decision-makers to make informed choices regarding hub network design and location. By integrating uncertainty and robust optimization techniques, this paper offers a comprehensive approach to address complex transportation network problems and improve overall efficiency in transportation systems. Manuscript profile