Integrated supply chain scheduling of procurement, production, and distribution under spillover effects

Abstract This paper considers an integrated scheduling problem in an e-commerce supply chain. The supply chain consists of heterogeneous suppliers, consumer-goods manufacturers that offer online channels, and a network of retailers. Suppliers provide raw materials or semi-finished products to manufacturers. Then, manufacturers produce and deliver end items to retailers. The retailers require that the manufacturers maintain a given fill rate, and, otherwise, a penalty will apply. Missing the fill rate can not only result in penalties, but also retailers’ switching, operational issues, and loss of image, and market value. Therefore, the total penalty costs are nonlinear with retailers’ unsatisfied quantities and the fill rate, which exhibits spillover effects. The problem is to select a subset of suppliers, assign retailers’ orders, and identify a production schedule with the manufacturers while minimizing the total costs that includes shipping and penalty. In this paper, we formulate a mixed-integer nonlinear program and develop a hybrid particle swarm optimization algorithm that can find a suitable solution within a reasonable time. The algorithm incorporates augmented Lagrangian relaxation and particle swarm optimization. We then perform computational testing on randomly generated cases and evaluate the performance of the proposed algorithm. Our numerical experiments show that the proposed algorithm is robust and efficient. Moreover, we provide a real case study, which demonstrates that the proposed model can lead to a substantial reduction of both the total and penalty costs.