A combined benders decomposition and Lagrangian relaxation algorithm for optimizing a multi-product, multi-level omni-channel distribution system

The development of supply chain distribution systems from single- to multichannel networks for delivering items to end customers has effected many changes in the retail sector. Following the adoption of multi-channel distribution strategies and rapid development of relevant technologies, the omni-channel approach can yield signicant benets and facilitate trade with customers. This paper aims to optimize a multi-product, multi-level omni-channel distribution network and shipping ows of products within the network under uncertain conditions. A multi-objective mathematical model is developed that minimizes the costs of supply chain while maximizing customer satisfaction over different scenarios. In order to solve the proposed model, a combined algorithm is developed based on Benders Decomposition (BD) and Lagrangian Relaxation (LR). The presented model and solution approach are implemented in the case study of a distribution system, a large e-commerce startup, and an online store. Five different scenarios with different service levels are investigated and the numerical results are discussed compared to previous ndings. The efficiency of the proposed combined BD-LR solution algorithm is also demonstrated. The results obtained from the case study show that higher service levels are correlated with the higher levels of customer satisfaction and lower costs of the system.