Stochastic Joint Replenishment Optimization under Joint Inbound Operational Cost

With e-commerce concentrating retailers and customers onto one platform, logistics companies (e.g., JD Logistics) have launched integrated supply chain solutions for corporate customers (e.g., online retailers) with warehousing, transportation, last-mile delivery, and other value-added services. The platform’s concentration of business flows leads to the consolidation of logistics resources, which allows us to coordinate supply chain operations across different corporate customers. This paper studies the stochastic joint replenishment problem of coordinating multiple suppliers and multiple products to gain the economies of scale of the replenishment setup cost and the warehouse inbound operational cost. To this end, we develop stochastic joint replenishment models based on the general-integer policy (SJRM-GIP) for the multi-supplier and multi-product problems and further reformulate the resulted nonlinear optimization models into equivalent mixed integer second-order conic programs (MISOCPs) when the inbound operational cost takes the square-root form. Then, we propose generalized Benders decomposition (GBD) algorithms to solve the MISOCPs by exploiting the Lagrangian duality, convexity, and submodularity of the sub-problems. To reduce the computational burden of the SJRM-GIP, we further propose an SJRM based on the power-of-two policy and extend the proposed GBD algorithms. Extensive numerical experiments based on practical datasets show that the stochastic joint replenishment across multiple suppliers and multiple products would deliver 13∼20% cost savings compared to the independent replenishment benchmark, and on average the proposed GBD algorithm based on the enhanced gradient cut can achieve more than 90% computational time reduction for large-size problem instances compared to the Gurobi solver. The power-of-two policy is capable of providing high-quality solutions with high computational efficiency.