Production routing decisions in a two‐echelon supply chain with multiple delivery modes

We study an original two-echelon production routing problem with multiple delivery modes (2E-PRP-MDM). In the first echelon, the primary production facility is tasked with satisfying the demands of two distinct entities: a set of warehouses and a set of customers through direct shipments. In the second echelon, warehouses become delivery hubs, meeting the needs of another group of customers with the possibility of delivering several customers using the same vehicle, which entails routing decisions. The use of two different delivery modes is justified by the segmentation of customers into very important customers with high volumes (first echelon) and low-volume customers (second echelon). This supply chain structure requires efficient decisions on production planning, routing, and practical resource allocation across both echelons. In order to address this challenging optimization problem, we have developed a mixed-integer linear programming (MILP) formulation and two heuristics, a three-phase iterative (3PI) approach, and a simulated annealing (SA) algorithm with path relinking. Extensive numerical experiments showed that the simulated annealing heuristic with path relinking (PR) outperforms the 3PI approach, which in turn outperforms the branch-and-cut procedure of the solver when run on the MILP formulation. In terms of managerial insights, we compared scenarios with and without delivery flexibility from the manufacturing to warehouses to the customers. Our findings provide valuable insights for managers seeking to reduce costs, based on the analysis of the supply chain of an Algerian soft drink company. The results show that an integrated approach achieves a cost reduction of over 2.73% compared to the current practice of the company. Additionally, they reveal that increasing the number of warehouses does not always lead to lower total costs.