Warehouse-distribution integration routing problem under real-world transport conditions with multiple time windows and variable loading efficiency

The growing trend of e-commerce enterprises establishing their own warehouses has significantly enhanced operational efficiency in urban delivery. This has given rise to the Warehouse-Distribution Integration Routing Problem (WDIRP), a variant of the Vehicle Routing Problem (VRP). However, this type of problem under real-world transport conditions, especially considering multiple time windows and variable loading efficiency, has been insufficiently studied in the existing literature. This research addresses these characteristics to more accurately reflect real-world urban delivery challenges. To solve the problem, we propose a Mixed Integer Linear Programming (MILP) model for the WDIRP with a novel methodological approach to formulate multiple time windows, which can be efficiently solved using IBM ILOG CPLEX Optimization Studio (CPLEX). Additionally, we develop a two-stage heuristic algorithm that incorporates a multi-greedy method and a Variable Neighborhood Search (VNS) method, featuring new problem-specific neighborhood structures. The computational experiments encompass 20 randomly generated small-scale instances, 20 benchmark instances, and 18 realistic instances derived from diverse geographical areas and periods in Chongqing, China. Eighteen larger-scale extended instances are also developed to further test scalability, involving up to 50 warehouses and 500 customers. The realistic instances incorporate real-world transport conditions, including road topology, traffic performance, node distribution, and customer demand, with their corresponding parameters extracted or predicted using big data technologies. Our results demonstrate that the proposed model outperforms common formulations in computational performance, and the two-stage heuristic algorithm is superior to alternative approaches in solving the WDIRP. In addition to presenting results for various instances, we implement a mountainous city simulation model to achieve the 3D simulation of the delivery scheme. The findings provide valuable insights for logistics enterprises aiming to optimize urban delivery operations.