Integrated optimization approach to multi-depot order splitting and heterogeneous vehicle routing with time windows

With the rapid development of online retail, order splitting and time-limited distribution have become two key issues of the order fulfillment process in a multi-depot environment. Existing studies and operations in practice usually deal with these two issues separately, ignoring the coupling relationship between them. This paper studies the integrated optimization of multi-depot order splitting and heterogeneous vehicle routing problems in the online retail environment, especially considering finite inventory and time windows constraints. We construct a mixed integer programming model for this problem and design an integrated optimization algorithm with branch price and neighborhood search nested in each other to solve it. Based on the initial order splitting scheme, we solve the heterogeneous vehicle routing problem with time windows by branch price algorithm, and a bidirectional label-setting algorithm is proposed to accelerate the solution of the pricing subproblem. Then, the neighborhood search algorithm is used to find a feasible order splitting scheme under the current optimal vehicle route solution. Optimize the distribution route when adjusting the order splitting scheme by alternating the branch price algorithm and the neighborhood search algorithm for iterative solution. The experimental analysis verifies the effectiveness of the model and algorithm, showing that the algorithm can reduce the order splitting rate, optimize the distribution route, and reduce the total cost of distribution, thus effectively realizing the integrated optimization of order splitting and heterogeneous vehicle route. © 2023 Systems Engineering Society of China. All rights reserved.