In the service-oriented modern society, logistics enterprises focusing solely on cost minimization can no longer meet market demands, as customers place greater emphasis on timely delivery and service satisfaction. Therefore, this paper constructs a multi-objective optimization model that simultaneously minimizes distribution costs and hierarchical customer delivery duration. From the perspective of symmetry, the two objectives form a symmetric complementary system, which reflects the mutually restrictive and trade-off relationship between the two objectives, thereby facilitating the achievement of a balance between enterprise benefits and customer satisfaction. An improved multi-objective grey wolf optimizer (IMOGWO) is proposed to solve the model, incorporating a chaotic mapping initialization mechanism, a cosine nonlinear convergence factor, and a learning factor-based hunting mechanism to enhance global optimization capability. The algorithm’s effectiveness is validated through comparisons on benchmark cases. Applied to a Zhengzhou food company, the solution improved distribution efficiency while prioritizing key clients, thereby enhancing service levels and stabilizing important customer relationships, providing a practical reference for logistics enterprises to increase revenue and undergo digital transformation.
Zhang et al. (Wed,) studied this question.