Modeling the impact of uncertain demand on intracity express delivery network design by adjustable data-driven robust approach

Abstract

With the rapid development of e-commerce, intracity express delivery services have become an integral component of modern logistics systems while facing unprecedented challenges. This paper addresses the service network design problem for capacity-constrained intracity express delivery systems. We propose a two-stage decision framework wherein the first stage determines vehicle routing plans and calculates transportation costs, and the second stage arranges parcel transportation based on actual demand and evaluates the associated penalty costs. Recognizing the uncertainty in demand inherent to real-world operations, this paper specifically examines how demand fluctuations affect system performance. To address this challenge, we construct an uncertainty set using support vector clustering (SVC) based on available historical data, which serves as the foundation for developing a data-driven adjustable robust optimization (ARO) model. Through linear decision rules and conic optimization theory, we transform the robust model into an equivalent mixed-integer linear programming formulation and develop a customized Benders dual decomposition algorithm for its solution. The proposed methodology is then applied to a case study concerning an autonomous delivery vehicle service network design in Yuhang, China. Computational results validate the effectiveness of our optimization approach.