Equity-Oriented Two-Echelon Vehicle Routing Problem: A Three-Phase Heuristic Algorithm - Xu, Shuling; Chen, Yue; Teng, Zeyu; Pu, Xujin (International Journal of Industrial Engineering: Theory, Applications and Practice, 2025)
Fierce competition and the requirement for sustainable development compel catering services and urban logistics industries to balance cost-efficient transportation with improved service quality and customer equity. The two-echelon vehicle cooperation system, where a primary vehicle (truck) serves as a mobile base for a secondary vehicle (UAV), has gained attention for its potential to leverage the strengths of both vehicle types, enhancing operational efficiency and service delivery. This paper presents an equity-oriented two-echelon vehicle operation problem, where trucks and UAVs cooperate to provide equitable services. We model the problem as a mixed-integer linear program (MILP), incorporating equity considerations through a set of constraints. Specifically, we adopt the relative range scheme from the literature as an equity indicator, aiming to minimize the relative deviation between the maximum and minimum arrival times for unit demand across customers. To solve it, we propose a three-phase heuristic algorithm that dynamically adjusts equity constraints while minimizing transportation costs. Numerical experiments across various instance sizes show that the algorithm consistently produces high-quality solutions with optimality gaps of less than 10%.