A branch-and-price method for a two-echelon location routing problem with recommended satellites

Abstract

In city logistics, the two-echelon location routing problem is crucial in coordinating resources and radiating nodes, enabling the efficient planning of relay stations and vehicle distribution routes. However, with the expansion of distribution scopes and changes in urban development, fixed relay stations may not be able to adapt to the evolving network demand structure, leading to reduced efficiency. This paper proposes a two-echelon location routing problem with recommended satellites (2E-LRPRS) to address this issue. These satellites are chosen from the customer set and can be reoptimized to enhance the network's adaptability. A mixed-integer linear program (MILP) is formulated to minimize the distribution cost of the two-echelon network. To solve this problem, a column-generation algorithm (CG) is proposed, which decomposes the original problem into a linear relaxation main problem and a series of two-stage shortest-path subproblems with resource constraints. The branch-and-pricing algorithm (B&P) is then designed to obtain the integer solution. The experimental results demonstrate that the proposed B&P is significantly more efficient and effective than the MILP solver - Cplex. Furthermore, by selecting relay stations from customers, the recommended satellites can be flexibly adjusted based on the locations and demands of distribution customers, leading to an average operating cost savings of 8.43%.