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The rapid development of smart cities and green logistics has stimulated a lot of research on reverse logistics, and the diversified data also provide the possibility of innovative research on location-routing problem (LRP) under reverse logistics. The purpose of this paper is to use panel data to assist in the study of multi-cycle and multi-echelon LRP in reverse logistics network (MCME-LRP-RLN), and thus reduce the cost of enterprise facility location.

First, a negative utility objective function is generated based on panel data and incorporated into a multi-cycle and multi-echelon location-routing model integrating reverse logistics. After that, an improved algorithm named particle swarm optimization-multi-objective immune genetic algorithm (PSO-MOIGA) is proposed to solve the model.

There is a paradox between the total cost of the enterprise and the negative social utility, which means that it costs a certain amount of money to reduce the negative social utility. Firms can first design an open-loop logistics system to reduce cost, and at the same time, reduce negative social utility by leasing facilities.

This study provides firms with more flexible location-routing options by dividing them into multiple cycles, so they can choose the right option according to their development goals.

This research is a pioneering study of MCME-LRP-RLN problem and incorporates data analysis techniques into operations research modeling. Later, the PSO algorithm was incorporated into the crossover of MOIGA in order to solve the multi-objective large-scale problems, which improved the convergence speed and performance of the algorithm. Finally, the results of the study provide some valuable management recommendations for logistics planning.