applied sciences Article Reverse Logistics Location Based on Energy Consumption: Modeling and Multi-Objective Optimization Method Lijun Chang 1, Honghao Zhang 2,3,*, Guoquan Xie 4, Zhenzhong Yu 5,*, Menghao Zhang 6, Tao Li 4, Guangdong Tian 1,2 and Dexin Yu 1,6 1 School of Transportation Engineering, Jilin University of Architecture and Technology, Changchun 130114, China; [email protected] (L.C.); [email protected] (G.T.); [email protected] (D.Y.) 2 Key Laboratory of High Efficiency and Clean Mechanical Manufacture, Ministry of Education, School of Mechanical Engineering, Shandong University, Jinan 250061, China 3 Chongqing Key Laboratory of Vehicle Emission and Economizing Energy, Chongqing 400000, China 4 School of Traffic and Transportation Engineering, Central South University, Changsha 410000, China; [email protected] (G.X.); [email protected] (T.L.) 5 HRG International Institute for Research & Innovation, Hefei 230000, China 6 School of Transportation Engineering, Jilin University, Changchun 130022, China; [email protected] * Correspondence: [email protected] (H.Z.); [email protected] (Z.Y.) Abstract: The low-carbon economy, as a major trend of global economic development, has been a widespread concern, which is a rare opportunity to realize the transformation of the economic way in China. The realization of a low-carbon economy requires improved resource utilization efficiency and reduced carbon emissions. The reasonable location of logistics nodes is of great significance in the optimization of a logistics network. This study formulates a double objective function optimization model of reverse logistics facility location considering the balance between the functional objectives of Citation: Chang, L.; Zhang, H.; the carbon emissions and the benefits. A hybrid multi-objective optimization algorithm that combines Xie, G.; Yu, Z.; Zhang, M.; Li, T.; a gravitation algorithm and a particle swarm optimization algorithm is proposed to solve this reverse Tian, G.; Yu, D. Reverse Logistics logistics facility location model. The mobile phone recycling logistics network in Jilin Province is Location Based on Energy applied as the case study to verify the feasibility of the proposed reverse logistics facility location Consumption: Modeling and model and solution method. Analysis and discussion are conducted to monitor the robustness of the Multi-Objective Optimization results. The results prove that this approach provides an effective tool to solve the multi-objective Method. Appl. Sci. 2021, 11, 6466. optimization problem of reverse logistics location. https://doi.org/10.3390/app11146466 Keywords: reverse logistics location; optimization; energy consumption; benefits; modelling Academic Editor: Giancarlo Mauri Received: 25 May 2021 Accepted: 7 July 2021 Published: 13 July 2021 1. Introduction China is the world’s most populous country, with a population of more than 1.41 bil- Publisher’s Note: MDPI stays neutral lion as of 2021. At present, the academic circles have extensive discussions on the resource with regard to jurisdictional claims in utilization of waste products, and the research on the reverse logistics of waste products published maps and institutional affil- is gradually being carried out with the continuous extension from both the academic iations. world and industries in recent years [1,2]. According to the findings of Rogers and Tibben- Lembke, the total logistics cost amounted to USD 862 billion in 1997, and the total cost spent in reverse logistics is enormous and amounted to approximately USD 35 billion, which was around 4% of the total logistics cost in the same year [3]. The concerns about Copyright: © 2021 by the authors. energy saving, green legislation and green manufacturing are increasing [4]. Licensee MDPI, Basel, Switzerland. The concept of reverse logistics was put forward by Stock in the 1990s, which aims This article is an open access article at high efficiency and environmental protection and which maximizes the application distributed under the terms and value of products by optimizing the operation structure [4]. With the ever-rising needs conditions of the Creative Commons of reverse logistics, firms possessing optimal planning of return routes, inventory and Attribution (CC BY) license (https:// warehouse layouts for returned products are more competitive than the others. Reverse creativecommons.org/licenses/by/ logistics has changed the original resource flow mode, and the single logistics system has 4.0/). Appl. Sci. 2021, 11, 6466. https://doi.org/10.3390/app11146466 https://www.mdpi.com/journal/applsci Appl. Sci. 2021, 11, 6466 2 of 25 evolved into a closed-loop system because of the participation of reverse logistics. Reverse logistics, including product return, maintenance, remanufacturing, waste disposal and other processes, is the mirror reverse process of traditional logistics. The purpose of this method is to extract and utilize the value in the waste repeatedly and to improve the production chain [5]. Regarding distribution paths, the routing and scheduling of reverse logistics are more complex than those of forward logistics. The routing of reverse logistics starts from the designated regional distribution center to the centralized return center and then to manufacturers for remanufacturing or to manufacturers directly without passing through the centralized return center. Due to the uncertainty of return quantities, the physical flow channel is more complicated than that in forward logistics. Since different areas have various product return rates, the locations of collection points can significantly affect the efficiency of recycling [3]. A series of systemic theoretical explorations and literature reports for reverse logis- tics location have been investigated in recent years [5,6]. For example, Savaskan et al. established a decentralized decision system with three schemes and concluded that the agent nearest to the customer is the best one to undertake product recycling [7]. Park et al. analyzed the influences of different subjects on recycling price and profit and built a closed-loop supply chain model with a single recycling channel [8]. Liu et al. investi- gated the competition between formal recycling channels and the informal, concluding that high-quality recycled products were more attractive to the two recycling channels, while the non-normal recycling channels were willing to recycle at a higher price [9]. Tas- birul et al. estimated the economic value generated in the recycling logistics of electronic waste gas based on the sales inventory life model and provided suggestions for decision makers [10]. In addition, construction of a reverse logistics model is an important part of the research on reverse logistics location. Shih et al. studied the recycling model of waste household appliances with the aim of minimizing the recycling cost and analyzed the influence of recovery rate and storage state on the recycling network [11]. Lee et al. built a two-stage recycling model and carried out an entry study on the problem of uncer- tain recycling quantity [12]. To solve the multi-objective optimization problem of reverse logistics location, some evolutionary algorithms have been applied, e.g., the ant colony algorithm [13], simulated annealing algorithm [14], particle swarm optimization [15] and the genetic algorithm [16]. In summary, most of the existing research literature starts from cost recovery or benefit recovery and takes the maximum benefit or minimum cost as the objective function. However, economic benefit is only one of the benefits of reverse logistics, and how to use recycling behavior to produce considerable environmental benefits cannot be ignored. It is contrary to the original intention of the circular economy to take economic benefit as a single goal. Thus, it is necessary to take energy consumption or other indicators that can reflect the utilization of resources into consideration and to consider the balance between each indicator and the profit of each objective. In addition, how to efficiently achieve optimal design under multiple factors and objective functions has become a significant research topic and can be regarded as a typical multi-objective optimization problem. This paper formulates a double objective function optimization model of reverse logistics facility location considering the symmetry among the functional objectives of the carbon emissions and benefits. A hybrid multi-objective optimization algorithm that combines a gravitation algorithm and a particle swarm optimization algorithm is proposed to solve this reverse logistics facility location model. Subsequently, an empirical case of a mobile phone recycling logistics network in Jilin Province is applied to verify the feasibility of the proposed reverse logistics facility location model and the multi-objective optimization method. Analysis and discussion are conducted to monitor the robustness of the results. The paper is organized as follows: Section2 introduces a reverse logistics facility location model with the functional objectives of addressing carbon emissions and the resulting benefits. In Section3, we develop a hybrid multi-objective optimization algorithm, Appl. Sci. 2021, 11, 6466 3 of 25 combining the theories of the gravitation algorithm and the particle swarm optimization algorithm. An empirical case of the mobile phone recycling logistics network in Jilin Province is applied to verify the effectiveness of the model and solution methodology in Section4. Analysis and