# Joint Location-Allocation Model for Multi-Level Maintenance Service Network in Agriculture
## 6 Conclusions and Future Work  
This paper considered a multi-level facility location-allocation problem in agricultural maintenance service networks to find the optimal location of service stations and spare part centres while allocating service units to service stations. Considering multi-level constraints and contiguity criteria, a MILP-based optimal model was formulated to minimize total service costs. A Benders decomposition-based solution algorithm with several improvements was developed to address the MILP model. Finally, a real case in East China was introduced to demonstrate the performance of the developed mathematical model and solution approach, and sensitivity analysis was conducted to evaluate the effect of several parameters.  
Computational results demonstrated that total service costs experience a downward trend with the increase in the number of service stations and the reduction becomes smaller with the increase in the number of service stations. In addition, total service costs also increase with the decrease in the value of the maximum service distance. In this case, the number of service stations may be set as 20 to 30, and the maximal service distance may be set as 130 km to 160 km from a comprehensive perspective. In addition, contiguity constraints should be considered to prohibit cross-region services and ensure a contiguous service area for managers in practical application. Lastly, considering the solution time, the proposed Benders decomposition can be applied in different size cases especially in the large size case.  
There exist several limitations in this work. First, the maintenance demands are calculated based on the number of agricultural machines and agricultural production areas; thus, the maintenance demands in one service unit can be determined based on a more scientific method, combining historical data, the number of agricultural machines, and the machine learning method. In addition, agricultural machinery may move dynamically to other service units during the busy farming seasons, and the influence of the dynamic movement of agricultural machinery on maintenance demands is not considered in this paper.  
Thus, this research can be improved in several ways in the future. On the one hand, considering the uncertain maintenance demand in agricultural service networks, robust optimization should be considered to construct a more stable maintenance service network. On the other hand, there are several service facilities participating in maintenance service in the busy farming season, and the location of these dynamic service facility locations should be considered in further studies.  
Figure 9: The practical application in Henan Province.  
**Author Contributions:** Methodology, J.L. and W.R.; Validation, J.L., W.R. and X.W.; Writing--original draft, J.L. and W.R. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Key R&D Program of China, grant number No. 2020 YFB1709601.  
**Data Availability Statement:** The key data are shown in the manuscript and all data can be obtained from the authors.  
**Acknowledgments:** We express our sincere gratitude to Weichai Lovol Heavy Industry Co., Ltd. for the case verification.  
**Conflicts of Interest:** The authors declare no conflict of interest.