Joint Location–Allocation Model for Multi-Level Maintenance Service Network in Agriculture

The maintenance service network is always designed as a multi-level service network to provide timely maintenance service for failed machinery, and is rarely studied in agriculture. Thus, this paper focuses on a three-level maintenance service network location–allocation problem in agriculture, which contains several spare part centres, service stations, and service units. This research aims to obtain the optimal location of spare part centres and service stations while determining service vehicle allocation results for service stations, and the problem can be called a multi-level facility location and allocation problem (MLFLAP). Considering contiguity constraints and hierarchical relationships, the proposed MLFLAP is formulated as a mixed-integer linear programming (MILP) model integrating with P-region and set covering location problems to minimize total service costs, including spare part centre construction costs, service vehicle usage costs, and service mileage costs of service stations. The Benders decomposition-based solution method with several improvements is then applied to decompose the original MLFLAP into master problem and subproblems to find the optimal solutions effectively. Finally, a real-world case in China is proposed to evaluate the performance of the model and algorithm in agriculture, and sensitivity analysis is also conducted to demonstrate the impact of several parameters.