A multi-objective districting problem applied to agricultural machinery maintenance service network

The prompt and reliable response to malfunctioning agricultural machinery of a maintenance service network is extremely critical for the safety and stability of agricultural production during the harvest. This research aims to cluster a set of given agricultural production areas into a specified number of service regions while assigning a service facility to maintenance demands in each region. The service region districting problem is formulated as a multi-objective mixed integer program (MIP) that seeks to minimize the total service mileage between facilities and demand points while minimizing the service demand overload in each service region. Additionally, we use modified contiguity constraints to enforce a single service region as geographically connected, which means that one can travel between any two locations in the region without leaving it. To solve our multi-objective MIP problem, the ɛ-constraint method is used to develop a set of non-inferior solutions that allow us to examine the trade-off between minimizing service mileage and minimizing demand overload and offer us a set of Pareto optimal decisions to consider for implementation. Lastly, our model and methodology are illustrated in handling a real-world problem in China. Computational results are presented that analyze the trade-off between objectives, examine the impact of selected parameters and demonstrate the advantage of implementing the modified contiguity constraints.