Optimizing dynamic facility location-allocation for agricultural machinery maintenance using Benders decomposition

Abstract

This paper focuses on optimizing a dynamic facility location-allocation problem with respect to a real-life agricultural machinery maintenance service network that is designed to achieve the prompt and reliable response to malfunctioning agricultural machinery during harvest. We consider a busy farming season divided into several time periods in which the problem is to determine where to locate temporary maintenance stations (TMSs) as well as identifying how many capacitated service-providing facilities to allocate to each TMS to satisfy maintenance demands. The problem is formulated as a mixed integer program (MIP) that seeks to minimize the total service mileage between TMSs and demand points. Additionally, considering that the service flow from a TMS to a demand point in this type of work takes place between potential district locations rather than discrete vertices, we use regional contiguity constraints to enforce agricultural production areas served by a TMS as geographically connected. To solve our MIP problem, an exact algorithm based on Benders decomposition is then developed along with several refinements. Lastly, our model and methodology are illustrated in the handling of a real-world problem in China. Computational results are presented that analyze the optimized facility location-allocation plan, examine the impact of selected parameters, demonstrate the advantage of implementing the contiguity constraints and discuss the performance of solution algorithm.