Designing a robust sustainable service network for agricultural machinery maintenance under demand uncertainty

Abstract A well‐designed agricultural machinery maintenance service network can facilitate manufacturers to provide prompt and sustainable responses to mechanical failures. This paper addresses a sustainable agricultural machinery maintenance service network design (MMSND) problem, and focuses on selecting the optimal locations for the maintenance centers and districting the area into distinct districts. The aims of this paper are to minimize the total service mileage, balance the service workload, and guarantee the compactness of districts. We adopt goal programming method to model these three conflicting objectives. In addition, we also address the uncertainty of demand to seek the sustainability of the service network. As a result, we first develop a novel globalized robust goal programming model with semi‐infinite constraints. Then the semi‐infinite constraints are reformulated to their computationally tractable robust counterparts via Fenchel duality theory. To effectively solve the obtained mixed‐integer linear goal programming, we design a tailored Benders decomposition algorithm based on the structural characteristics of our model reformulation. Finally, we verify the credibility of the proposed method via a real case about the agricultural MMSND problem from Hunan province in China and a set of randomly generated larger scale instances. The computational results reveal that it is necessary and effective to consider the uncertain demand and our globalized robust optimization method can alleviate the conservatism of robust optimal solutions resulted from uncertain demand.