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

Highlights

• Models agricultural machinery maintenance service network districting.

• Considers the contiguity criteria enforcing a service region as geographically connected.

• Explores non-inferior solutions with fewer service mileage and comparable demand overload.

• Examines sensitivity of solutions to selected parametric assumptions.

Abstract

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.

Introduction

Agricultural machinery has become a foundational resource and essential tool in modern agricultural production even in developing countries, e.g. China (He, Li & Wang, 2018; Sopegno, Calvo, Berruto, Busato & Bocthis, 2016; Zhang, Hao & Sun, 2017). In busy farming seasons, agricultural machinery always works highly efficiently to complete production tasks at high temperatures and over complex geography, which can easily result in machine failure (Caffaro, Mirisola & Cavallo, 2017; Lorencowicz & Uziak, 2015; Molari, Badodi, Guarnieri & Mattetti, 2014). To ensure that agricultural production is carried out safely and stably, a service network needs to be designed by the agricultural machinery manufacturer, known as the service provider, to provide prompt and reliable maintenance services for failed machines.

This research focuses on the strategic and operational districting issues of a service network for agricultural machinery maintenance. During the harvest, many agricultural machines, e.g. rice harvesters, tractors and other farm transport vehicles, are geographically distributed across different production areas (Zhang et al., 2017). When designing a maintenance service network for failed machines, the agricultural machinery manufacturer clusters a set of production areas into a specified number of service regions and assigns a service facility to attend to demands in each service region. This can be seen as a service region districting problem in service network design.

Service network design problems are a challenging class of combinatorial optimization problems that have been the subject of great development over the past decades, e.g. supply chain networks (Contreras, Fernández & Reinelt, 2012; Eskandarpour, Dejax, Miemczyk & Péton, 2015; Farahani, Rezapour, Drezner & Fallah, 2014), emergency medical service networks (Başar, Çatay & Ünlüyurt, 2012; Bélanger, Kergosien, Ruiz & Soriano, 2016; Beraldi, 2009; Kergosien, Bélanger, Soriano, Gendreau & Ruiz, 2015; Syam & Côté, 2010) and after-market service networks (Gómez Fernández & Crespo Márquez, 2009; Wheatley, Gzara & Jewkes, 2015). In general, the majority of research aforementioned combines two main types of decisions, facility location-allocation and vehicle routing decisions, which focus on determining the location-allocation of service facilities and the routes of vehicles for serving customers. However, there are few studies to address district-based service network design. Particularly, almost no research has been proposed on districting a service network in the area of agricultural machinery maintenance.

This paper aims to present an optimization model to handle the proposed districting problem and the contributions are threefold:

• Multiple objectives are considered that seek to minimize the total service mileage between service facilities and their demands served while also minimizing the demand overload in each service region. Minimizing the total service mileage reflects the manufacturer attempting to reduce the total service cost incurred, meanwhile, lower demand overload always means a faster response to demands by a service facility and indicates a higher level of customer satisfaction.

• In contrast to that demands and facilities in service network design are always assumed to be located at discrete vertices, the service flow from a facility to failed machines in this work takes place in connected production areas. Because the crop ripening time varies with different geographic areas due to differences in climate and terrain, connected production areas always imply a similar climate, terrain and crop ripening time. Demands in such connected areas are assigned to the same service facility, which could effectively reduce service opening hours and resource waste. Thus, the contiguity criteria, which refers to the level of quality within a single service region being connected, is required when districting the service network.

• To solve a multi-objective mixed integer programming (MIP) problem finally formulated, the ɛ-constraint method is employed to find a set of non-inferior solutions that allow a decision maker to assess the trade-off between objectives and examine the impact of selected parametric assumptions.

The remainder of this paper is structured as follows. Section 2 reviews the literature related to districting problems. Section 3 presents the multi-objective MIP model in this study and describes the solution method. In Section 4, a real-world application in China illustrates the effectiveness of this research. Lastly, concluding remarks and further avenues of study are given in Section 5.