Fields distinguished by edges and middles visited by heterogeneous vehicles to minimize non-working distances

In rice-wheat rotation systems in China, all vehicles working in fields have to make turns because these fields are surrounded by canals on three sides. All fields can be divided into two parts – the middle and edges which include the head, tail, and two sides of the field. In general, a field's edge is visited only by a small vehicle because it has a lighter weight and the soil does not easily become compacted due to the vehicle's many turns and sideways cuts. In addition, workers in heavy vehicles cannot easily distinguish ridges and crops on the two sides of the fields. Therefore, heavy vehicles can only visit the middle after the edges of these fields have already been completely worked by small vehicles. A general framework including a bi-level programming model and a two-stage algorithm constructed by a tabu search is proposed to optimize the non-working distance in intra- and inter-fields for heterogeneous vehicles based on distinguishing a field's edges and middle. In the bi-level programming model, the lower level determines the small vehicles’ routes and the middles of which fields will be visited by heavy vehicles, and the upper level determines the optimal routes for the heavy vehicles. Then, a case study is presented to verify the effectiveness and efficiency of the solution approach. The total non-working distance is reduced by 24.2%, a significant amount compared with the operational schedule on the farm. This study proposes a general framework for farmers to optimize the non-working distance for heterogeneous vehicles working in the edges and middles of fields.