The Agricultural Spraying Vehicle Routing Problem With Splittable Edge Demands

TL;DR

This paper introduces a new splittable vehicle routing problem for agricultural spraying, allowing demand splitting among multiple sprayers, and develops solution methods that outperform classical models in cost and efficiency.

Contribution

It formulates the splittable agricultural vehicle routing problem as a mixed integer linear program and proposes novel solution techniques, including formulations, lazy constraints, and heuristics.

Findings

Proposed methods effectively solve the SCARP with real-world data.

SCARP can yield cheaper solutions than classical CARP in some cases.

Heuristic repair improves solution quality for large problems.

Abstract

In horticulture, spraying applications occur multiple times throughout any crop year. This paper presents a splittable agricultural chemical sprayed vehicle routing problem and formulates it as a mixed integer linear program. The main difference from the classical capacitated arc routing problem (CARP) is that our problem allows us to split the demand on a single demand edge amongst robotics sprayers. We are using theoretical insights about the optimal solution structure to improve the formulation and provide two different formulations of the splittable capacitated arc routing problem (SCARP), a basic spray formulation and a large edge demands formulation for large edge demands problems. This study presents solution methods consisting of lazy constraints, symmetry elimination constraints, and a heuristic repair method. Computational experiments on a set of valuable data based on the properties of real-world agricultural orchard fields reveal that the proposed methods can solve the SCARP with different properties. We also report computational results on classical benchmark sets from previous CARP literature. The tested results indicated that the SCARP model can provide cheaper solutions in some instances when compared with the classical CARP literature. Besides, the heuristic repair method significantly improves the quality of the solution by decreasing the upper bound when solving large-scale problems.