  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.
