Optimal treatment of agricultural land – special multi-depot vehicle routing problem

Abstract

This paper describes a problem of optimal agricultural land treatment using aviation. The studied problem consists of determining the optimal routes for a given set of aircraft used for chemical treatment of arable agricultural land divided into parcels. This NP (nondeterministic polynomial time) problem is represented on a graph and a mixed integer mathematical programming model of the problem is formulated. This mathematical model is a specific variant of the multi-depot vehicle routing problem where a min-cost plan for the transportation of a homogeneous product (chemicals used for land treatment) from different supply locations (airfields) to different demand locations (agricultural parcels) should be generated. Some specifics of the agricultural land chemical treatment are described in the paper and the following specific conditions are taken into consideration: each parcel is treated only by one way of treatment and one aircraft; for each aircraft its chemical and fuel reservoir capacities are sufficient to serve its route. The complexity of the problem and the impossibility to obtain exact solutions for larger dimensions of the problem led to the formulation of a special heuristics which is presented in this paper. Numerical experiments are successfully conducted for larger problem dimensions and results are presented.