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.
Andrić Gušavac B., Stojanović D., Sokolović Ž. (2014): Application of some locational models in natural resources industry – Agriculture case. In: Marković A., Barjaktarović Rakočević S. (eds): Operational Research and Quantitative Methods in Management. Serbia, 1141–1148.
Clark G., Wright J.W. (1964): Scheduling of vehicles from a central depot to a number of delivery points. Operations Research, 12: 568–581. https://doi.org/10.1287/opre.12.4.568
Conesa-Munoz J., Pajares G., Ribeiro A. (2016): Mix-opt: A new route operator for optimal coverage path planning for a fleet in an agricultural environment. Expert Systems with Applications, 54: 364–378. https://doi.org/10.1016/j.eswa.2015.12.047
Dantzig G.B., Ramser J.H. (1959): The truck dispatching problem. Management Science, 6: 80–91. https://doi.org/10.1287/mnsc.6.1.80
Desrochers M., Laporte G. (1991): Improvements and extensions to the Miller-Tucker-Zemlin subtour elimination constraints. Operations Research Letters, 10: 27–36. https://doi.org/10.1016/0167-6377(91)90083-2
Ewers R.M., Scharlemann J.P., Balmford A., Green R.E. (2009): Do increases in agricultural yield spare land for nature? Global Change Biology, 15: 1716–1726. https://doi.org/10.1111/j.1365-2486.2009.01849.x
Gaur D.R., Mudgal A., Singh R.R. (2013): Routing vehicles to minimise fuel consumption. Operations Research Letters, 41: 576–580. https://doi.org/10.1016/j.orl.2013.07.007
Gracia C., Velazquez-Marti B., Estornell J. (2014): An application of the vehicle routing problem to biomass transportation. Biosystems Engineering, 124: 40–52. https://doi.org/10.1016/j.biosystemseng.2014.06.009
Hameed I., Bochtis D., Sorensen C.A.G. (2013): An optimised field coverage planning approach for navigation of agricultural robots in fields involving obstacle areas. International Journal of Advanced Robotic Systems, 10: 1–9.
Harasimowicz S., Janus J., Bacior S., Gniadek J. (2017): Shape and size of parcels and transport costs as a mixed integer programming problem in optimisation of land consolidation. Computers and Electronics in Agriculture, 140: 113–122. https://doi.org/10.1016/j.compag.2017.05.035
Hayashi K. (2000): Multicriteria analysis for agricultural resource management: A critical survey and future perspectives. European Journal of Operational Research, 122: 486–500. https://doi.org/10.1016/S0377-2217(99)00249-0
JetBrains (2018): Python IDE for Professional Developers. Available at https://www.jetbrains.com/pycharm/download/#section=windows (accessed July 11, 2018).
Kulkarni R.V., Bhave P.R. (1985): Integer programming formulations of vehicle routing problems. European Journal of Operational Research, 20: 58–67. https://doi.org/10.1016/0377-2217(85)90284-X
Kung Ch.-Ch. (2018): A dynamic framework of sustainable development in agriculture and bioenergy. Agricultural Economics – Czech, 64: 445–455. https://doi.org/10.17221/281/2017-AGRICECON
Mahmud M.S.A., Abidin M.S.Z., Mohamed Z. (2018): Solving an agricultural robot routing problem with binary particle swarm optimisation and a genetic algorithm. International Journal of Mechanical Engineering and Robotics Research: 7: 521–527.
Mahmud M.S.A., Abidin M.S.Z., Mohamed Z., Rahman M.K.I.A., Iida M. (2019): Multi-objective path planner for an agricultural mobile robot in a virtual greenhouse environment. Computers and Electronics in Agriculture, 157: 488–499. https://doi.org/10.1016/j.compag.2019.01.016
Mghirbi O., Le Grusse P., Fabre J., Mandart E., Bord J.-P. (2017): OptiPhy, a technical-economic optimisation model for improving the management of plant protection practices in agriculture: a decision-support tool for controlling the toxicity risks related to pesticides. Environmental Science and Pollution Research, 24: 6951–6972. https://doi.org/10.1007/s11356-016-6775-1
Mosleh Z., Salehi M.H., Amini Fasakhodi A., Jafari A., Mehnatkesh A., Esfandiarpoor Borujeni I. (2017): Sustainable allocation of agricultural lands and water resources using suitability analysis and mathematical multi-objective programming. Geoderma, 303: 52–59. https://doi.org/10.1016/j.geoderma.2017.05.015
Sawik T. (2016): A note on the Miller-Tucker-Zemlin model for the asymmetric traveling salesman problem. Bulletin of the Polish Academy of Sciences Technical Sciences, 64: 517–520. https://doi.org/10.1515/bpasts-2016-0057
Seyyedhasani H., Dvorak J.S. (2017): Using the Vehicle Routing Problem to reduce field completion times with multiple machines. Computers and Electronics in Agriculture, 134: 142–150. https://doi.org/10.1016/j.compag.2016.11.010
Sorensen C.G., Bochtis D.D. (2010): Conceptual model of fleet management in agriculture. Biosystems Engineering, 105: 41–50. https://doi.org/10.1016/j.biosystemseng.2009.09.009