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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

A Mathematical Model for Vineyard Replacement with Nonlinear Binary Control Optimization

Discontinuity, Nonlinearity, and Complexity 9(2) (2020) 173--186 | DOI:10.5890/DNC.2020.06.001

Aníbal Galindro$^{1}$, Adelaide Cerveira$^{2}$, Delfim F. M. Torres$^{3}$, João Matias$^{4}$, AnaMarta-Costa$^{1}$

$^{1}$ Centre for Transdisciplinary Development Studies, University of Tr´as-os-Montes and Alto Douro, Polo II–ECHS, Quinta de Prados, 5000-801 Vila Real, Portugal

$^{2}$ INESC-TEC, Department of Mathematics, University of Tr´as-os-Montes and Alto Douro, Quinta de Prados, 5000-801 Vila Real, Portugal

$^{3}$ Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal

$^{4}$ CMAT-UTAD, Department of Mathematics, University of Tr´as-os-Montes and Alto Douro, Quinta de Prados, 5000-801 Vila Real, Portugal

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Abstract

Vineyard replacement is a common practice in every wine-growing farm since the grapevine production decays over time and requires a new vine to ensure the business sustainability. In this paper, we formulate a simple discrete model that captures the vineyard’s main dynamics such as production values and grape quality. Then, by applying binary non-linear programming methods to find the vineyard replacement trigger, we seek the optimal solution concerning different governmental subsidies to the target producer.

Acknowledgments

This work was supported by the R&D Project INNOVINE & WINE – Vineyard and Wine Innovation Platform – Operation NORTE-01-0145-FEDER-000038, co-funded by the European and Structural Investment Funds (FEDER) and by Norte 2020 (Programa Operacional Regional do Norte 2014/2020). Torres was supported by FCT through CIDMA, project UIDB/04106/2020. The authors are very grateful to two anonymous Reviewers for several suggestions, questions and remarks, which helped them to improve the paper.

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