A Mathematical Model for Vineyard Replacement with Nonlinear Binary Control Optimization

TL;DR

This paper develops a discrete nonlinear binary control model to optimize vineyard replacement timing, considering production decay, grape quality, and subsidies, aiming to enhance farm sustainability.

Contribution

It introduces a novel nonlinear binary programming approach to determine optimal vineyard replacement strategies under subsidy influences.

Findings

Optimal replacement triggers depend on subsidy levels.

The model effectively captures vineyard dynamics and economic incentives.

Results suggest improved decision-making for vineyard management.

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.