Mathematical Modeling and Stability Analysis of Agri-Food Tomato Supply Chains via Compartmental Analysis

Israel Benítez-García, Yasser A. Davizón (), Carlos Hernandez-Santos (), Nain de la Cruz, Amadeo Hernandez, Aureliano Quiñonez-Ruiz, Eric D. Smith, Jaime Sánchez-Leal and Neale R. Smith
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Israel Benítez-García: Unidad Académica de Ingeniería en Biotecnología, Universidad Politécnica de Sinaloa (UPSIN), Mazatlán 82199, Sinaloa, Mexico
Yasser A. Davizón: Tecnológico Nacional de México/IT Los Mochis, Juan de Dios, Batiz y 20 de Noviembre, Los Mochis 81259, Sinaloa, Mexico
Carlos Hernandez-Santos: Tecnológico Nacional de México/IT de Nuevo León, México, Av. Eloy Cavazos 2001, Guadalupe 66170, Nuevo León, Mexico
Nain de la Cruz: Centro de Investigación y de Estudios Avanzados del IPN, Unidad Monterrey, Vía del Conocimiento 201, Parque de Investigación e Innovación Tecnológica, Apodaca 66600, Nuevo León, Mexico
Amadeo Hernandez: Tecnológico Nacional de México/IT de Pachuca, Mexico, Blvd. Felipe Ángeles Km. 84.5, Venta Prieta, Pachuca de Soto 42083, Hidalgo, Mexico
Aureliano Quiñonez-Ruiz: Tecnológico Nacional de México/IT Los Mochis, Juan de Dios, Batiz y 20 de Noviembre, Los Mochis 81259, Sinaloa, Mexico
Eric D. Smith: Industrial, Manufacturing and Systems Engineering Department, University of Texas at El Paso (UTEP), El Paso, TX 79968, USA
Jaime Sánchez-Leal: Industrial, Manufacturing and Systems Engineering Department, University of Texas at El Paso (UTEP), El Paso, TX 79968, USA
Neale R. Smith: School of Engineering and Sciences, Tecnológico de Monterrey, Monterrey 64849, Nuevo León, Mexico

World, 2025, vol. 6, issue 3, 1-20

Abstract: Agri-food supply chains have experienced notable changes in recent decades, with tomatoes ( Solanum lycopersicum ) maintaining their status as a key global crop in terms of both production and consumption. These supply chains comprise a complex network of stakeholders—including producers, processors, distributors, and retailers—who collectively ensure the delivery of tomatoes from farms to consumers. This study develops mathematical models of agri-food tomato supply chains (AFTSCs) and examines their behavior through stability analysis and dynamic simulations based on a compartmental approach. Furthermore, the environmental impact is evaluated using a sustainability index, to which the waste diversion rate is introduced. This metric is defined as the proportion of diverted waste (i.e., materials recycled, reused, or composted) relative to the total waste generated, thereby enabling the quantification of sustainability performance within the system. Finally, a sensitivity analysis is conducted on the proposed dynamical models to validate and reinforce the findings.

Keywords: agri-food supply chains; mathematical modeling; compartmental analysis; stability analysis (search for similar items in EconPapers)
JEL-codes: G15 G17 G18 L21 L22 L25 L26 Q42 Q43 Q47 Q48 R51 R52 R58 (search for similar items in EconPapers)
Date: 2025
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