Ana Esteso1, MME Alemany1, Ángel Ortiz1 and Hervé Panetto2

1 Research Centre on Production Management and Engineering (CIGIP), Universitat Politècnica de València, Camino de Vera S/N, 46022 Valencia, Spain;

2 University of Lorraine, CNRS, CRAN, France,,,

Keywords: Agri-Food, Perishability, Quality, Unfairness, Collaboration, Optimization.

1. Introduction

Vegetables’ consumers are increasingly looking for fresher and higher quality products. However, some farmers do not have the resources or knowledge to improve the quality and freshness of their products. This problem is widespread among small farmers with plantation areas of less than two hectares that are responsible for the 80% of the world’s agricultural production [1]. As a solution, some authors propose to create a collaboration program between retailers and farmers to improve the quality of agri-food products through funds given by retailers to farms.

Most of them consider that retailers directly select the farmers on which invest by maximizing the supply chain profits to be obtained [2-4]. However, these approaches do not take into account the role of farm cooperatives in the distribution of funds nor model some characteristics of the agri-food sector such as the perishability of vegetables or the relation between prices and the freshness of sold products.

2. Multi-Objective Model Proposal

This paper proposes a multi-objective model to support the distribution of funds among farmers in which the perishability of vegetables and the dependence of prices on the freshness of vegetables are modelled, being these last two characteristics novel in literature. Other novelties lie in the joint optimization of the supply chain profits, the economic unfairness among farmers, the unfairness in the distribution of funds, the generated waste and the freshness of vegetables sold. This last two objectives have neither been previously modelled in the analyzed papers.

The multi-objective model is defined for a supply chain composed by small farmers, cooperatives, retailers, and markets. It is assumed that farmers harvest vegetables, classify them according to their quality, and send them to the cooperative to which the farmers are affiliated. Retailers send vegetables with higher qualities to retailers while the rest are directly sold to markets at a lower price.

In this context, retailers fund farmers to increase the proportion of high-quality vegetables to be harvested at their lands. The budget for such funds is limited. Farmers can use the obtained funds to improve their skills and consequently the quality of their harvest by receiving formation, acquiring new machineries or technologies, among others.

3. Conclusions

After proposing the model, it was implemented in the optimization software MPL® 5.0.8 and solved with GurobiTM 8.1.1. First, the conflict between the objectives was verified by performing a partial correlation analysis on a set of non-dominated solutions. These solutions were obtained through lexicographic optimization.

Once the conflict among objectives was verified, the ε-constraint method was applied to solve the multi-objective model. Results were analyzed in terms of supply chain profits, waste generated along the supply chain, economic unfairness perceived by farmers, unfairness in the distribution of funds perceived by farmers, freshness of products at their sale, and percentage of demand that cannot be met.

Results show that similar profits are obtained in most non-dominated solutions while the rest of the indicators can be considerably improved, facilitating the willingness of stakeholders to implement the solution obtained by the model.

Acknowledgements. The authors acknowledge the support of the Project 691249, “RUCAPS: Enhancing and implementing Knowledge based ICT solutions within high Risk and Uncertain Conditions for Agriculture Production Systems”, funded by the EU under its funding scheme H2020-MCSA-RISE-2015.


  1. Lowder SK, Skoet J, Raney T (2016) The Number, Size, and Distribution of Farms, Smallholder Farms, and Family Farms Worldwide. World Dev 87:16-29.
  2. Wahyudin RS, Sutopo W, Hisjam M, et al (2015) An Agri-food Supply Chain Model for Cultivating the Capabilities of Farmers in Accessing Capital Using Corporate Social Responsibility Program. Proc Int MultiConference Eng Comput Sci II:877-882
  3. Esteso A, Alemany MME, Ortiz Á, Guyon C (2018) A Collaborative Model to Improve Farmers’ Skill Level by Investments in an Uncertain Context. IFIP Adv Inf Commun Technol 590-598.
  4. Esteso A, Alemany MME, Ortiz Á, Zaraté P (2020) Optimization Models to Improve First Quality Agricultural Production Through a Collaboration Program in Different Scenarios. IFIP Adv Inf Commun Technol 546-559.



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Proceedings of the 15th International Conference on Industrial Engineering and Industrial Management and XXV Congreso de Ingeniería de Organización Copyright © by (Eds.) José Manuel Galán; Silvia Díaz-de la Fuente; Carlos Alonso de Armiño Pérez; Roberto Alcalde Delgado; Juan José Lavios Villahoz; Álvaro Herrero Cosío; Miguel Ángel Manzanedo del Campo; and Ricardo del Olmo Martínez is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.

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