Optimization models for nopal crop planning with land usage expansion and government subsidy

Abstract

This paper studies the production planning of edible nopal cactus in Morelos (a state of Mexico), considering the land usage expansion to account for the increase of the demand along the years. To this end, two optimization models are proposed and formulated as mixed-integer linear programs. One mimics the current practice of minimizing the total production costs while satisfying all the demand in each planning period; whereas, the other reflects a policy of maximizing the total profit of the farmer and calculates the proportion of the demand to be satisfied in each planning period. Additionally, a lexicographic programming model is introduced to estimate the minimum government subsidy that compensates the lack of profit in periods with lower demand and higher costs. Historical harvesting data was obtained from annual reports of the Agrifood and Fisheries Information Service, and used in the formulated models. A comparison of both optimization models shows that the profit maximization model provides the best balance between profit and subsidy. Finally, a sensitivity analysis on variations of price, minimum profit, and production costs, shows that the price has the strongest effect on all KPIs in all the cases. This work shows that the current practice of producing all the amount of demanded nopal is inadequate. The profit maximization policy shows a slight less profit but needs significant less subsidy to meet the minimum monthly profit. Moreover, as the optimization models converge in less than a second, the decision maker has the opportunity to analyze a wide variety of scenarios in a short period of time.