Optimization Modelling of Agricultural Production under Resource Constraints

Abstract

Agriculture plays a crucial role in the economy of India by contributing to food security, employment generation, and economic development. This study examines the growth performance, instability, and optimization of major agricultural crops in India using time series data from 1980–81 to 2024–25. The analysis focuses on cereals (wheat, rice, maize), pulses (tur and lentil), and cash crops (sugarcane and cotton). Compound Annual Growth Rate (CAGR) and Cuddy-Della Valle Instability Index were employed to evaluate the growth and variability in area, production, and yield across three sub-periods and the overall study period. The results indicate that wheat and rice exhibited relatively stable growth due to irrigation facilities, technological advancement, and government support, whereas pulses showed lower growth and higher instability because of their dependence on rainfall and climatic variability. Maize emerged as the fastest-growing cereal crop, while cotton demonstrated high growth accompanied by significant instability. To achieve efficient utilization of limited agricultural resources, a linear programming optimization model was developed under constraints of land, water, fertilizer, and labor availability. The simplex method was applied to obtain the optimal crop allocation pattern. The model produced a maximum agricultural production of 2064.77 million tonnes, with sugarcane receiving the highest optimal allocation. The study highlights the importance of optimization modelling for sustainable agricultural planning and efficient resource management in India.