A Fuzzy Multi-Objective Stochastic Programming Model for Allocation of Lands in Agricultural Systems

Abstract

In this chapter, a fuzzy stochastic multi-objective programming model is presented for planning proper allocation of agricultural lands in hybrid uncertain environment so that optimal production of several seasonal crops in a planning year can be achieved. In India, demands of various seasonal crops are gradually increasing due to rapid growth of population, whereas agricultural lands are gradually decreasing due to urbanization. Therefore, it is a huge challenge to the planners to balance this situation by proper planning for the utilization of agricultural lands and resources. From that viewpoint, the methodology is developed in this chapter. To make the model more realistic, the resource parameters incorporated with the problem are considered either in the form of fuzzy numbers (FNs) or random variables having fuzzy parameters. The two main objectives of this agricultural land allocation model are considered as maximizing the production of seasonal agricultural crops and minimizing the total expenditure by utilizing total cultivable lands in a planning period. These objectives are optimized based on the constraints: land utilization, machine-hours, man-days, fertilizer requirements, water supply, etc. As the parameters associated with the constraints are imprecise and uncertain in nature, the constraints are represented using either FN or fuzzy random variables (FRVs). The reasons behind the consideration of fuzzy constraints or fuzzy chance constraints (i.e., the reason for considering the parameters associated with the constraints as FNs or FRVs in the model) are clarified in detail. As a study region, the District Nadia, West Bengal, India is taken into account for allocation of land. To illustrate the potential use of the approach, the model solutions are compared with the existing land allocation of the district.