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

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

Copyright: © 2019 |Pages: 35
DOI: 10.4018/978-1-5225-8301-1.ch010

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.
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10.1 Background And Planning In Agricultural Sector

In agricultural sector proper utilization of cultivable lands and production planning are two most important tasks for both social and economic perspectives. Agricultural sector is the oldest and most essential sectors in the world. Due to the increasing growth of population, the demand for the agricultural products is rapidly increasing. One way to meet the demand of the society is to increasing the cultivating land areas scientifically. But a developing country, like India, is losing land due to rapid population growth, urbanization and industrialization. Therefore, there is an increasing need for designing appropriate mathematical models for land allocation planning in agricultural systems. Mathematical Programing (MP) models for agricultural planning problems are widely used since Heady (1954) demonstrated the use of linear programming (LP) for land allocation to crop planning problems.

Thereafter, LP models are widely used for maximizing the production of various crops (Arnold and bennet, 1975), allocation of cultivable lands (Glen, 1987), and minimizing the cost of cultivation of the farmers (Barnard and Nix, 1973). Thereafter, several LP models of different farm planning problems are extensively studied (Nix, 1979; Black and Hlubik, 1980). The potential use of LP for agricultural planning was studied further by Tsai et al. (1987). Qingzhen et al. (1991) developed an optimal production plan for crop and livestock. Some researchers (Wiens, 1976; Adams et al., 1977; Simmons and Pomareda, 1975) used quadratic programming techniques to formulate the relationship between demand and prices and also to incorporate certain risk factors in agricultural problems. Mathematical models for agricultural water management which are essential for crop area planning were developed by Leenhardt et al. (2004) and Ding et al. (2006).

Generally, several conflicting objectives such as maximizing production of crops, minimizing expenditures, maximizing profit, etc., are involved with agricultural planning. As demonstrated in this book, Goal Programming (GP) appeared as a powerful tool for solving different types of problems with conflicting objectives. GP was first introduced by Charnes and Cooper (1961) and its methodological developments were performed by Ijiri (1965), Ignizio (1976) and several others. A review on GP was made by Romero (1986), Tamiz and Jones (1995) and others. Lee and Clayton (1972) successfully implemented GP methodology in different decision making problems. The use of preemptive priority based GP to land-use planning problem was discussed by Pal and Basu (1996). Saker and Quaddus (2002) formulated a nationwide crop planning model using GP and discussed the importance of three different goals for the case problem. Oliveria et al. (2003) presented a GP model for forest farm planning problems. Ghosh et al. (2005) suggested a GP formulation for nutrient management for rice production.

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