Planning and Optimal Allocation of Agriucltural Production Resources under Uncertainty Application of Multi-Objective Fuzzy Goal Programming approach



Extended Abstract
1- Introduction
Uncertainty is an unavoidable aspect of decisions in agricultural planning. Inclusion of uncertainty in the optimization of crop planning and soil and water resources management has been provided by means of fuzzy mathematical programming approaches. Optimization procedures have been receiving much attention in agricultural economic research over several decades. LP is a single objective optimization technique and most of the farm planning problems are multi-objective in nature. Crop area planning or agricultural planning arenas involve multiple, conflicting and non-commensurable criteria and a satisfying decision is desired. Issues of risk, resources conservation and sustainability, environmental quality and social aspects of farming systems are as important as economic efficiency. It is clearly impossible to develop a single objective that satisfies all interests, all adversities and all political and social viewpoints. These are called multiple-criteria decision problems (MCDM), where the decision maker generally follows a satisfying solution rather than the maximization of objectives. Hence, decisions in the real world are often made on the basis of vague information or uncertain data and are fuzzy rather than precise.
Purpose and scope
This paper attempts to offer a solution to a crop planning problem using GP philosophy in an imprecise context of goals and constraints. Thus, the general objective of the paper is to introduce the technique of fuzzy goal programming (FGP) as a tool for area allocation models considering various socio-economic and environmental conflicting objectives involved in managing agricultural systems. Crop planning and allocation of production resources was performed in a comprehensive and imprecise manner to consider the whole environmental and socio-economic aspects of the farming system of the region. To this aim, the maximization of total area allocated to crops, net return and labor employment were fuzzily considered as problem objectives in order to maintain the population in the system and its durability. Monthly water availabilities were also considered fuzzily as the main problem constraints with regard to the recent drought periods and hence the crucial role of water in the region’s cropping pattern determination. Additionally, monthly labor force availability and requirements, seasonality (crop rotation), capital requirement, a lower bound constraints on fodder crops' cultivated area, and seasonal land availabilities are other fuzzy constraints of the problem.
2-Materials and methods
To simultaneously consider these multiple fuzzy objectives and fuzzy constraints (fuzzy goals), the problem of the study has been modeled as a multi-objective fuzzy goal programming procedure. Therefore, the socio-economic aspects of the farming system were considered in terms of maximizing the net return and labor employment opportunities fuzzily to include uncertainty.
The study area consists of two rural districts located in the northern and southern parts of the Zayandeh-Roud river, the most important central river of Iran, with fertile alluvial lands, namely northrn Baraan and southern Baraan. Total arable lands of area are close to 27000 ha, of which about 26000 ha are currently allocated to 9 major crops cultivated in two cropping seasons under irrigation.
The data to formulate the study problem were collected by completing the standard cropping cost-benefit questionnaire, by interviewing the farmers and also experts of the Regional Center of Agricultural Services, and provided finally per unit of area. Monthly preparation of the irrigation water requirements (IWR) data was carried out by considering two major national available data bases in this field. Additional processing operations were then applied to calibrate them for the region, based on the climatological circumstances and crop calendar. Adding together these monthly requirements, the seasonal IWR coefficients were provided to calculate the total water consumption. The monthly water resources availabilities from both groundwater and surface sources were also computed using the records of the regional water organization of the Isfahan and additional detailed geostatistical processing operations in GIS environment.
3-Results and discussion
Quantitative analysis of the results showed the precedence of FGP, based on the simultaneous achievement to the objectives over the others. Expenditure and water consumption of the FGP pattern are also less than the existing pattern, despite the nearly equal cultivated area of them, which indicates non-optimality of existing resources utilization in study area. The crop-mix in the FGP pattern has been changed so that the crops barley, rice, corn and onion have been excluded, area of alfalfa decreased and wheat and potato have also been increased in area.
Under the framework of the proposed model, all the objective functions and different environmental and socio-economic constraints can imprecisely be incorporated and a proper cropping plan can be made without involving any computational difficulty. Applying the multi-objective programming framework, the objectives of area, net return and employment maximization and the constraints of land, water, labor force and capital availability, rotation and a lower bound production are all fuzzily considered to determine an optimal cropping plan in a farming system. The comparison of the goal achievements and productive resources consumption in existing situations with the obtained goals of fuzzy multi-objective programming plan indicated the inoptimality of the current resources allocation and cropping pattern around the region. Changing the study rural region's existing pattern of cropping corresponding to the identified FGP results can help achieve considerable conservation of environmental and financial water and capital resources. Additionally, the income generation of the farming system is also increased as a result while the total area under cultivation remains unchanged. The only negligible drawback is that the employment rate is somewhat decreased. An extension of the investigated and applied fuzzy goal programming approach in agricultural systems planning for optimizing the ratio goal functions relating the outputs to the inputs may be one of the current research problems, which can be dealt with in the fields of fractional programming procedures.