Optimum Allocation of Agricultural Land to the Vegetable Crops under Uncertain Profits using Fuzzy Multiobjective Linear Programming

Abstract

Key words:Optimum Land allocation, Multiobjective LPP, Uncertain profits, Solver in Excel. I. IntroductionThe quantities of yield produced from agriculture farms and demand for that commodity influence the market prices significantly. Generally farmers follow a traditional method for a cropping pattern or allocation of land to various crops varies depending onthe available resources. Over the decade it has been observed that the net profit per acre is greater in vegetable crops (cash crops) than that of food crops. Thus for each cultivation pattern of vegetable crops, maximization of the profit will be the major objective of any farmer. These problems of allocation of land for different crops, maximization of production of crops, maximization of profit, minimization of production cost are addressed in agricultural management system with the help of Operations Research approach particularly with Linear programming Problem (LPP), Integer Programming problem(IPP), Assignment problem(AP) and Transportation Problem (TP). Initially, these problems of agriculture sector were modeled as single objective linear programming problem by dealing with one objective at a time. But with changing scenario of multifaceted real time problems, several objectives need to be handled simultaneously subject to the same set of constraints. Thus, the situation demands for new methodologies which are capable in handling the complex problem of decision making, as the maximization of crop production can"t guarantee the maximization of profit. In the agriculture sector, profit or loss also depend on fluctuating demand, supply and pricing of a particular crop with minimization of cost of cultivation needed for that crop. Thus the maximization of profit turns out to be a multiobjective decision making problem.The success of aneconomic model depends on the fact that how effectively it can sustain for volatility of market prices. Thus, a good model must accommodate the conditions of uncertainty and complexity, while handling imprecise information. For example, in financial engineering, the stock market prices aretreated as random variable and the efforts are provided for optimal plans with guaranteed return. Similarly, management of agribusiness plans at farmer"s level are very much needed to achieve the guaranteed returns despite the price fluctuations. In general food grains prices are not much volatile in nature and give almost guaranteed return, as in many countries (India) food grains have government support prices, whereas vegetable prices are mostly random variables and its cropping is also highly cost effective. In fact the vegetable cropping needs to manage the several costs viz., capital investment in insecticides, pesticides, fertilizers, frequent irrigation, labours and transportation cost. Sometimesunexpected production of same crops from local areas will also influence the market prices due lack of storagefacility. Surprisingly vegetable prices also vary on day to day basis even in the same season. By keeping in view of volatility ...

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