Fuzzy Goal Programming for Agricultural Land Allocation Problems

This paper presents a fuzzy goal programming (FGP) approach for optimal allocation of land under cultivation and proposes an annual agricultural plan for different crops. In the model formulation, goals such as crop production, net profit, water and labor requirements, and machine utilization are modeled as fuzzy. A tolerance based FGP technique is used to quantify fuzziness of different goals for the problem. The fuzzy goals are transformed to linear constraints by introducing tolerance variables. The program then minimizes the values of the weighted sum of tolerance allowance variables for the highest membership grades, providing the most satisfactory set of allocations possible. As a measure of sensitivity, the problem is solved using different weight structures specified by the decision maker. A case study is provided to illustrate the usefulness of the method.