A priority based interval-valued Goal Programming approach for land utilization planning in agricultural system: A case study

Abstract

This paper demonstrates a Goal Programming (GP) Procedure for modeling and solving land utilization planning problems having interval-valued objective goals for optimal production of seasonal crops in agricultural system. In the proposed approach, utilization of total land for cultivation, aspiration levels of production of crops, expected profit from the farm as well as certain ratios of crops production and profit achievement are described interval-valued for goal achievement in the context of making proper cropping plan. In the model formulation of the problem, the defined interval-valued goals are converted into conventional goals by using interval arithmetic technique in interval programming (IP) and introducing under- and over-deviational variables to each of them. Again, certain ratio goals which are inherent to the problem are transformed into linear goals by employing the linear transformation approach to solve the problem by using the linear GP methodology. In the decision process, both the minsum GP and minmax GP approaches are addressed in the achievement function for minimizing the possible regret towards goal achievement from the optimistic point of view in the inexact decision making environment. The potential use of the approach demonstrated via a case example of the Nadia District, West Bengal (W.B), INDIA.