Optimization with fuzzy constraints in agricultural production planning

Abstract

Agricultural production systems are operated under severe uncertainty. One possibility in coping with the uncertainty in the decision-making process, is to create several plans for different expert assumptions of the unpredictable factors dominating the production, to evaluate the expected value of each plan and to select the largest one. This can be done by using linear programming (LP). In the suggested method, as in the above mentioned one, LP is used as the first stage of the decision-making process. However, in this method, we use the LP's post-optimal sensitivity analysis (POSA). POSA's insensitivity limits of the decision variables of the various solutions are used to create a set of two-sided non-equivalent inequalities. On the basis of this set and a fuzzy solution of a system of inequalities, fuzzy constraints are formulated. An algorithm to optimize a linear objective function with varied coefficients subjected to fuzzy constraints has been developed and is presented. The approach and the method are introduced and demonstrated using an unirrigated farm whose production is dominated by unpredictable rainfall. To evaluate the method, its production and the regular LP production plans were compared, with a significant advantage to the suggested method.