Towards the stochastic farmer´s problem and its L-shaped algorithm with fuzzy probability distribution

This work is concern with stochastic farmer´s problem where the fuzzy probability distribution is taken into consideration. We present a two-stage stochastic programming with fuzzy probability distribution (SPFPD) for farmer´s problem, and solve this model by making use of the improved L-shaped algorithm. The developed approach in this paper has two major transformation steps with fuzzy transformation and stochastic transformation. In the fuzzy transformation step, we use the alpha cut technique to defuzzify, and in the stochastic transformation step, we adopt minimax rule to establish the deterministic equivalent program associated to the stochastic programming. The numerical examples show the efficiency of the method developed in this paper.