Determination of Non–inferior Set by Incorporating Risk in Multi-Objective Programming: A Case Study of Farmers in Fasa District

The endogenous selection and determination of return reference level is important in specifying risk efficient set. Thus, using multi-objective programming, Target–MOTAD in the framework of Mean-PAD and maximin parametric analysis models was established to obtained reference level of return endogenously. To determine non–inferior set for the farmers understudy, at first, the pay-off matrix was obtained through maximizing objectives under consideration. Then, upper and lower bounds of non-inferior set were determined using non- inferior set estimation (NISE) technique. The results obtained from maximin model indicated that Min and Max of maximin model were 270252 and 217753 thousands Rials, respectively. Furthermore, a subset of non-inferior set was obtained using different return reference levels. Comparing the results of model and the current farmers' plan showed that the current acreage of crops, except for sugar beet was approximately placed in the range determined by the model. In addition, the results also indicated that farmers' plan could be a non- inferior set. Considering the importance and also scarcity of water in the study area, average water return in the farmers' plan was compared to non-inferior set which included all the upper and lower non-inferior set. The results showed that farmers obtained 18150 Rials per hours of used water. However, average water return changed the range of 19100 to 30200 Rials for non-inferior set, indicating that farmers are able to use water more efficiently. The results also showed that changing farmers' cropping pattern is a complicated task and that it is necessary to have a systematic view in ordere to achieve desirable change.