the cost and income efficiency models with molp structure

in this paper, the cost and income efficiency models have been considered with regard to the multiple objective programming structures. for finding the efficient points in purposed molp problem, some various methods like lexicography & the weighted sum can be used. so by introducing the molp problem the cost & income efficiencies will be achieved. in the present study, the molp problem is converted to an objective function by the weighted sum of the objective function. so we determine the efficient hyperplanes gradient by finding the dual linear programming (lp) problem.