Traditional Data Envelopment Analysis (DEA) models evaluate the efficiency of decision making units (DMUs) with common crisp input and output data. However, the data in real applications are often imprecise or ambiguous. This paper transforms fuzzy fractional DEA model constructed using fuzzy arithmetic, into the conventional crisp model. This transformation is performed considering the goal pr...

the environmental rules of reverse logistic networks have caused important economic growth in the past decades. to integrate forward logistic networks with reverse logistics networks a helpful method is to design both networks simultaneously. considering more retrieval choices in modeling reverse logistic systems can be very critical. this article contains a mixed integer linear programming mod...

The increasing consumption of electricity over time forces different countries to establishnew power plants and transmission lines. There are various crisp single-objective mathematicalmodels in the literature for the long-term power generation and transmission expansion planning tohelp the decision makers to make more reasonable decisions. But, in practice, most of the parametersassociated wit...

in ordet to investigate economic efficiency of five cultural systems in sugar beet crop, including high input, medium input  low input , high  and medium inputs without 3 times irrigation after emergence, an experiment was conducted over  two years  (2002-2003) in agricultural and natural resources research center of khorasan. these systems were analysed by marginal analysis and  linear program...