Microgrids are new challenging power systems under development. This report presents a feasibility study of microgrid development. This is an essential task before implementing microgrid systems. It is extremely important to know the number and size of distributed energy resources (DERs) needed and it is necessary to compare investment costs with benefits in order to evaluate the profitability of microgrids. Under the assumption that a large number of DERs improves the reliability of microgrids an optimization problem is formulated to get the accurate mix of distributed energy resources. Uncertainty in physical and financial parameters is taken into account to model the problem considering different scenarios.  Uncertainty takes place in load demanded, renewable energy generation and electricity market price forecasts, availability of distributed energy resources and the microgrid islanding. It is modeled in a stochastic way. The optimization problem is formulated firstly as a mixed-integer programming solved via branch and bound and then it is improved formulating a two stage problem using Benders’ Decomposition which shortens the problem resolution. This optimization problem is divided in a long-term investment master problem and a short-term operation subproblem and it is solved iteratively until it reaches convergence. Bender’s Decomposition optimization problem is applied to real data from the Illinois Institute of Technology (IIT) and it gives the ideal mix of distributed energy resources for different uncertainty scenarios. These distributed energy resources are selected from an initial set. It proves the usefulness of this optimization technique which can be also applied to different microgrids and data. The different solutions obtained for different scenarios are explained and analyzed. They show the possibility of microgrid implementation and determine the most favorable scenarios to reach the microgrid implementation successfully.  Reliability is a term highly linked to the microgrid concept and one of the most important reasons of microgrid development. Thus an analysis of reliability importance is implemented using the importance index of interruption cost (  ) in order to measure the reliability improvement of developing microgrids. It shows and quantifies the reliability improvement in the system.