: One of the main principles in an energy management system is achieving efficiency and equity in resources allocation. In the Multi-objective optimization solution leads to a number of Pareto efficient answers (called Pareto front) where each solution demonstrates an equilibrium of the cooperative game. Then by introducing three criteria namely, Minimum Distance (MD), Minimum Normalized Distance (MND) and Minimum Difference Normalized Distance (MDND) finding an equilibria point, in which allocation is equitable, would be achievable. Therefore, we achieve to an allocation that is the most efficient and equitable, simultaneously. By using the proposed criteria, a bi-level optimization problem is modeled in which in the upper level the criteria is optimized and in the lower level all the possible equilibria points are found. The proposed model is implemented in a test system. The numerical results appreciate the capability of the proposed model. Keywords: energy management, equity in allocation, cooperative game, optimization problem constrained by other optimization problems, multi-objective optimization
