Nowadays, to meet the enormous computational requests, energy consumption, the largest part which is related to idle resources, is strictly increased as a great part of a data center's budget. So, minimizing energy consumption is one of the most important issues in the field of green computing. In this paper, we present a mathematical model formed as integer-linear programming which minimizes energy consumption and maximizes user’s satisfaction, simultaneously. However, migration variables, as principal decision variables of the model, can be relaxed to continuous activities in some practical problems. This constraint relaxation helps a decision maker to find faster solutions that are usually good approximations for optimum. Near feasible solutions (infeasible solutions that are desirably close to the feasible region) have been investigated as another relaxation considering the kind of solutions. For this purpose, we initially present a measure to evaluate the amount of infeasibility of solutions and then let the model consider an extended region including solutions with remissible infeasibility, if necessary.