Assignment problem (AP) has been usually used to solve decision-making problems in the industrial organization, manufacturing system, developing service system, etc., is to optimally resolve the problem of n-activities to n-devices such that total cost/time can be minimized or total profit/sales can be maximized. In today’s optimization problems, the single objective optimization problems (SOOPs) are not more sufficient to hold the problem facts, hence multi-objective optimization problems (MOOPs) are considered. The purpose of MOOPs in the mathematical programming (MP) structure is to optimize several objective functions under some constraints. In research, the multi-objective field does not give a single optimal solution, but a set of efficient solutions because there are frequently conflicts between the various objectives. In the multi-objective assignment problem (MOAP), significant research concerns related to the study of effective solutions. The current chapter focuses on a genetic algorithm (GA) based approach to find a solution to MOAP. In order to achieve an effective allocation plan, the decision-maker (DM) must specify different aspiration levels (ALs) according to his/her preferences and different shape parameters (SPs) in the exponential membership function (EMF) to show the effect of integration on the effective solution of MOAP. Numerical illustrations are provided to express the usefulness of a specific approach related to the data set from realistic circumstances. This research turned out to be a GA based approach provides effective output based on analysis to take the decision regarding the situation.