Many research works in mathematical modeling of the facility location problem have been carried out in discrete and continuous optimization area to obtain the optimum number of required facilities along with the relevant allocation processes. This paper proposes a new multi-objective facility-location problem within the batch arrival queuing framework. Three objective functions are considered: (I) minimizing the weighted sum of the waiting and the traveling times, (II) minimizing the maximum idle time pertinent to each facility, and (III) minimizing the total cost associated with the opened facilities. In this way, the best combination of the facilities is determined in the sense of economical, equilibrium, and enhancing service quality viewpoints. As the model is shown strongly NP-hard, two meta-heuristic algorithms, namely genetic algorithm (GA) and simulated annealing (SA) are proposed to solve the model. Not only new coding is developed in these solution algorithms, but also a random search algorithm is proposed to justify the efficiency of both algorithms. Since the solution-quality of all meta-heuristic algorithms severely depends on their parameters, design of experiments and response surface methodologies have been utilized to calibrate the parameters of both algorithms. Finally, computational results obtained by implementing both algorithms on several problems of different sizes demonstrate the performances of the proposed methodology.