A multi-objective parameter-tuned soft computing-based algorithm to optimize competitive congested location-pricing problem within multi-type service

One of the issues that has attracted many researchers in the last decade is the problem of locating facilities i.e. hospitals, shops, banks and ATMs. One of the basic needs of the people of the community is easy access to the facilities, so that by spending little time can reach to the facility and with spending low cost to receive their facilities. In this paper, the location-pricing problem of the congested facilities by considering competition between available facilities and new facilities were investigated and bi-objective non-linear mathematical model that follow from M/M/m/k queuing system, was presented. In the first goal, maximize the profit of system by minimizing the total cost of establishing the facilities, shipping costumers and expectation time of the costumers in the queue and in the second goal the share of facility market minimized. The proposed model is in the category of non-linear integer programming problems, that, due to the complexity of the problem in the large scales and in order to solve the model, different approaches such as multi-objective meta-heuristic algorithms including non-dominated sorting genetic algorithm (NSGA-II) and multi-objective particle swarm optimization (MOPSO) has been presented. At the end, by applying the Taguchi method, the efficiency performance of NSGA-II algorithm perform better than MOPSO.