Presenting a three-objective model in location-allocation problems using combinational interval full- ranking and maximal covering with backup model

Covering models have many applications in a wide variety of real-world problems. but some assumptions of covering models are not realistic enough. accordingly, a general approach would not be able to answer the needs of encountering varied aspects of real-world considerations. assumptions like the unavailability of servers, uncertainty, and evaluating more factors at the same time, are assumptions with which covering models are always faced; however, these models are not able to find any answers for them. therefore, how to deal with these sorts of assumptions has been always a question. in this research, for facing unavailability and uncertainty in input data, backup covering and interval full-ranking models are addressed, respectively. furthermore, by combining backup covering and interval full-ranking models (also conceptions), not only time is saved and more factors like efficiency and cost are simultaneously evaluated, but also covering considerations will be reachable in real aspects. the proposed model in this paper is searching for three assumptions to cover major features. emergency services are harshly sensible to delay, so the problem of server’s unavailability should be solved by considering backup coverage. moreover, inefficient facilities were absolutely neglected in covering literature despite their destructive role in serving customer demands. to overcome this problem, we have entered efficiency to our model by considering location of each facility as an input for a revised version of data envelopment analysis which is called full-ranking model. as many research have proved to believe in uncertainty, no one can neglect this feature in real-world, we have just defined data in intervals to consider this feature. in final, the evident absence of research in three mentioned key features in one frame has left covering literature in defect and brought about the proposed three-objective model in this paper which is called combined maximal covering with backup model (mcbm) and interval full-ranking.