A mathematical model for sustainable probabilistic network design problem with construction scheduling considering social and environmental issues

Recent facility location allocation problems are engaged with social, environmental and many other aspects, besides cost objectives. Obtaining a sustainable solution for such problems requires development of new mathematical modeling and optimization algorithms. In this paper, an uncapacitated dynamic facility location-network design problem with random budget constraints is considered. Social issues such as public satisfaction as a function of construction time, number of missed jobs incurred in the regions under study and environmental considerations are incorporated in the model.Sincethe proposed model is expected to be capable of dealing with probabilistic network design, a new chance constraint formulation is proposed and manipulated to increase the applicability of the model in uncertain decisions. Moreover, the proposed method enables decision makers to determine the completion rate of projects through a time horizon while this notion is not achievable by applying other methods in the literature. The optimization of the proposed model is performed using anovel bi-section procedure in which a heuristic and a Simulated Annealing (SA) method are applied interactively. The efficiency of the proposed method is verified through a real world application of establishing a set of health care centers and the connecting links in Meshgin Shahr, Iran. The results of case study showed that all considered sustainable objectives come to a steady status in the fifth year. Also according to geographical data, the results about creating links are regional and the health centers have dispersed geographically in order to serve the demands of the whole under study region.