عنوان مقاله [English]
In traditional covering problems, it does not depend on the distance of the demand nodes from the facility services for the level of coverage to receive the services. In a gradual cover location problem (GCLP), the covering objective depends on the distance of customers from the service centers. So, as distance from the facilities increases, the coverage level decreases. The gradual covering location problem, which tries to maximize all covered demand points, is one of the practical problems in facility location scope. In this study, facilities are considered as hierarchical modes with different capacities, nested, non-coherent, and multi-flow. In the real world, since the number of facilities and covering radii is different (due to societal issues such as traffic, weather, etc.) within time periods, a new dynamic backup hierarchical gradual covering mathematical model is proposed in this study to improve the systems distribution efficiency such as delays, covering, and general satisfaction of the system performance. In the proposed model, demand nodes which are not in the coverage radius of hierarchical facilities can be covered by intermediate facilities to increase the total coverage. Moreover, the proposed model considers the dynamic aspects of the problem such as dynamic locations and allocations in different periods. Based on the experimental results, the developed model can cover higher values of demands in comparison with the existing models in the literature. The application of the proposed model is in emergency management system which tries to rescue human life. Moreover, in order to solve the large-sized problems optimally, a simulated annealing Algorithm (SA) is proposed. To check the accuracy of presented heuristic method, some illustrative examples are given and solved by both exact and proposed metaheuristics approaches for classic gradual covering problems. The comparison of the obtained results verifies the efficiency of the proposed model and the algorithms in both optimality and computational time aspec.