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• Determining the urban critical infrastructures in the event of an earthquake. • Designing Location-Routing-Inventory decisions in humanitarian relief chain. • Simulation of interaction of urban infrastructure in earthquake conditions. • Using a cooperative game to examine the manner of cooperation of disaster relief supply chain players. • Application of the model to a real-world disaster relief logistic case study. This paper describes a new simulation based mathematical model for locating distribution centres, vehicle routing, and inventory problems under earthquake conditions. In this paper, the proposed network includes affected areas, suppliers, distribution centres, and hospitals. Additionally, the basic infrastructures of the city, which are very fragile at the time of the earthquake, are identified. Then, the demand of each relief commodity is calculated depending on the different earthquake scenarios using simulation. The estimated demand is incorporated into the mathematical model as an uncertain parameter. The proposed methodology is designed as a two-stage model so that in the first stage the location and inventory of distribution centres are addressed. Thereafter, in the second stage the routing decisions are taken for the distribution of relief commodities from the distribution centres and suppliers to the affected areas. Due to the NP-hardness of the second stage model, this model is solved using multi-objective stochastic fractal search. This algorithm is one of the population-based and stochastic optimization techniques and inspired by the natural phenomenon of fractal growth. It should be noted that in the second stage, a cooperative game theory of coalition type is considered, which resulted in synergies that minimize the relief golden time. The kind of cooperation is the use of potential of co-operators' vehicle. In this stage, the possibility for the players to cooperate by sharing people and commodities transportation requests is considered. Also, to validate the model, a real case study is provided for a possible earthquake in Tehran. Finally, the comparison between the simulation results and the values obtained from the real system evaluates the performance of the implemented model. Considering normality and a 95% confidence interval, it can be concluded that the proposed model provides a precise representation of the real system's performance. [ABSTRACT FROM AUTHOR]

Cascade disasters can destroy urban infrastructures, kill thousands of people, and permanently displace millions of people. The paramount goal of disaster relief programs is to save lives, reduce financial loss, and accelerate the relief process. This study proposes a bi-level two-echelon mathematical model to minimize pre-disaster costs and maximize post-disaster relief coverage area. The model uses a geographic information system (GIS) to classify the disaster area and determine the optimal number and location of distribution centers while minimizing the relief supplies' inventory costs. A simulation model is used to estimate the demand for relief supplies. Initially, vulnerable urban infrastructures are identified, and then the interaction among them is investigated for cascade disasters. The aims of this study are threefold: (1) to identify vulnerable urban infrastructures in cascade disasters, (2) to prioritize urban areas based on the severity of cascade disasters using a GIS, and (3) to develop a bi-objective multi-echelon multi-supplies mathematical model for location, allocation, and distribution of relief supplies under uncertainty. The model is solved with an epsilon-constraint method for small and medium-scale problems and the invasive weed optimization algorithm for large-scale problems. A case study is presented to demonstrate the applicability and efficacy of the proposed method. The results confirm the difficulty of relief operations during the night as the cost of night-time relief operations is higher than daytime. In addition, the results show the coverage area increases as the demand surges. Therefore, establishing more distribution centers will increase operating costs and expand coverage are. [ABSTRACT FROM AUTHOR]

In Iran, location is usually done by temporary relief organizations without considering the necessary standards or conditions. The inappropriate and unscientific location may have led to another catastrophe, even far greater than the initial tragedy. In this study, the proposed locations of crisis management in the region and the optimal points proposed by the Geographic Information System (GIS), taking into account the opinions of experts and without the opinion of experts, were evaluated according to 18 criteria. First, the optimal areas have been evaluated according to standard criteria extracted by GIS and the intended locations of the region for accommodation in times of crisis. Then, the position of each place is calculated concerning each criterion. The resulting matrix of optimal options was qualitatively entered into the Preference Ranking Organization Method for Evaluation (PROMETHEE) for analysis. The triangular fuzzy aggregation method for weighting and standard classification of criteria for extracting optimal areas using GIS and integrating entropy and the Multiobjective Optimization Based on Ratio Analysis (MOORA) method for prioritizing places in the region are considered in this research. Finally, by applying constraints and using net input and output flows, optimal and efficient options are identified by PROMETHEE V. Among the research options, only four options were optimal and efficient. A case study of the Tehran metropolis is provided to show the ability of the proposed approach for selecting the points in three modes, with/without applying weights and applying crisis management. [ABSTRACT FROM AUTHOR]