Multi-Objective Distributionally Robust Optimization for Earthquake Shelter Planning Under Demand Uncertainties

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Deciding the locations of shelters and how to assign evacuees to these locations is crucial for effective disaster management. However, the inherent uncertainty in evacuation demand makes it challenging to make optimal decisions. Traditional stochastic or robust optimization models tend to be either too aggressive or overly conservative, failing to strike a balance between risk reduction and cost. In response to these challenges, this research proposes a multi-objective distributionally robust optimization (MODRO) model tailored for shelter location and evacuation allocation. First, an ambiguity set (moment-based or distance-based) is constructed to capture the uncertainty in evacuation demand, reflecting the possible range of outcomes based on demand data from a disaster simulation model. Then, the distributionally robust optimization model considers the “worst-case” distribution within this ambiguity set to minimize construction cost, travel distance, and unmet demand/unused capacity, balancing the trade-off between overly conservative and overly optimistic approaches. The model aims to ensure that shelters are optimally located and evacuees are efficiently allocated, even under the most challenging scenarios. Furthermore, Pareto optimal solutions are obtained using the augmented ε-constraint method. Finally, a case study of Ogu, a wooden density built-up area in Tokyo, Japan, compares the DRO model with stochastic and robust optimization models, demonstrating that the cost obtained by the DRO model is higher than a stochastic model while lower than the worst-case robust model, indicating a more balanced approach to managing uncertainty. This research provides a practical and effective framework for improving disaster preparedness and response, contributing to the resilience and safety of urban populations in earthquake-prone areas.