A Dynamic Multi-Objective Model for District-Level Post-Earthquake Resource Allocation Integrating Social Vulnerability, Occupational Safety, and Markov-Based Updating: An Istanbul Case Study

Post-earthquake emergency response planning requires rapid and adaptive resource allocation under disrupted accessibility, uneven district-level demand, and hazardous field conditions. In large metropolitan areas, these challenges are intensified by spatial differences in social vulnerability, infrastructure disruption, operational feasibility, and responder exposure. Static allocation approaches are often insufficient in such environments because they cannot adequately reflect temporal change or the evolving relationship between urgency, accessibility, and operational risk. This study proposes a dynamic multi-objective model for district-level post-earthquake resource allocation that integrates social vulnerability, occupational safety, and Markov-based updating within a single analytical framework. First, district priority scores are derived through an Analytic Hierarchy Process based on building damage ratio, intervention time, social vulnerability, critical infrastructure damage, secondary hazard risk, team capacity, and occupational safety. Second, a Markov-based updating mechanism is used to represent time-dependent redistribution across response periods. Third, a constrained weighted-sum multi-objective optimization model is formulated to balance district priority, social vulnerability, and responder safety under capacity and accessibility limits. The model is applied to Istanbul using official district-level data from national and local institutional sources. Scenario-based analysis is conducted under balanced, priority-oriented, vulnerability-oriented, and safety-oriented settings, together with static and dynamic model comparisons. The results show that the dynamic structure produces a more adaptive allocation profile than the static structure, with the share of the Very High allocation class declining from 37.66% to 34.95% and the Low allocation class increasing from 12.89% to 16.00% over the response horizon. The findings also indicate that greater emphasis on social vulnerability shifts allocation toward more fragile districts, whereas stronger safety emphasis reduces cumulative operational exposure at the cost of moderate reductions in immediate coverage. Overall, the study contributes to the disaster response literature by linking multi-criteria district prioritization, dynamic redistribution, and safety-aware allocation within a unified district-level decision structure. Beyond the Istanbul application, the proposed framework offers a practical basis for more responsive, equitable, and operationally sustainable post-earthquake planning in complex urban environments.