Multi-Objective Optimization with Fuzzy Demand for Integrated Facility Location and Dynamic Relief Response: Toward Balancing Cost and Efficiency

This paper studies the integrated facility location and dynamic relief response problem by developing a multi-objective optimization model with fuzzy demand that simultaneously optimizes the facility location cost and the total rescue cost, thereby balancing cost and efficiency. An optimal relief plan involves decisions on which facilities to open and which appropriate capacity levels to select, as well as how to dynamically manage inventory, replenishment and delivery for multi-type relief resources at each time period. To address fuzzy demand, we represent it as a trapezoidal fuzzy number and convert the multi-objective optimization model with fuzzy demand into a crisp one. We first propose a weighted metric method that relies on solving a single-objective mixed-integer linear program; however, it suffers from efficiency loss on larger-sized problem instances. To this end, we further develop a non-dominated sorting genetic algorithm II (NSGA-II) that integrates an enhancement strategy with approximate dynamic programming (ESADP). Computational experiments using real-world data from Gongyi City show that the NSGA-II algorithm with ESADP outperforms both the weighted metric method and the standard NSGA-II algorithm in terms of the number of non-dominated solutions, hypervolume ratio, average e-dominance and computational time. The results also highlight the advantage of our model in incorporating fuzzy demand and dynamic relief operations. Sensitivity analysis demonstrates the impact of changing the number of capacity levels and resource types with respect to the Pareto front, assessing the effectiveness of the proposed model.