Joint reserve-dispatch optimization for emergency supplies: a dual-penalty NSGA-II approach under fuzzy transportation uncertainty

Amid the escalating frequency of natural disasters and public emergencies worldwide, this research addresses the joint optimization of emergency material reserve allocation and distribution scheduling under conditions of fuzzy transportation uncertainty. A multi-echelon, multi-supply collaborative optimization model is formulated with the dual objectives of minimizing total transportation duration and overall system cost. Transportation time, cost, and loss rate parameters are characterized using triangular fuzzy numbers, while robust constraints are implemented to ensure performance underworst-case scenarios. A modified Dual-Penalty NSGA-II algorithm is introduced, integrating both constraint violation penalties and objective-based penalties alongside hybrid initialization sampling. Validation through a case study of the COVID-19 outbreak in Wuhan demonstrates that the proposed solution achieves an effective equilibrium between economic expenditure and temporal efficiency, whilesimultaneously optimizing reserve quantities and dispatch configurations. Comparative analysis reveals the superior performance of the proposed algorithm over the classical NSGA-II approach, withadditional sensitivity analysis examining the operational implications of varying minimum satisfaction thresholds. This research provides substantive decision-support insights for emergency managementauthorities and practitioners.