An improved fractional-order grey model with Simpson quantum-behaved particle swarm optimization for emergency material demand prediction

Purpose To improve emergency-demand prediction under small-sample, high-volatility conditions, this study proposes a conformable quantum Simpson fractional grey model (CQSFGM). Design/methodology/approach The CQSFGM models fractional memory through conformable fractional accumulation (CFA) and conformable fractional difference (CFD), reconstructs background values using Simpson rule discretization to reduce truncation error compared with the trapezoidal rule, optimizes the fractional order via quantum-behaved particle swarm optimization (QPSO) to avoid subjective tuning, and updates the data in combination with the metabolic mechanism to adapt to non-stationary emergency demand data. Findings In the practical case, the mean absolute percentage error (MAPE) of CQSFGM is consistently lower than that of other benchmark models. Furthermore, robustness analyses confirm that this predictive advantage remains statistically significant under varying small-sample sizes and high-intensity noise perturbations, thereby providing support for emergency supply. Originality/value The CQSFGM model improves both accuracy and adaptability for emergency demand prediction.