Probabilistic forecasts are essential for inventory management, where decisions depend on the full distribution of future demand. While probabilistic forecast combination is widely used to improve statistical accuracy, most existing approaches optimize statistical loss alone and overlook operational objectives. However, in inventory settings, higher forecast accuracy does not necessarily translate into better decision performance, especially under nonlinear cost structures and multiple, potentially conflicting, decision targets. To address this gap, we propose a multi-objective probabilistic forecast combination framework that simultaneously considers forecast accuracy and inventory decision performance. The framework formulates forecast combination as a multi-objective optimization problem and derives a set of Pareto-optimal combinations, enabling explicit trade-offs between forecasting and operational goals. Empirical studies using Walmart retail data and Royal Air Force spare parts data demonstrate that the proposed approach achieves more balanced and robust performance than individual models, simple averaging, and single-objective optimization. Our results provide a practical and flexible framework for aligning probabilistic forecasting with inventory decision-making.

翻译：概率预测对于库存管理至关重要，因为决策依赖于未来需求的完整分布。尽管概率预测组合被广泛用于提升统计准确性，但现有方法大多仅优化统计损失，忽略了运营目标。然而，在库存场景中，更高的预测准确性并不一定转化为更好的决策性能，尤其是在非线性成本结构和多个潜在冲突的决策目标下。为填补这一空白，我们提出了一种多目标概率预测组合框架，该框架同时考虑预测准确性和库存决策性能。该框架将预测组合表述为多目标优化问题，并推导出一组帕累托最优组合，从而在预测目标与运营目标之间实现显式权衡。使用沃尔玛零售数据和英国皇家空军备件数据进行的实证研究表明，与单一模型、简单平均和单目标优化方法相比，所提方法能够实现更均衡且更稳健的性能。我们的结果为将概率预测与库存决策相统一提供了一个实用且灵活的框架。