Multi-objective probabilistic forecast combination for inventory demand

2026-06-03

AI Summary

This study addresses a critical limitation in conventional ensemble methods for probabilistic forecasting, which focus solely on statistical accuracy while neglecting their downstream impact on multi-objective inventory management decisions—often resulting in high forecast accuracy without commensurate operational gains. To bridge this gap, the paper formulates probabilistic forecast combination as a multi-objective optimization problem that jointly optimizes forecast accuracy and nonlinear, conflicting inventory decision objectives. By employing multi-objective optimization algorithms, the approach generates a Pareto-optimal set of solutions, thereby explicitly aligning prediction with decision-making. Empirical evaluations on Walmart retail data and UK Royal Air Force spare parts demonstrate that the proposed method achieves a more robust trade-off between predictive accuracy and inventory performance compared to single models, simple averaging, and single-objective optimization baselines.

Abstract

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.

Problem

• probabilistic forecast combination
• inventory demand
• multi-objective optimization
• decision performance
• forecast accuracy

Innovation

• multi-objective optimization
• probabilistic forecast combination
• inventory decision-making
• Pareto-optimal
• forecast-operations alignment