A Probabilistic and adaptive strategy for the newsvendor problem with periodic demand

• A Probability-based Adaptive Strategy (PAS) is proposed for the Periodic-Featured Newsvendor problem (PFNV), integrating bounded rationality and regret psychology to balance effectiveness and operability. • PAS utilizes dual reference points (data-driven) and probabilities (guided by minimax regret) in a four-step decision process, with two schemes (random sampling and expectation construction) for flexibility. • Experiments on simulated mixed distributions and real-world restaurant data show PAS captures periodic trends, with PAS_2 (weekday-classified) paired with EC achieving the lowest average cost in most cases. • PAS outperforms several traditional benchmarks, offers practical guidance for retailers on data usage and reference point design, and extends research on cognition-model-data integration in supply chains. The newsvendor problem with periodic demand (PFNV) is a common and significant challenge in practice, where traditional methods such as optimization, statistical analysis, and artificial intelligence often struggle to balance effectiveness and operability. We propose the Probability-based Adaptive Strategy (PAS) for the PFNV problem, which formulates decisions through the dual reference points and probabilities. The decision-making process comprises four steps that simulate human behavior based on bounded rationality. The design of reference points is data-driven, using either a linear method or a multi-armed bandit (MAB), while probability calculation is guided by an optimization objective that reflects human regret psychology. The final decision is made through either a random sampling (RS) or an expectation construction (EC) scheme. Experiments with both simulated and real-world data show that PAS effectively captures periodic trends in both stable and volatile datasets. The PAS combining classification, MAB, and the EC scheme performs better in average cost in most cases, while other variants exhibit different characteristics under varying conditions. Compared with several benchmarks, PAS demonstrates potential for cost optimization in certain scenarios while maintaining both operability and interpretability.