A data-driven problem for integrating carbon-sensitive pricing into inventory optimization

In the face of increasingly stringent carbon regulations and volatile energy markets, integrating environmental constraints into inventory optimization problems raises crucial questions: Is it always economically justified? And what level of problem complexity is appropriate? This paper proposes a data-driven threshold framework that helps businesses assess when and how to incorporate carbon emission constraints and whether to optimize for simpler or more advanced formulations. Three profit-maximizing inventory problems are developed with varying levels of carbon constraints and order cancellation flexibility and compared across a wide range of scenarios reflecting different demand, cost, and energy profiles. A novel feature of our approach is the integration of an emission-sensitive dynamic pricing function , linking production quantity and carbon impact directly to market demand. The preparation and simulation of data construct a model based on realistic operational conditions of manufacturing enterprises, incorporating input parameters such as inventory holding costs, energy consumption levels, average market demand, and standard deviation to replicate real-world scenarios. Using simulation, Principal Component Analysis (PCA), and machine learning classification, we identify distinct operational regions where each problem is most effective. Our results show that carbon constraints are not universally beneficial: in some contexts, simpler problems yield higher profits, while in others, more complex carbon-aware strategies are essential. The proposed framework provides both a scientific basis and actionable guidelines for managers looking to align profitability with environmental responsibility under uncertainty. • Identify threshold conditions guiding problem choice for carbon-sensitive inventory decisions. • Integrate carbon pricing directly into inventory and pricing optimization problems. • Use Principal Component Analysis and Decision Trees to simplify complex operational trade-offs. • Provide data-driven rules to enhance sustainable and cost-efficient decisions. • Validate a decision framework with over 87% accuracy across diverse scenarios.