A Rough Interval-Based Inventory Model for Sustainable Production with Carbon Emission Considerations

With growing concerns over environmental pollution, production firms are increasingly focusing on minimizing carbon emissions alongside achieving financial sustainability. So, in recent years, researchers have concentrated on developing production inventory models with carbon emissions and various emission regulatory policies. However, a significant limitation in most of the existing models is the assumption that carbon emission rates from various inventory processes are constant throughout the inventory cycle. In reality, these rates fluctuate due to factors such as the efficiency of carbon filtration systems, machine breakdowns, variations in raw material quality, and the type of fuel or energy used. Additionally, these parameters often exhibit uncertainty, either varying within specific ranges or being assessed at multiple levels. This chapter proposes a production inventory model considering carbon emission where both emission rates and product demand are represented as rough interval numbers. Since precise assessment of these factors is often impractical due to limited data, expressing them as rough intervals provides a more realistic approach compared to conventional fuzzy or interval-based representations. By applying the expected value approach for rough intervals, the optimal inventory decisions are obtained using the Particle Swarm Optimization (PSO) algorithm within the framework of the cap-and-trade carbon emission policy. To illustrate the proposed methodology, a numerical example is provided, and a subsequent sensitivity analysis is conducted on critical parameters to extract meaningful managerial implications.