A Sustainable Production Inventory Model for Power-Pattern Demand with Carbon Emissions and Shelf Life Considerations

Growing environmental concerns, especially those related to carbon emissions from production and supply chain activities, have highlighted the need for sustainable practices. Implementing policies that incentivize low-carbon operations is crucial. To foster sustainable development, implementing penalties for high-emission commercial activities is crucial. This study investigates a sustainable production-inventory system for a product with a power-pattern demand, considering limited shelf life and gradual deterioration. The analysis integrates carbon emissions from stockholding, transportation, and deterioration, along with the impact of shortages on total costs. Two distinct scenarios are examined: Case I (without deterioration) and Case II (with deterioration). Each case is further divided into two models: one allowing shortages and the other prohibiting them. The primary objective is to determine an optimal production-inventory policy that maximizes profit per unit time while accounting for carbon emission taxes related to transportation, storage, and deterioration. Numerical results demonstrate that the total cost in Case I (without deterioration) is significantly lower than in Case II (with deterioration), with reductions of $$24.89\%$$ and $$22.02\%$$ , respectively. These findings underscore the financial implications of deterioration and shortages on sustainable inventory management. The proposed model offers valuable insights for decision-makers seeking to optimize production cycles, manage carbon footprints, and develop sustainable supply chain policies.