Cooperative sustainable supply chain for deteriorating item and imperfect production under different carbon emission regulations

Operational adjustments in a supply chain and efficient inventory management, especially when demand is uncertain, can turn out to be an effective way in emission reduction. Different emission regulation strategies influence the firms to redesign their supply chain for sustainable management. This paper develops a sustainable supply chain inventory management (SSCIM) model for a single-manufacturer and a single-buyer’s integrated approach by considering item deterioration and imperfect production simultaneously. Rework facility of produced imperfect items is available. Carbon emissions through production, transportation, warehousing and disposal of the deteriorated items are considered. Our objective here is to implement different regulatory policies (mainly carbon tax, carbon cap-and-offset and cap-and-trade) of emission reduction which mitigate the effect of carbon emission by reducing its volume. We also focus on finding a trade-off between overall generated cost and carbon emission. Hence, the mathematical model of proposed SSCIM is formulated in bi-objective framework for the purpose to minimize the operational cost and carbon emission. Furthermore, fuzzy rule base approach, which is based on some existing survey records over the past years, is employed to predict the customers’ demand. The derived mathematical model and solution methodology are discussed and thereby illustrated with the help of numerical examples. Sensitivity analysis accounting to changes in the parameter values is also examined to highlight the managerial insights. •Sustainable supply chain inventory management problem is studied.•Item deterioration and imperfect production are considered with re-work facility.•Carbon emission regulation strategies are discussed.•A bi-objective optimization problem is formulated to determine the optimal policies.•Fuzzy rule base approach is employed to predict the customers’ de-mand1.