A sustainable production inventory model for two deteriorating complementary products under preservation technology and carbon cap regulation

Abstract

Abstract Complementary items are very important for any business organization because it can increase the sells as well as profit of the company. Bundle item together can attract the customers. So, a sustainable production inventory system for two deteriorating complementary items is designed for optimal lot sizing and optimal number of deliveries for both decentralised and centralised supply chain coordination. To protect items from deterioration, both the supply chain members applied the technology for preservation. Carbon (mainly carbon dioxide) emits from various inventory operations such as production, setting up, holding. In this production supply chain, carbon cap-and-trade policy is used to lessen that emission. Due to market demand fluctuation, retailer may face shortages and based on these, two models for the retailer are designed for zero ending case and shortage case. Consumer waiting time dependent partially backlogging shortage are applied to the cover the shortage for the case of the retailer. Here, the manufacturer generates the entire production batch in a single operation but distributes it to the retailer in multiple shipments of fixed quantities at constant time intervals. The effect of decision variables on profit function for both centralized and decentralized system are derived. Finally, numerical explanations are illustrated to find the impact of carbon emission in different pricing systems. It is concluded from the numerical results that the profit function is totally dependent on degree of complementarity of the product. Sensitivity analysis is performed to find the stability of the proposed model.