System Functionality Dependent Imperfectness of a Production Inventory Model Considering Development Cost Under Carbon Emission

This study develops a manufacturer-retailer integrated production-inventory model considering carbon emissions. The model addresses two conflicting objectives: minimizing carbon emissions and maximizing the system’s integrated profit per lot. Carbon emissions from production cells and transportation vehicles are considered with emission rates influenced by production rate and order quantity. The model also accounts for imperfect production caused by the gradual decline in system functionality over time. To address this, a new development cost is introduced to reduce imperfect production along with a novel labor cost structure based on production rate. Additionally, a quantity-dependent trade credit policy and warranty-dependent demand and selling price are incorporated. A numerical example and sensitivity analysis are conducted, solved using a Multi-Objective Genetic Algorithm (MOGA). Results show that a higher investment in development cost significantly benefits the system, enabling the achievement of both objectives although it raises production costs. Moreover, while a longer warranty period increases customer demand, it does not always maximize integrated profit but proves advantageous for the retailer. The study emphasizes the importance of optimizing production rates to balance profitability and environmental sustainability.