Optimal Decisions on Greenness, Carbon Emission Reductions, and Flexibility for Imperfect Production with Partial Outsourcing

Global emphasis on sustainable development is widespread, with industries playing a pivotal role in advancing global sustainability within the business and retail sectors. Consumer awareness of environmental concerns, such as pollution, prompts a focus on product biodegradability and eco-friendliness. Consequently, customers are drawn to products with higher green credentials. This study delves into the effectiveness of green attributes in retail industries, exploring the optimization of profit through a variable production rate and variable unit production cost, considering the selling price and the demand dependent on the product’s green level. In the long run, production systems may shift to an “out-of-control” state, resulting in the random production of imperfect items that must be remanufactured to maintain the industry’s positive brand image. To mitigate the impact of defective items, the industry opts to partially outsource a percentage of items, preventing shortages. However, this complex retailing system generates a significant amount of carbon emissions. This study introduces investments aimed at reducing carbon emissions to address this issue. In contrast with the existing literature, a green-level-dependent unit raw material cost is considered here for variable unit production cost. Ultimately, this study seeks to maximize the overall system’s profit by optimizing the selling price, order quantity, production rate, green level, and carbon emission reduction investments. The classical optimization technique is utilized to obtain analytic optimum results for the decision variables and total profit. Special cases and sensitivity analyses illustrate the real-world applicability and impact of green levels. Numerical findings indicate that considering the product’s green-level-dependent demand and unit production rate is 22.44 % more beneficial than nongreen products, partial outsourcing provides a 1.28 % advantage, and flexibility in the production rate yields a 69.60 % benefit over traditional systems without green elements. Additionally, technological investments to reduce carbon emissions result in a notable reduction of up to 4.53 % .