This paper aims to propose a comprehensive inventory model including pricing, pre-sale incentives, advance sales, trade credit, and carbon tax policies. The novelty of this study lies in its holistic approach to addressing these relevant and practical issues. The major purpose is to determine the optimal pricing, pre-order discount, and replenishment decisions to maximize the total profit under carbon tax policy. Through theoretical analysis, this study develops several theorems to demonstrate properties of optimal solutions and an easy-to-use algorithm to derive optimal solutions. Further, several numerical examples are provided to demonstrate the solution process for different scenarios and the effects of various parameters on optimal alternatives and solutions. This study provides companies management implications to address the challenges posed by the global movement to reduce carbon emissions while maintaining their profitability.

Advertisements play an important role in communicating with target customers. A higher advertisement frequency increases costs but may increase the chances of acquiring new customers. Moreover, faced with a wide-ranging array of products that might fit specific needs, customers usually buy according to expectations about value and satisfaction. When customers are satisfied with a purchasing experience, they are more likely to buy again and share their experiences with others. Hence, companies are concerned about increasing customer value and service satisfaction to develop and manage customer relationships. This maintains a company’s competitive edge and can improve its market share. In this article, we incorporate the frequency of advertisements and the cost of customer relationship management (CRM) into the demand function under a product life cycle (PLC). Customers can return products in the appreciation period offered by a retailer. A profit-maximizing model is developed to analyze the joint marketing and ordering policy of each stage of a product’s life cycle with a product return guarantee. We construct an algorithm to identify the optimal decisions. Finally, numerical examples are presented to illustrate the proposed model, and managerial insights are obtained from a sensitivity analysis, followed by conclusions and future research.

In today’s global context of environmental protection, companies increasingly need to consider carbon emission policies in their operations. The purpose of this study is to develop a mathematical decision framework for jointly determining pricing and replenishment decisions in a subscription-based inventory system under carbon tax policies, while considering both subscription and regular sales. To achieve this objective, an inventory model incorporating subscription demand, regular sales demand, and carbon-related costs is developed. The novelty of this study lies in its integration of subscription-based demand dynamics with carbon taxation, showing how the length of the subscription delivery interval and the replenishment cycle jointly affect profitability and carbon emissions over time. The proposed model is examined through theoretical analysis, numerical analysis, and sensitivity analysis to investigate how key parameters influence optimal decisions, profitability, and emissions. A real-time, interactive inventory management dashboard is developed to enhance practical applicability. The dashboard integrates cost structure analysis, sensitivity results, price–profit relationships, and demand profiles over the replenishment cycle, while also offering a model-based carbon emission indicator that supports firms in assessing their emission performance. By bridging theoretical modeling with practical decision-making tools, this study provides actionable strategies and economic insights for businesses, with the ultimate goal of supporting sustainable development while maximizing profits.