An integrated inventory model for a supply chain system with two competing retailers, carbon emissions, and price-and-service dependent demand

This study develops a mathematical model for a supply chain system with a single supplier and two competing retailers. The selling price and service level are two aspects determining the demand. Investments in service level are also considered to enhance the service environment in the stores. Both parties in the supply chain system employ a periodic review policy to regulate the inventory level in a stochastic setting. This study includes a carbon tax regulation to reduce emissions in the observed system. The proposed model contributes to the current inventory literature by allowing the inclusion of price and service-dependent demand, competition between two retailers, investment in service level, and carbon emissions. The objective of this study is to maximize the joint total profit by optimizing the selling price, service level, safety factor, review period, and number of shipments. An algorithm is developed to solve the proposed problem and its application is validated with a numerical example. The results show that retailers' demand level, selling price, and service are sensitive to emissions and profit. Additionally, investment and carbon tax regulations are effective in raising service levels and reducing emissions, respectively. This research can help decision-makers select the optimal action to improve the effectiveness of the supply chain system, optimize product sales, and emphasize environmental considerations.