A Competitive Newsvendor Problem with Product Substitution under the Carbon Cap-and-Trade System

This study investigates the competitive issues of the newsvendor problem with product substitution under the carbon cap-and-trade system. Building on existing research, this paper introduces the carbon cap-and-trade system under uncertain market demand and considers that the original equipment manufacturer (OEM) can choose to procure raw materials from the contract manufacturer (CM), with both final products being substitutable. Furthermore, we explore the different substitution relationships between OEM and CM products under both pure competitive and co-opetitive modes. For this problem, decision models are developed for various scenarios, and optimal solutions satisfying given conditions are provided. We find that in one-way substitution, under pure competition, an increase in the OEM's (or CM's) green investment and substitution rate only leads to an increase in OEM's (or CM's) yields, while an increase in the OEM's (or CM's) green investment does not necessarily reduce CM's (or OEM's) yields. In the co-opetitive mode, an increase in the substitution rate and green investments of both manufacturers may lead to an increase in the yields of both manufacturers. Furthermore, an increase in carbon trading prices does not necessarily inhibit the manufacturer's yields. Moreover, we find that under the same competition mode, under certain conditions, two-way substitution between OEM and CM can bring better profits to both manufacturers and the entire supply chain. When the two modes are in the same substitution scenario, and the CM cannot substitute for the OEM, the optimal decisions and total supply chain profits of the two modes are equal. Finally, through numerical analysis, we find that neither mode is necessarily optimal when CM can substitute for OEM. Additionally, it is observed that when the same mode is in different substitution scenarios, total supply chain profits may be enhanced in the presence of product substitution.