The food industry is a major source of greenhouse gases (GHG). Given that consumers in this industry are aware of the negative consequences of GHG emissions, such as global warming and climate change, members of the food supply chain should consider mechanisms to reduce GHG emissions. The purpose of this paper is to examine the effects of supply chain structure and cooperation methods on the objectives and decisions of a sustainable food supply chain composed of one manufacturer and two suppliers. In the first scenario, a single-level problem is solved for a centralized supply chain. Other scenarios consider the decentralized structure, in which supply chain members face constraints such as maximum additive use and GHG emission, budget, and capacity. The bi-level programming is used to model competition between members of the sustainable food supply chain. It is demonstrated first that the lower-level models in decentralized scenarios can be converted to a single-level model, and then the proposed bi-level model is converted to a single-level one using the KKT method. Computational results show that the alliance of the manufacturer and the first supplier yields the highest total profit for all decentralized scenarios. Because the lowest GHG emission rate among decentralized scenarios is achieved through alliance and cost-sharing mechanisms, the use of these mechanisms concurrently is appropriate for environmental purposes. In scenarios where supply chain members compete with each other, it is found to be cost-effective to increase the budget. Additional considerations can be made regarding the effects of other variables such as distance and advertising on demand as well as alternative forms of the demand function.
