A bi-objective model for scheduling green investments in two-stage supply chains

Investing in green technologies to increase sustainability in supply chains has become a common practice for two reasons: the first is directly related to the defense of the environment and people's health to smooth the emissions of pollutants; the second is the increasing consumer awareness of green products. Despite the higher costs of producing with green technologies and processes, there is also a higher markup on the price of products which rewards the former costs. This study proposes a mathematical model for scheduling green investments over time in a two-stage supply chain to minimize the impact of production on the environment and the economic costs deriving from the investment. The resulting bi-objective model has nonlinear constraints and is solved using a commercial solver. Given its complexity, we propose an upper-bound heuristic and a lower-bound model to reduce the optimality gap attained at a given time limit. Tests on synthetic instances have been conducted, and an example demonstrates the applicability and efficacy of the proposed model.