A Quadratic-Linear Bilevel Programming Approach to Green Supply Chain Management

Green Supply Chain Management requires coordinated decisions between the strategic and operational organization layers to address strict green goals. Furthermore, linking CO2 emissions to supply chain operations is not always easy. This study proposes a new mathematical model to minimize CO2 emissions in a three-layered supply chain. The model foresees using a financial budget to mitigate emissions contributions and optimize supply chain operations planning. The three-stage supply chain analyzed has inbound logistics and handling operations at the intermediate level. We assume that these operations contribute to emissions quadratically. The resulting bilevel programming problem is solved by transforming it into a nonlinear mixed-integer program by applying the Karush-Kuhn-Tucker conditions. We show, on different sets of synthetic data and on a case study, how our proposal produces solutions with a different flow of goods than a modified linear model version. This results in lower CO2 emissions and more efficient budget expenditure.