A belief degree-based uncertain scheme for a bi-objective two-stage green supply chain network design problem with direct shipment

Abstract

In the lack of historical data for an uncertain event, the belief degree-based uncertainty becomes more applicable than other types of uncertainty like fuzzy theory, stochastic programming, etc. This study focuses on an uncertain bi-objective two-stage supply chain network design problem. The problem consists of plants, depots, and customers with cost and environmental impacts (CO₂ emission) where direct shipment between plants and customers is allowed. As such network could be designed for the first time in a geographical region, such problem is modeled in a belief degree-based uncertain environment. This is almost the first study on belief degree-based uncertain supply chain network design problem with environmental impacts and direct shipment. Three approaches of expected value model, chance-constrained model, and their combination are applied to convert the proposed uncertain problem to its crisp form. The obtained crisp forms are solved by two multi-objective optimization approaches of goal programming (GP) and global criterion method (GCM). An extensive computational study with various test problems is performed to study the performance of the crisp models and the solution approaches. As result, the obtained crisp formulations are highly sensitive to the changes in the cost parameters’ values, and the GP performs better than the GCM from the solution quality point of view.