Sustainable rough multi-objective two-stage solid transportation problem of third-party e-commerce logistic providers with conditional fixed parameter on safety

Unsafe transportation causes fluctuation in the planned distribution expense, time, and emission factor and should never be ignored especially in e-commerce as it is a significant platform for global marketing. Though there are many e-commerce models available in literature, not many discussed the transportation model of integrated logistics by third-party logistic providers with safety and its impacts in rough interval scenario. So, the paper investigates a multi-objective two stage rough transportation model with a new concept called conditional fixed charge, time and emission on the overall safety achieved over the target in both forward and reverse logistics to emphasize the importance of safety factor and its effectiveness in the overall transportation system. A case study on the distribution data of smartphones is considered and solved using existing methods like Fuzzy Programming Approach and Global Criterion Method in LINGO (19.0). The paper also furnishes a comparative analysis by replacing the solution obtained for the case study with equivalent Compressed Natural Gas vehicles to reflect on its sustainable benefits in transportation.