To maintain a healthy environment in our lives, it is very important to control the carbon emission (CaE) from the transport system. CaE from vehicles depend on a few factors such as the nature of the routes, length of the route, fuel purity, vehicle type, speed and load of the vehicle, etc. Thus these factors play an important role in controlling CaE in the transport system. In real life, nowadays people are slowly becoming aware of healthy environment and sustainable development. In this article, under disaster response scenario, we analyzed an uncertain green bi-objective four-dimensional transportation model (GBOFDTM) that can assume a significant role in social and environmental development. Under the uncertain scenario, a multi-objective chance-constrained model is developed, and then to convert a multi-objective optimization model into a single-objective optimization model, two methods namely weighted sum method and weighted exponential method are employed. Using some properties of uncertainty theory, each model transformed into the corresponding deterministic equivalent form. The hybrid GA and LINGO optimization solver are implemented to generate an efficient optimal solution for the deterministic equivalent form of the proposed model. A real-life-based numerical example is presented—which shows how a decision maker controls minimum costs and CaE. After solving this proposed model, some specific cases are analyzed. At last, managerial insights, conclusions and future scopes are depicted.