•A new model formulation integrating facility location and transportation problem.•Analyzed multi-objective model under reflection of carbon tax, cap and trade policy.•Consideration of variable carbon emission cost due to variable potential sites.•Hybrid approach based on locate-allocate heuristic and neutrosophic programming.•Exhibition of the effect of variable carbon emission with numerical example. Several industries locate a pre-assigned number of facilities in order to determine a transportation way for optimizing the objective functions simultaneously. The multi-objective transportation-p-facility location problem is an optimization based model to integrate the facility location problem and the transportation problem under the multi-objective environment. This study delineates the stated formulation in which we need to seek the locations of p-facilities in the Euclidean plane, and the amounts of transported products so that the total transportation cost, transportation time, and carbon emission cost from existing sites to p-facilities will be minimized. In fact, variable carbon emission under carbon tax, cap and trade regulation is considered due to the locations of p-facilities and the amounts of transported flow. Thereafter, a hybrid approach is improved based on an alternating locate-allocate heuristic and the neutrosophic compromise programming to obtain the non-dominated solution. Additionally, the performance of our findings are evaluated by an application example. Furthermore, a sensitivity analysis is incorporated to explore the resiliency of the designed model. Finally, conclusions and further research areas conclude the paper.