Over the years, oil-related energy sources have played an irreplaceable role in both developed and developing countries. Therefore, the efficiency of petroleum supply chains is a key factor that significantly affects the economy. This research aimed to optimize the configuration of the uncertainty multimodal petroleum supply chain in terms of economy, energy and environment (3E assessment). This study proposes a novel integration methodology between a heuristic algorithm and exact solution optimization. In the first stage, this study determines the facilities’ potential geographical coordinates using heuristic algorithm. Then, the fuzzy min-max goal programming model (FMMGPM) was developed to find the multi-objective solutions. In particular, this model allows analysis of supply chain uncertainty through simultaneous factors such as demand, resource, cost and price. These uncertainty factors are expressed as triangular fuzzy parameters that can be analyzed in terms of both probability and magnitude. Moreover, the model is applied to the entire petroleum supply chain in Vietnam, including downstream and upstream activities. In addition, another novelty is that for the first time, pipeline systems in logistics activities are considered in Vietnam’s petroleum supply chain optimization study. The results also show the short-term and long-term benefits of developing a pipeline system for oil transportation in Vietnam’s petroleum supply chain. To evaluate the effects of uncertainty on design decisions, this study also performed a sensitivity analysis with scenarios constructed based on different magnitudes and probabilities of uncertainty.