Pipelines permit to transport large volumes of a wide range of products from supply nodes to demand nodes. They have been considered as the most effective and safest way of transporting gases. Transportation of gas through the pipeline is an energy-intensive process. Energy management in gas allocation networks (GANs) is needed. In this paper, a fuzzy mathematical model is developed for targeting multi-objective transportation problem i.e. simultaneous minimization of energy budget and investment budget in GANs where the model parameters exhibit fuzzy relaxed boundaries. The proposed procedure is explained via an illustrative example where the process data is represented through interval-typed triangular fuzzy data. The result shows that there is almost 38 % reduction in energy budget while 2.26 % increase in the investment budget. The proposed model also utilizes fuzziness in supply pressures while optimization and calculates the optimum values of pressures within its limit. For example, if pressures are maintained at their mean values in the illustrated example, the energy requirement increases by 11 %. The presented model provides the optimal balance between the conflicting goals. The novelty of this work is its ability to combine investment budget, energy budget and environmental aspect using a fuzzy non-linear programming approach to provide a suitable functioning point or exact value of pressure at which CS is supplying in GANs.