Neutrosophic sets have been commenced as a generalization of crisp, fuzzy and intuitionistic fuzzy sets to depict vague, incompatible and deficient information about a real world dilemma. Interval-valued fuzzy sets have widely been acknowledged as more proficient in modeling suspicions and practical in assigning an interval of values where allotting an accurate and precise number to an expert’s outlook is too restrictive. They endow with a more appropriate background to characterize higher order of uncertainties and fuzziness of real world. To solve linear programming network problems with constraints concerning interval-valued neutrosophic numbers, a technique has been established by using score function and upper and lower membership functions of interval-valued neutrosophic numbers. An application of energy scheduling problem with constraints represented as interval-valued trapezoidal neutrosophic numbers has been discussed and solved via this technique. Also an additional example to exemplify the proposed method by implementing it on minimum spanning tree and shortest path problem is employed. Furthermore, a comparative examination was performed to validate the effectiveness and usefulness of the projected methodology.