The methodology of heat integration has been used to optimize and satisfy the demands of external utilities and resources. In the real process plants, it can easily be observed that due to unexpected process troubles and changes in environmental and operating conditions, equipment and processes do not run on the deterministic values of parameters upon which they are designed. Variations and uncertainties developed for any reason have some impacts on the process parameters, which may affect the profitability if not optimized. To optimize the utility requirements, the use of Pinch Analysis has been integrated with robust optimization where uncertainties in source quality (inlet temperature of source) are incorporated in the nominal formulation of the mathematical programming and are converted to deterministic equivalents. In this methodology, under the conditions of parametric uncertainties, decision-makers would have the choice to make a trade-off between the protection level of the constraint and the degree of conservatism of the solution. This model will assist the planner to decide the hot and cold utility requirements under uncertain flow situations and the source temperatures and to do the essential grounding accordingly.