A two-objective, two-stage mathematical model was developed considering demand uncertainty and operational risk assessment in constructing a utility supply network for steam generation and steam exchange in a petrochemical industrial park. This study defined two objective functions, the total economic cost and risk cost, where the demand uncertainty enhanced the reliability of the utility network design. The economic and risk cost present a holistic study, where the actual operation cost and additional costs in case of industrial operation failure can be determined. For this, two stages were established for both objective functions, a deterministic stage and a stochastic stage. The deterministic stage fixed the parameter values for the optimization problem, while the stochastic stage included the steam supply-demand uncertainty. A case study of the Yeosu industrial park in South Korea was used to show the feasibility of the proposed method, proposing five scenarios for risk assessment analyses. A Pareto set was drawn, showing the optimal values of the optimization scenarios studied. From the optimization analysis, scenario 5 showed the best utility supply network design providing a more realistic network with a balanced total economic cost and risk cost, which presented the lowest risk operation of all facilities. From scenario 5, the results showed a decrease in economic cost by 65.5% to 67.6% compared to the current situation considering the risk costs for the operational risk.