Chemical process optimization problems often have multiple and conflicting objectives, such as capital cost, operating cost, production cost, profit, energy consumption and environmental impact. There are several conversion technologies that can convert Synthetic Natural Gas (SNG) into power, heat and electricity; of these, Solid Oxide Fuel Cell with Gas Turbine (SOFC-GT) has shown higher thermodynamic performance. In this study, design and operation of SOFC-GT is optimized for levelized electricity cost and annualized capital cost per kWh, simultaneously. The final selection of a solution from the obtained Pareto-optimal front depends on its sensitivity to the uncertain parameters, such as fuel and product prices, plant life and operating time. Practitioners are mainly interested in selecting one or few robust solutions which are less sensitive to the uncertain parameters, and so the uncertainty analysis of the obtained non-dominated solutions may help in identifying robust solutions. In this study, effect of several uncertain operating and market parameters namely, yearly operation, economic life time, interest rate, fuel cell capital cost factor, electricity price, oxygen price and SNG price, is studied on the performance of SOFC-GT system. The uncertainty analysis is able to idetify most promising non-dominated solutions, based on the levelized electriicty cost as main decision crieriton.