Generally,synthesis and design of an optimal process is a challengingtask. The procedure includes specifying and optimizing system configurationsin order to achieve a certain aspect, such as maximizing economicperformance, minimizing environmental impact, etc. However, uncertaintiesof the design parameters (e.g., volatility of raw materials and productsprice, variability of feedstock supply and product demand, etc.) mayundermine the effectiveness of such systematic design approaches.In response to this issue, various optimization works have been presentedto address such problems. In this paper, a robust mixed integer linearprogramming (MILP) with input–output model is presented toaid decision-makers in addressing process synthesis problems due touncertainties that arise from variation in feedstock supply and productdemand. This work primarily encompasses multifunctional energy systemsthat can be described by a system of linear equations, which entails“black box” modeling. The robust model helps to determinethe design capacity of each process unit in a flexible network whichinvolves sizing of equipment. This network is assumed to be able tooperate in all uncertain scenarios considered, with a minimum costof the plant. In addition, the intended model also helps to determinethe requirement to operate additional equipment in a plant in thepresence of uncertainties. This is especially true with designs ofplants that are incapable of meeting any increase in demand. Theseaspects of the work are novel and an important contribution as suchanalysis is not available in the literature, to date. Three case studiesthat include a polygeneration plant and palm oil based integratedbiorefinery are presented to demonstrate the proposed novel approachin a more descriptive manner. [ABSTRACT FROM AUTHOR]