The flexibility of a manufacturing process is defined as its ability to accommodate variations and thus, operate in a stable manner for a range of conditions. The subject of flexibility arises in the space of uncertain design parameters that include volatility of raw materials and products price, variability of feedstock supply, and product demand, etc. In this paper, a flexibility model is developed to assess the capacities of process units in a plant to absorb variations in product demand. The flexibility index is introduced in this work to quantitatively measure the capability of the plant to accommodate to the maximum or minimum changes in the demand of multiple products. This involves determining the region for change in the production portfolio at which the plant still operates feasibly while absorbing tolerances between each product demand. The concept of corner points is adapted which forms a geometric boundary to the region of feasible operation. The region considered accounts for process adjustments made to accommodate the different parameter realizations. Fuzzy optimization is then used to determine the best trade-off between two important objectives of maximizing plant flexibility while simultaneously minimizing the total cost associated with the plant. A case study of a palm oil-based integrated biorefinery is presented to demonstrate the proposed novel approach in a more descriptive manner.