<p>In this work, we explore the concept of gene deletion (knockout) in metabolic engineering using the well-known bi-level optimisation approach. The objective is to identify a knockout strategy that maximises the production of a desired chemical without hindering the cell growth. The most popular method in the literature to solve this bi-level problem is to reformulate it into a single-level model using KKT conditions, which is then solved as a mixed integer programme after linearising the quadratic terms. In contrast, we propose a branch-and-cut algorithm starting from a high-point relaxation of the problem. Existing techniques that rely on KKT reformulations scale poorly as they introduce auxiliary binary variables for linearisation. We avoid the need of auxillary binary variables in our approach. We add cuts to prune off solutions that are neither optimal nor feasible within the branch-and-bound exploration. We propose this as a framework capable of handling both optimistic and pessimistic strategies by appropriately parametrising the separation problem and selecting the cuts. No unified framework currently exists that permits the decision maker to bracket the production ranges and select strategies that matches their biological assumptions. Our computational results indicate that both our strategies are competent when compared to the single-level reformulation with a slight deterioration in solution time for pessimistic strategies as the problem size increases. We show the convergence of the algorithm and share our computational experience.</p>