Synthetic lethality is a promising concept in cancer research, potentially opening new possibilities for the development of more effective and selective treatments. Here, we present a computational method to predict and exploit synthetic lethality in cancer metabolism. Our approach relies on the concept of genetic minimal cut sets and gene expression data, demonstrating a superior performance to previous approaches predicting metabolic vulnerabilities in cancer. Our genetic minimal cut set computational framework is applied to evaluate the lethality of ribonucleotide reductase catalytic subunit M1 (RRM1) inhibition in multiple myeloma. We present a computational and experimental study of the effect of RRM1 inhibition in four multiple myeloma cell lines. In addition, using publicly available genome-scale loss-of-function screens, a possible mechanism by which the inhibition of RRM1 is effective in cancer is established. Overall, our approach shows promising results and lays the foundation to build a novel family of algorithms to target metabolism in cancer.