At the system level, cancer is viewed as the malfunctioning of proteins synthesized by the mutated genes. One of the effective ways of cancer treatment is personalized combinational drug therapy, where a best-suited mixture of drugs is given to the patient. Finding the most effective combination requires the study of mutations which is an exponentially complex task. In this work, we considered case study of melanoma. Signal transduction pathways for melanoma are mapped into Boolean networks (BNs), the plausible mutation sights in the biological pathway are marked as stuck-At faults, and drugs are marked as inhibitory inputs. Finding mutations or stuck-At faults in the BN is an NP-complete problem, which needs heuristic algorithms to determine the solutions. We used the Boolean satisfiability (or SAT) algorithm MiniSAT2.2 to determine such possible fault locations and consequently, the optimal drugs. In this work, we modified the previously published algorithm for SAT-based drugs therapy to obtain faster results and freshly applied the methods on melanoma pathways. We expect the best therapy in minimum time, which is a crucial factor in the rapidly growing disease like cancer.