In the United States, there is one death out of every four due to cancer. Cancer chemotherapy is one of the few practices adopted for the treatment of this disease that uses anti-cancer drugs. However cancer chemotherapy comes hand in hand with a large number of side effects due to which the patients being unable to bear it leave the treatment in the midway. In day to day life, it is not possible to find a chemotherapy drug regime which is free of side effects. In the present work, an attempt is made to design a suitable cancer chemotherapy drug regime with the help of elitist Genetic Algorithm (GA) with side effects as minimum as possible. This present works proposes a drug schedule so that the number of cancer cells is reduced over the period of treatment interval and the toxic side effects are to be minimum as well. In order to increase the robustness of the proposed algorithm, the GA operators like crossover and mutation has been suitably investigated over their possible permutations. A complete elitism has been employed at the end of each GA cycle that helps to retain the good individuals for the next iteration. Based on the numerical results and statistical analysis the out performance of elitist GA has been substantiated to be better competent over the state-of-the-art techniques in finding optimal drug scheduling in cancer chemotherapy.