Leukemia is a malignant disease of the bone marrow and blood where immature white blood cells which are not able to develop into normal functioning blood cells are overproduced and build up in the bone marrow and blood. The most common treatment for most types of leukemia is intensive chemotherapy. This therapy can itself be life-threatening since only relatively few patient-specific and leukemia-specific factors are considered in current protocols; choice of chemotherapy, intensity and duration often depends on the treating physician's experience with significant international protocol variability. With the advent of novel treatments and large amounts of patient- and leukemia-specific genomic data, there is a clear need for a systematic approach to the design and execution of chemotherapy regimens. We have developed a model for the simulation of patients with Acute Myeloid Leukemia (AML) undergoing treatment with two standard chemotherapy protocols, one intensive and the other non-intensive. The proposed model combines critical targets of drug actions on the cell cycle, together with pharmacokinetic (PK) and pharmacodynamic (PD) aspects providing a complete description of drug diffusion and action after administration. Tumour-specific and patient-specific characteristics are incorporated into the model in order to gain insights into the personalised cell dynamics during treatment. Sensitivity analysis of the developed model identifies cell cycle times as the critical parameters that control treatment outcome. For model analysis, clinical data of 6 patients who underwent chemotherapy are used for the estimation of cell cycle time distribution. The chemotherapy process is formulated as an optimisation scheduling algorithm aiming to obtain the chemotherapeutic schedule which would maximise leukemic cell kill (therapeutic efficacy) whilst minimising death of the normal cell population, thereby reducing toxicities. This optimisation algorithm is solved for all the patient case studies and the results clearly demonstrate the potential improvement of treatment design through optimisation.