The assessment of algorithms and their potential to enhance healthcare delivery, patient outcomes, and various healthcare issues, along with considerations of ethical, stakeholder, and workforce implications, has brought about transformative changes in Saudi Arabia's healthcare system. Regression analysis, simulation modelling, and optimization algorithms have played a pivotal role in advancing digital health adoption, refining data infrastructure, governance, healthcare culture, and leadership. The study underscores that algorithmic applications have positively impacted clinical outcomes, resource optimization, and patient satisfaction, demonstrating their cost-effectiveness and economic influence on the Saudi healthcare industry. Utilizing regression analysis and fostering interdisciplinary collaboration has yielded commendable results, showcasing performance metrics with 81% accuracy, 75% precision, and 85% recall in the study's findings. An in-depth examination of drug properties, experimental conditions, optimization results, and cost comparisons has further enhanced the overall outcomes. The integration of mathematical algorithms has reshaped decision-making processes, with algorithms guiding managers in strategic planning. Data-driven decision-making has enhanced organizational efficiency, adaptability, and healthcare business practices. Despite these advancements, challenges persist in healthcare and pharmaceutical algorithms. Limitations, including dataset biases and trend oversights affecting predictive algorithms, underscore the need for ongoing research to enhance the robustness and transparency of algorithmic applications. It is imperative for data scientists and healthcare professionals to collaborate closely in implementing algorithms, addressing limitations, and ensuring the effectiveness and reliability of algorithmic applications in improving healthcare outcomes.