Uncertainty is an inherent challenge in digital transformation, where organizations often face unpredictable changes in technology, customer behavior, and market dynamics. Whether deciding on resource allocation, optimizing processes, or assessing risks, handling uncertainty effectively is crucial to success. Probability theory provides a structured way to model this uncertainty, empowering managers to make data-driven decisions and embrace digital transformation with confidence. In this unit, we focus on the role of probability in quantifying and understanding uncertainty. By applying these mathematical principles, learners will develop the skills to predict outcomes, assess risks, and design more informed strategies. From anticipating market shifts to evaluating system performance, probability theory is a foundational tool in navigating the complexities of digital transformation.

At this point in the course, you are able to use analytics to predict future outcomes based on historical data. Now, we will learn how to create a more sophisticated, expansive picture of possible outcomes through the use of simulation. By modeling complicated, interconnected processes, simulation techniques can bridge the gap between predictive and prescriptive analytics: not only can we generate outcomes of various actions, but we are also able to identify which action best solves the problem at hand. Specifically, we will explore discrete event simulation which allows us to incorporate many more variables—to ask many more “what if” questions such as: “What would happen if we made this price adjustment?” or “What would happen if we reduced the time spent on manufacturing that part?” By finding answers to such questions, we can generate more focused information to drive better decision-making and more effectively manage risk.

By generating random variables from desired distributions, decision-makers can predict outcomes, optimize processes, and evaluate scenarios with precision. Whether it’s forecasting customer behavior or optimizing operational workflows, the ability to simulate random variables forms the foundation of effective predictive and prescriptive analytics. For example, e-commerce platforms use these techniques to simulate purchase behaviors based on historical customer data, while logistics companies rely on them to optimize delivery routes by accounting for variable factors such as traffic and weather. This unit, we will focus on two essential approaches: the inversion method and the rejection method, each with unique strengths suited for different types of distributions.

Discrete event simulation is a critical tool in digital transformation, enabling organizations to analyze complex systems, manage uncertainty, and make data-driven decisions. This unit builds on foundational knowledge by applying discrete event simulation to real-world scenarios, allowing students to develop complete end-to-end models. These case studies illustrate how simulation can address operational challenges in various industries, from improving customer experience in retail to optimizing manufacturing processes. Students will use Python to implement simulations, applying techniques such as the inversion and rejection methods for generating random variables. By exploring steady-state and non-steady-state systems, students will learn to model customer behavior, optimize operational workflows, and evaluate system performance under uncertainty. These skills are essential for leveraging digital transformation technologies to inform managerial decisions.\

Unit 6 brings together all the concepts and techniques learned throughout the course, providing students with the opportunity to develop and analyze complete simulations. The focus is twofold: building trustworthy simulations and exploring the role of simulation in prescriptive analytics. Trustworthy simulations are essential for ensuring that the insights derived from models are accurate, reliable, and actionable. In the context of prescriptive analytics, simulations extend beyond predicting outcomes to recommend actions that optimize decision-making, particularly in complex systems undergoing digital transformation. Note: (if you haven’t taken the Prescriptive Analytics course in this program) Prescriptive analytics uses data, models, and simulations to suggest the best course of action in scenarios with multiple possible outcomes. For example, it can help optimize resource allocation, improve supply chain efficiency, or design customer experiences by running simulations of different strategies and identifying the one that delivers the best results. In this unit, students will use simulation to answer "what-if" and "what-should" questions, equipping them to design solutions that balance trade-offs and achieve organizational goals.

The final unit of this course is a practicum that serves as a mini-capstone project, allowing you to consolidate your learning and demonstrate mastery of the tools and techniques introduced throughout the course. This project is your opportunity to apply simulation, cloud-based tools, and data science methodologies to a practical business problem, providing actionable insights that align with digital transformation initiatives.