Optimization is a valuable prescriptive analytics tool for any organization looking to undertake digital transformation, as it maximizes the power of data and computer programming languages which are increasingly available to even small business owners. The ability to predict outcomes, such as unit costs, market shares, prices, and capacities, and to then take the best course of action that maximizes returns and minimizes cost and risk, is the force behind many of the world’s most successful companies. The key to long-term success, though, is the ability to continually integrate the insights of both predictive and prescriptive analytics.

In this unit, you will explore how linear optimization models serve as a powerful tool for decision-making within the framework of digital transformation. By leveraging analytics and digital technologies, linear optimization enables managers to make strategic decisions efficiently. You will deepen your understanding of when and how non-linear models can be transformed into linear ones. Specifically, you’ll learn to identify scenarios where linearization techniques work effectively, including the use of absolute values and piecewise linear functions. Through real-world examples, such as inventory management and advertising optimization, you’ll gain practical insights into translating complex decision-making problems into linear formulations. This unit will also introduce the geometric representation of linear optimization problems, helping you develop intuition about their solution methods. You will learn about active and inactive constraints at optimality and perform sensitivity analysis, empowering you to assess how changes in resources or constraints impact optimal solutions. Finally, you will see how digital tools and cloud-based platforms, such as Pyomo, make implementing linear optimization models both scalable and accessible in modern business environments.

In this unit, we build upon the foundational principles of linear optimization and explore how introducing integer variables into optimization models allows for greater flexibility in solving complex, real-world decision-making problems. While integer variables can increase computational complexity, they unlock the ability to model many important constraints and relationships that are integral to effective business strategies. Through practical examples, such as warehouse location optimization and infrastructure project selection, you will learn how to formulate and solve mixed-integer linear optimization problems. These examples will demonstrate how integer variables enable precise modeling of discrete decisions, such as whether to open a warehouse, invest in a project, or allocate resources to specific activities. You will also explore advanced techniques, such as combining constraints to enforce logical rules and leveraging logic tables to verify model formulations. By the end of this unit, you will understand how to apply mixed-integer linear optimization to enhance managerial decision-making within the context of digital transformation.

This unit delves into advanced optimization techniques using Python, focusing on how digital transformation can leverage prescriptive analytics tools to solve complex decision-making problems. Building on your knowledge of linear and integer optimization, you will explore the branch-and-bound method for solving binary integer optimization problems. This technique is crucial for addressing real-world scenarios where decisions are discrete, such as investment portfolios, resource allocation, or facility planning. Through the example of portfolio optimization, you will learn to formulate and solve binary integer optimization models using Python, understand the concept of linear relaxation and its role in generating bounds for optimal solutions, and apply the branch-and-bound method to systematically explore and prune solution spaces, ensuring efficient and effective problem-solving. This unit bridges theoretical optimization techniques with practical implementation, empowering you to use Python to make data-driven, optimized decisions for digital transformation initiatives.

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 prescriptive analytics, cloud-based tools, and data science methodologies to a practical business problem, providing actionable insights that align with digital transformation initiatives. You will synthesize your project into a short written report. This report should detail how you developed your mathematical model(s) and how you ran the code in Python. What challenges did you encounter? What adjustments were needed to successfully run the code? What insights did you glean from the data analyses? How might you formulate recommendations for action to key stakeholders in a way that would be understandable and persuasive? The ability to answer these and other similarly applicable questions will prepare you for data science roles that help businesses harness the power of analytics.