Piecewise linear approximations are one of the most practical tools we have for solving nonlinear optimization problems, and they deserve more attention from anyone working with constrained models. The recent article on Towards Data Science does a solid job of making this technique accessible, and that matters because most spreadsheet users eventually hit a wall where linear assumptions break down. When your model needs to capture diminishing returns, step costs, or other nonlinear relationships, you have two choices: abandon the familiar LP/MIP solvers you trust, or find a way to make them work. Piecewise linear approximations are that bridge.
Here is what this means for you in practical terms. Instead of learning an entirely new optimization paradigm or switching to specialized nonlinear solvers that may not integrate with your existing workflows, you can approximate the nonlinear curve using a series of connected linear segments. The approximation is not exact, but it is often good enough, and the trade-off is that you stay within the LP/MIP framework that Gurobi and similar solvers handle efficiently. Setting up these approximations using binary variables and SOS2 constraints sounds technical but is actually a straightforward pattern once you see it. For anyone managing supply chain models, financial forecasting, or engineering design, this is a way to get better fidelity without restarting your entire modeling approach.
We think this matters because the spreadsheet community has long been underserved when it comes to nonlinear optimization. Traditional spreadsheet tools encourage linear thinking, not because the problems are linear, but because the tools make nonlinear work painful. Piecewise linear approximations change that dynamic. They let you keep your familiar solver, your familiar modeling language, and your familiar workflow, while still capturing the curvature that real-world data demands. A gentle introduction with a clear, example-driven explanation that does not assume a PhD in operations research is exactly what the field needs. It treats the reader as capable of learning a new technique without talking down to them.
If you have ever struggled with a model that required a nonlinear function, say, a cost curve that flattens at high volumes or a response surface with diminishing sensitivity, try this approach. Start with a small number of breakpoints and test whether the approximation holds for your use case. The technique is mature, the solver support is robust, and the payoff is immediate: you solve a problem that previously felt out of reach using tools you already understand. That is the kind of practical progress that moves spreadsheet work from constrained to capable.