Why I Started Thinking About This

Every time a new problem hits — tariffs change, capacity tightens, labor gets constrained — enterprise software vendors show up with a "purpose-built solution."

Tariff optimizer. Rough-cut capacity planner. Labor scheduling engine.

Different names. Same math. New invoice.

At some point, I started wondering: are these actually different problems, or are we just changing the labels? That question led me to an experiment. Could a network optimization algorithm solve something completely unrelated to supply chains, like Sudoku?

It turns out, it can — and that changes everything.

A Technical Detour: Solving Sudoku with Network Optimization

Let me be explicit: a network optimization algorithm has no idea what Sudoku is.

It doesn't understand numbers, grids, or puzzles.

It understands decision variables, constraints, and objectives.

That's enough.

At a high level, a Sudoku puzzle can be modeled as:

• Decision variables representing whether a number is assigned to a cell

• Constraints ensuring each number appears exactly once in each row, column, and subgrid

• An objective that simply finds a feasible solution

There are no flows, plants, or warehouses here — just structure.

The Same Sudoku as a Supply Chain Problem

But the same Sudoku can also be expressed explicitly as a supply chain problem.

There are 81 customers, representing the 81 cells in the puzzle: R1C1, R1C2, …, R9C9.

There are 9 vendors, V1 through V9, each representing a number from 1 to 9.

The decision is to determine which vendor supplies which customer — in other words, which number is assigned to which cell.

We then define customer groups corresponding to:

• Each row: R1, R2, … R9

• Each column: C1, C2, … C9

• Each 3×3 subgrid: SG1, SG2, … SG9

These groups enforce Sudoku rules through standard network constraints:

• Each customer (cell) must be supplied by exactly one vendor

• Each vendor can supply exactly 9 customers (each number appears nine times)

• Vendor n supplies n units to a customer (encoding the value)

• The total quantity flowing into each row, column, and subgrid must equal 45

The Key Insight

What we've done is convert a Sudoku puzzle into a supply chain network so we can use a network optimization algorithm to solve it.

At that point, all that's left is to define an input data model that captures a specific Sudoku puzzle and wrap it in an application layer that lets users interact with it — instantly turning the same algorithm into a completely new solution.

Nothing about the algorithm changed. Only the data model and the constraints did.

That's the key point.