Mathematical optimization
Good optimization starts with data you can explain
Objectives and constraints only help when the data behind them has a clear meaning. Lineage makes those assumptions easier to inspect.
A scheduling model might minimize cost subject to capacity and delivery constraints. Its mathematics can be internally consistent while its inputs describe the wrong system. A capacity field might mean available hours, contracted hours, or a forecast that already subtracts downtime.
A simple production model chooses quantities x_i with unit costs c_i, resource consumption a_i, minimum demand d_i, and available capacity C:
Trace the inputs before solving
Before choosing a solver, write down what each input means, its units, its time horizon, and how it is produced. Follow important fields through their transformations. A join that duplicates capacity or a filter that removes late orders changes the feasible decisions before the optimizer runs.
Keep assumptions explicit
Separate measured inputs from assumptions and decision variables. Record which constraints are firm requirements and which express preferences. If an assumption changes, you should be able to identify both the affected data transformations and the affected model constraints.
Test the decision, too
Compare model outputs against small cases where the answer is understood. Explore how recommendations change when capacity, demand, or costs move. A useful result includes its tradeoffs and limits, so a team can decide when to trust it and when to investigate.
This is where data engineering and mathematical optimization meet: understandable inputs, explicit models, and decisions that can be checked.