Optimization model infeasible or too slow? Get it solving
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If your optimization model reports "infeasible", or runs for hours without closing the gap, the solver usually isn't the problem: the formulation is. A rule that contradicts another, a "big M" that's too large, or a model that's correct but weak can each stop a good solver cold. Finding which one is most of the work, and it's work I've done on scheduling, loading, routing and other combinatorial models.
Why models fail
- Infeasible: two or more constraints can't all hold at once. Often it's a data problem (a due date before the parts arrive) or a rule written stricter than the business really needs.
- Too slow: the model is valid but gives the solver little to work with: loose bounds, big-M constraints, many equivalent (symmetric) solutions, or a size that grows faster than the data.
- Wrong answers: it solves, but the plan breaks a rule nobody wrote down.
Ways to fix it
| What it does | Good for | Limits | |
|---|---|---|---|
| Solver settings and time limits | Tune parameters, accept a "good enough" gap | Models that are almost fast enough | Doesn't fix a weak formulation |
| Find the conflicting rules | The solver's conflict analysis (an irreducible infeasible set), or soft constraints with penalties that show which rules break | "Infeasible" with no clue why | You still decide which rule gives way |
| Reformulate | Tighter constraints, fewer big-Ms, symmetry breaking, a different modeling approach (e.g., constraint programming for scheduling) | Slow but valid models | Needs modeling experience |
| Decompose or combine methods | Split the problem, or use a heuristic around an exact solver | Large real instances | More code to maintain |
What I've worked with
Mixed-integer models in OR-Tools, CPLEX and Gurobi; Pyomo and PuLP formulations; constraint programming for scheduling; metaheuristics (simulated annealing, tabu search, genetic algorithms) when an exact solver can't scale; and hybrids of the two. The scheduler behind my factory case plans 746 tasks across 8 bays and 26 workers.
What I need from you
The model (code or a written description), a data instance that shows the problem, and what "infeasible" or "too slow" means for you (how long it may run, how good the answer must be).
How to start
Email me at cdesivo92@gmail.com with a short description of the model and what goes wrong, or hire me on Freelancer.com if you prefer the platform's contracts and payment protection.