Combinatorial Optimization

Opening — Why this matters now Enterprise Resource Planning (ERP) systems are excellent at recording what has happened. They are far less impressive at deciding what should happen next. When decision-making involves combinatorial explosions—packing furnaces, sequencing machines, allocating scarce inputs—ERP often falls back on brittle heuristics, slow solvers, or human intuition. None scale gracefully. ...

Opening — Why this matters now Large Language Models are increasingly invited into optimization workflows. They write solvers, generate heuristics, and occasionally bluff their way through mathematical reasoning. But a more uncomfortable question has remained largely unanswered: do LLMs actually understand optimization problems—or are they just eloquent impostors? This paper tackles that question head‑on. Instead of judging LLMs by what they say, it examines what they encode. And the results are quietly provocative. ...