LLMs Can Design Near-Optimal OR Algorithms

This paper tests whether frontier LLMs can design operations-research algorithms from a single untuned prompt, precise mathematical specifications, and a Python sandbox. It compares OpenAI’s gpt-5.1, gpt-5.4, and gpt-5.6-sol with Anthropic’s claude-fable-5 across inventory control, queueing-network control, and assortment optimization, using both level 1, instance-specific solutions, and level 2, reusable algorithms written before evaluation instances are revealed. On 26 lost-sales inventory instances, gpt-5.6-sol beats the best tuned benchmark on 23 at level 1 and 21 at level 2, while staying within 0.5% on all instances. Its level-2 inventory policy extends capped base-stock control with a projected inventory statistic that combines expected usable inventory and variance. In queueing, it recovers dynamic-programming optima on small criss-cross networks and beats per-instance PPO on five of six extended reentrant-line instances through pressure-based scheduling. For assortment, it reaches the best known revenue on all 628 MMNL instances and all 1794 constrained-MMNL instances, although nested logit remains difficult: it is within 0.1% of the comparator on 87.4% of 971 instances and loses on a hard tail. Overall, gpt-5.6-sol is no worse than the best existing method in eight of ten problem classes at both levels and matches it on every instance in six classes. The generated artifacts are inspectable combinations of dynamic programming, simulation-tuned policies, relaxations, greedy search, and local improvement rather than black-box neural controllers, but the evidence remains empirical and limited to well-specified benchmark families.