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Enhancing Decision Making Through the Integration of Large Language Models and Operations Research Optimization
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Position/vision paper proposing a Decision Optimization CoPilot (DOCP) that uses LLMs to turn business-level problem descriptions into efficient, verifiable optimization models, supported by a literature survey and ChatGPT-4 experiments.
Problem
Building optimization models requires rare OR expertise, so decision-makers cannot easily use mathematical optimization; existing LLM work needs precise problem descriptions, produces errors, and does not address efficiency or non-expert verification.
Approach
Envisions an LLM-based copilot that interacts with business users in natural language, guides them through the optimization modeling process, validates models, and produces efficient MILO formulations, identifying three requirements and showing via ChatGPT-4 experiments that current LLMs fall short on each.
Key results
- ChatGPT-4 produced correct optimization models in 4 of 5 runs for both the vaccination clinic and radiotherapy problems, with one incorrect objective in each case.
- For the bike hub problem, ChatGPT-4 produced a model reformulation with fewer variables in only 1 of 5 attempts.
- In the business-level bike hub example, the generated MILO model incorrectly assigned demand and lacked coverage constraints.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Ask ChatGPT 4 to generate models from precise problem descriptions | ChatGPT 4 · Vaccination clinic optimization | correct model generations: four out of five times | Mixed |
| Ask ChatGPT 4 to generate models from precise problem descriptions | ChatGPT 4 · Radiotherapy treatment optimization | correct model generations: four out of five times | Mixed |
| Prompt ChatGPT to restructure the bike hub model into an equivalent form with fewer variables | ChatGPT · Bike hub optimization | successful equivalent reformulations: one out of five attempts | Hurt |
| Ask ChatGPT to reformulate convex absolute-value constraints with ≤ | ChatGPT · Absolute-value constraint reformulation | reformulation correctness | Helped |
| Ask ChatGPT to reformulate concave absolute-value constraints with ≥ | ChatGPT · Absolute-value constraint reformulation | reformulation correctness | Hurt |
| Ask ChatGPT to linearize sums of maximums of linear functions in ≥ constraints | ChatGPT · Production-inventory constraint reformulation | reformulation correctness | Hurt |
Surprising findings
- ChatGPT asked the business user to validate the mathematical formulation, which is an unrealistic request for non-expert decision-makers.
- ChatGPT struggled with producing efficient reformulations, including introducing nonlinear terms and omitting binary variables for concave constraints.
Limitations
- Experiments are small-scale, using a handful of problems and five runs each with a single LLM.
- Existing works need precise problem descriptions and do not handle business-level dialogue or efficiency.
- No standard benchmark or metrics for business-level optimization modeling exist yet.
Experimental setup
Metrics: correctness of generated optimization model (4 of 5 runs cor fraction of equivalent efficient reformulations (1 of 5 succ
Builds on: NL4Opt OptGen Chain-of-Thought prompting CRISP-DM Learning to Optimize
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