Natural‑language descriptions of optimization problems often omit numerical data required by solvers, such as costs, capacities, demands, bounds and penalties. A language model can translate the description into code, but when a needed value is missing it must either halt or guess.
SAILOR is a proof‑of‑concept system that automatically detects missing numerical choices, asks the user targeted follow‑up questions, updates the model with the answers, and finally returns a solution. The pipeline first converts the natural description into a mathematical model, then runs a solver to identify any undefined parameters.
For each missing value SAILOR computes two signals: an uncertainty estimate derived from the model and a sensitivity estimate provided by the solver indicating how strongly the value influences the current objective. A weighted combination of these signals determines the questioning order, prioritizing the most impactful gaps.
The approach was evaluated on seven masked benchmarks covering 1,723 instances, using an idealized simulator that supplies ground‑truth values as user responses. Exact objective‑value agreement ranged from 27.0% to 87.6% across datasets, with an average of 1.4 to 5.7 questions per instance.
The implementation is publicly available at https://github.com/sshaghayeghs/SAILOR.
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