The Value of Stochastic Modeling in Two-Stage Stochastic Programs with Cost Uncertainty
Bibliographic record
Abstract
Although stochastic programming is probably the most effective frameworks for handling decision problems that involve uncertain variables, it is always a costly task to formulate the stochastic model that accurately embodies our knowledge of these variables. In practice, this might require one to collect a large amount of observations, to consult with experts of the specialized field of practice, or to make simplifying assumptions about the underlying system. When none of these options seem feasible, a common heuristic has been to simply seek the solution of a version of the problem where each uncertain variable takes on its expected value (otherwise known as the solution of the mean value problem). In this paper, we show that when 1) the stochastic program takes the form of a two-stage mixed-integer stochastic linear programs, and 2) the uncertainty is limited to the objective function, the solution of the mean value problem is in fact robust with respect to the selection of a stochastic model. We also propose tractable methods that will bound the actual value of stochastic modeling: i.e., how much improvement can be achieved by investing more efforts in the resolution of the stochastic model. Our framework is applied to an airline fleet composition problem. In the three cases that are considered, our results indicate that resolving the stochastic model can not lead to more than a 7 % improvement of expected profits thus providing arguments against the need to develop these more sophisticated models. 1
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.017 | 0.049 |
| Meta-epidemiology (narrow) | 0.002 | 0.002 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.004 | 0.008 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.003 | 0.007 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".