A robust optimization formulation for dynamic pricing of a web service with limited total shared capacity
Bibliographic record
Abstract
Abstract This article provides a robust optimization formulation to tackle the demand uncertainty in the web service dynamic pricing problem where a provider offers a web service with different service levels (i.e., web service classes) to manage capacity and maximize profit. Consumers may buy their required web service through a reservation system and have the right with no obligation to cancel their purchases as long as they pay the penalty. In this article, we develop a robust optimization formulation for the model in which the demand of a service class is a linear function of the price; the total shared capacity of the provider for the web service is limited; the demand function coefficients and cancelation rate are time‐dependent. We demonstrate that the robust formulation is of the equivalent order of complexity as the nominal problem. Eventually, we obtain the optimality condition and some managerial insights into the problem according to the maximum principal and provide an algorithm to find the optimal pricing policy as a function of the time on a finite time horizon. Numerical analyses are performed to evaluate the effect of uncertainty on the objective function. Furthermore, the proposed algorithm is compared with some existing approaches. The preliminary results show that the proposed algorithm offers better results than other algorithms such as QCP, NLP, GA, and SA in terms of time and accuracy.
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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 | 0.002 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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".