Congestion-Based Lead-Time Quotation for Heterogenous Customers with Convex-Concave Delay Costs: Optimality of a Cost-Balancing Policy Based on Convex Hull Functions
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Bibliographic record
Abstract
We consider a congestible system serving multiple classes of customers who differ in their delay sensitivity and valuation of service (or product). Customers are endowed with convex-concave delay cost functions. A system manager offers a menu of lead times and corresponding prices to arriving customers, who then choose the lead-time–price pair that maximizes their net utility (value minus disutility of delay and price). We investigate how such menus should be chosen dynamically (depending on the system backlog) to maximize welfare. We formulate a novel fluid model of the problem and show that the cost-balancing policy (based on the convex hulls of the delay cost functions) is socially optimal if the system manager can tell customer types apart. If types are indistinguishable to the system manager, the cost-balancing policy is also incentive compatible under social optimization. Finally, we show through a simulation study that the cost-balancing policy does well in the context of the original (stochastic) problem by testing it against various natural benchmarks.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it