Robustness of Order-Up-to Policies in Lost-Sales Inventory Systems
Bibliographic record
Abstract
We study an inventory system under periodic review when excess demand is lost. It is known (Huh et al. 2009) that the best base-stock policy is asymptotically optimal as the lost-sales penalty cost parameter grows. We now show that this result is robust in the following sense: Consider the base-stock level which is optimal in a backordering system (with a per-unit-per-period backordering cost) in which the backorder cost parameter is a function of the lost-sales parameter in the original system. Then there is a large family of functions (mapping the lost-sales cost parameter to the backorder cost parameter) such that the resulting base-stock policy is asymptotically optimal. We also demonstrate the robustness phenomenon through a second result. We consider the base-stock level which is optimal in a backordering system in which a unit of backorder is charged a penalty cost only once (such a system has been studied by Rosling). We show that this base-stock policy is also asymptotically optimal. Furthermore, we show that a modification suggested by Archibald of this base-stock level also results in an asymptotically optimal policy. Finally, we numerically test the performance of this heuristic policy for a wide spectrum of values for the lost-sales penalty cost parameter and illustrate the superior performance of Archibald's method.
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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 | 0.005 | 0.023 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".