Average Cost Single-Stage Inventory Models: An Analysis Using a Vanishing Discount Approach
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Bibliographic record
Abstract
An important problem in the theory of dynamic programming is that of characterizing sufficient conditions under which the optimal policies for Markov decision processes (MDPs) under the infinite-horizon discounted cost criterion converge to an optimal policy under the average cost criterion as the discount factor approaches 1. In this paper, we provide, for stochastic inventory models, a set of such sufficient conditions. These conditions, unlike many others in the dynamic programming literature, hold when the action space is noncompact and the underlying transition law is weakly continuous. Moreover, we verify that these conditions hold for almost all conceivable single-stage inventory models with few assumptions on cost and demand parameters. As a consequence of our analysis, we partially characterize, for the first time, optimal policies for the following inventory systems under the infinite-horizon average-cost criterion, which have thus far been a challenge: (a) capacitated systems with setup costs, (b) uncapacitated systems with convex ordering costs plus a setup cost, and (c) systems with lost sales and lead times.
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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 | 0.003 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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