Technical Note—Joint Inventory and Pricing Control with General Additive Demand
Bibliographic record
Abstract
This paper analyzes a periodic-review, joint inventory and pricing control problem for a firm that faces stochastic, price-sensitive demand under a nonstationary environment with fixed ordering costs. Any unsatisfied demand is backlogged. The objective is to maximize expected profit over a finite selling horizon by coordinating the inventory and pricing decisions in each period. We show that for an additive demand model, an (s, S, p) policy is optimal when the expected revenue is quasi-concave in price, the inventory cost (of holding and/or backlogging) is quasi-convex, and the nonnegative random demand has a Pólya or uniform density function. For the special case with no fixed ordering cost, the optimality of a base stock list price policy is demonstrated for more general demand distributions and convex inventory cost. These sets of sufficient conditions generalize the existing conditions in the literature that require, for example, the demand and/or revenue functions to be concave or the model parameters to be stationary in time. Our generalization makes the structural results applicable to models broadly supported by economic theory and empirical data. In addition, our proof uses a distinct sequential optimization technique for iteratively establishing the quasi-K-concavity of dynamic optimal value functions.
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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 | 0.003 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.007 | 0.001 |
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".