Optimal Control and Equilibrium Behavior of Production-Inventory Systems
Bibliographic record
Abstract
The relationship between commodity inventory and short-term price variations has received considerable attention, but the understanding has been limited to single-stage cross-sectional relation. In this paper, we aim to deepen our understanding of the inventory–price relationship in two dimensions: across time and across production stages. We first examine an individual firm controlling production and two stages of inventory under uncertain input and output prices and operating costs. We next establish and characterize the rational expectations equilibrium for an economy in which competitive production firms link a raw material market and a finished goods market, with uncertain and price-sensitive supply and demand. We characterize the dynamics of inventory, market price, and gross margin based on theoretical analysis, simulation, and empirical evidence from the petroleum industry. We find that inventory fluctuations lag behind price variations, and the length of the lags depend on how far the inventory is from the source of the supply or demand shocks. We also find that shocks are both dampened and delayed when propagating through the production stages, and that shocks have a prolonged effect on inventories and prices at both stages.
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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 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 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".