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Record W4214775112 · doi:10.24193/fpt-ro.2022.1.11

A stochastic production planning problem

2022· article· en· W4214775112 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.
fundA Canadian funder is recorded on the work.

Bibliographic record

VenueFixed Point Theory · 2022
Typearticle
Languageen
FieldEconomics, Econometrics and Finance
TopicEconomic theories and models
Canadian institutionsMcMaster University
FundersNatural Sciences and Engineering Research Council of CanadaUnitatea Executiva pentru Finantarea Invatamantului Superior, a Cercetarii, Dezvoltarii si Inovarii
KeywordsHamilton–Jacobi–Bellman equationProduction (economics)Mathematical optimizationExtension (predicate logic)MathematicsBounded functionProduction planningDynamic programmingPoint (geometry)Mathematical economicsCharacterization (materials science)Bellman equationComputer scienceEconomicsMicroeconomicsMathematical analysis

Abstract

fetched live from OpenAlex

Stochastic production planning problems were studied in several works; the model with one production good was discussed in The extension to several economic goods is not a trivial issue as one can see from the recent works [8], [9] and The following qualitative aspects of the problem are analyzed in In this paper, we stylize the model of [8] and [9] in order to provide some quantitative answers to the problem. This is possible especially because we manage to solve the HJB equation in closed form. We point to a fixed point characterization of the optimal production rates. Among other results, we find that the optimal production rates adjusted for demand are the same across all the goods and they also turn to be independent of some model parameters. Moreover we show that production rates (adjusted for demand) are increasing in the aggregate number of goods produced, and they are also uniformly bounded. Numerical experiments show some patterns of the output.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.002
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesInsufficient payload (model declined to judge)
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.327
Threshold uncertainty score0.998

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0020.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0030.000

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.

Opus teacher head0.027
GPT teacher head0.205
Teacher spread0.179 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it