Joint Production and Replacement Planning for an Unreliable Manufacturing System Subject to Random Demand and Quality
Bibliographic record
Abstract
We consider a problem of optimal production and replacement control for a deteriorating manufacturing system containing a single unreliable machine that produces one type of products. The random phenomena are the breakdowns and repairs of the machine, the quality deteriorations and the demand of customers. The machine is subject to deteriorations and minimal repairs, which affect its failure rate and the defective rate of the parts produced, both increasing with the age of the machine. Due to the aging process, the option to replace the machine should be taken to eliminate these effects in order to be able to meet long-term demand. The objective is to find the simultaneous production and replacement control policies in order to minimize the total cost over an infinite planning horizon. The optimality conditions are developed in the form of the second-order Hamilton-Jacobi-Bellman (HJB) due to randomness in demand and quality. Numerical methods are used to obtain the optimal control policies. Finally, to illustrate the contribution of the paper and the robustness of the obtained control policies, a numerical example and a sensitivity analysis are presented.
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How this classification was reachedexpand
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 | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".