A sustainable supply chain network under the Stackelberg and Nash equilibrium policy in a reverse logistic model with multiple deliveries and a single distribution center
Bibliographic record
Abstract
This paper presents a framework for reverse logistics aimed at managing reusable items within supplier-buyer relationships to promote sustainability and reduce environmental impact. In this model, the supplier produces and inspects items, shipping only perfect items to buyers, while recycling or disposing of imperfect ones. Returned items from consumers are categorized as either reusable or damaged at a collection center. The concept of a circular economy encourages the return and refilling of reusable items, while damaged items are recycled. Additionally, the model incorporates carbon emissions considerations across production, storage, transportation, and landfilling, emphasizing the importance of environmental factors. To evaluate the sustainability and economic efficiency of the supply chain network, both Stackelberg and Nash equilibrium strategies are employed. The paper provides a mathematical framework based on lemmas to analyze the impact of the network and promote sustainable supply chain practices. In this cycle, consumers use the items and eventually discard them. To support a zero-waste policy, the supplier labels the bottles with barcodes to identify used items upon collection. The supplier has two different rates at which they purchase used bottles from consumers. Refilled bottles are sent back for reuse, while damaged bottles are either repurposed as raw materials or disposed of. The research paper aims to develop a mathematical model that determines the buyer's cycle time and the number of deliveries from the supplier to the buyer, ensuring that the buyer's demand is met without shortages.
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.002 | 0.002 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.003 | 0.002 |
| Insufficient payload (model declined to judge) | 0.006 | 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".