Coordinating the Discount Policies for Retailer, Wholesaler, and Less-than-Truckload Carrier Under Price-Sensitive Demand: A Tri-Level Optimization Approach
Bibliographic record
Abstract
Quantity discounts have been broadly examined in decisions on the sale or purchase of goods. The analysis of coordinating the discount decisions for the retailer (buyer), the wholesaler (supplier), and the public transportation service provider (Less-Than-Truckload carrier), however, is still in its infancy. In this paper, we develop a tri-level programming approach to coordinate the three supply chain members' decisions on discount policies, when the demand is sensitive to the change in price. Both decentralized and centralized scenarios are examined, and a heuristic algorithm is presented to assist the three parties in establishing their discount schemes in a decentralized environment. Through a series of comprehensive numerical experiments based on the linear demand, we show that the price-sensitivity is a key motivation, for all parties, especially the carrier, to offer discounts. Specifically for the wholesale quantity discount, the data analyses also illustrate the different purposes and corresponding structures for the decentralized and centralized cases. For the former case, the discount is quantity-based, which encourages the buyer to increase the size of each order; while for the latter case, the discount is volume-based, which is used to boost the annual demand. The significant improvements to each party and to the entire supply chain resulting from the discount coordination are also demonstrated under various situations.
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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 | 0.004 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.003 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 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".