Investigation of a multi-objective fixed charge transportation problem with quantity dependent transportation cost and discount policy <i>via</i> metaheuristics
Bibliographic record
Abstract
Efficient transportation of goods is a primary economic concern for any business organization. For this reason, research on transportation-related issues is becoming increasingly important. It should be noted that the shipping amount is determined by taking the unit transportation cost into account in a traditional transportation problem (TP). However, in reality, there are many situations where the transported quantity is used to determine the unit cost. Regarding this, in this work, a TP has been addressed in which a manufacturing company has agreements with a few suppliers to deliver the products to the retailers. For this contract, the suppliers receive a commission from the company. Here, two types of transportation costs (actual and demanded) per unit are taken into account. The unit charge that suppliers impose on retailers is known as the ‘demanded unit transportation cost’, while the ‘actual unit transportation cost’ is the cost that suppliers bear during the transportation. In order to establish a business relationship with the retailers, suppliers offer a discount on the demanded charge based on the amount they receive. Here, two types of products are considered: products with lower rate of deterioration and products with higher rate of deterioration. The cost of transportation is relatively higher for later items with a larger quantity of deteriorating items. Based on these two categories, two deterministic models have been developed here. Subsequently, we have looked at the models in an uncertain setting while taking the commission and cost parameters into account as interval numbers. The objective of this study is to minimize the retailers’ overall cost and maximize the suppliers’ total profit simultaneously. To demonstrate the models, four numerical examples have been considered. Then we have used the artificial bee colony (ABC) algorithm in conjunction with four multi-objective optimization techniques that are currently in use to solve the multi-objective transportation models: the global criterion method (GCM), the Tchebycheff method, the weighted Tchebycheff method and the weighted sum method. Finally, a few more metaheuristic algorithms are used to compare the results.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.003 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".