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A mixed integer linear programming model for vehicle routing problem for non-complete graphs: Behshahr (Iran) case study | ||
| Journal of Mathematical Modeling | ||
| مقاله 3، دوره 13، شماره 4، اسفند 2025، صفحه 787-801 اصل مقاله (262.72 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2025.29552.2627 | ||
| نویسنده | ||
| Maria Afsharirad* | ||
| Department of Mathematics, University of Science and Technology of Mazandaran, P.O. Box: 48518-78195, Behshahr, Iran | ||
| چکیده | ||
| We consider Vehicle Routing Problem (VRP) for non-complete graphs. In order to avoid converting all networks to complete graphs, as in travelling salesman problem, we model VRP for non-complete graphs. Subtours are allowed in this model, since they are unavoidable in non-complete structure, while disconnected subtours are not allowed. Since disconnected subtour elimination constraints are time-consuming, we provide a separation problem for these constraints and provide an extended formulation based on this separation problem. This extended formulation turns to be equivalent to the original model. In order to reduce the size of the graph, a blocking procedure is proposed in this paper. In addition, we provide two types of valid inequalities to strengthen the formulation. Finally we test our model on a real case study and compare it to the classical model for complete graphs. | ||
| کلیدواژه‌ها | ||
| Vehicle routing problem؛ extended formulation؛ disconnected subtour elimination constraints؛ separation problem؛ blocking procedure | ||
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آمار تعداد مشاهده مقاله: 43 تعداد دریافت فایل اصل مقاله: 63 |
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