A mathematical Model and Solving Method for Multi-Depot and Multi-level Vehicle Routing Problem with Fuzzy Time Windows

Vahid Mahdavi, Seyed Amir Sadeghi, Soheil Fathi


Abstract – Multi-depot and multi-level vehicle routing problem with fuzzy time windows is considered as one of the most important and complicated decision problems in transportation field. Up to present, different heuristic, Meta-heuristic and accurate methods have been represented for solving vehicle routing problems. In this article, a mathematical model for multi-depot and multi-level vehicle routing problem with fuzzy time windows (MD-MLVRPFTW) and it’s solving method has been offered. Never In transportation scheduling problems, the time window is achieved completely and precisely. And actually the deviation of the servicing time from the customer’s time window is a parameter that can indicate the level of customer’s satisfaction. In multi-depot vehicle routing problems, in order to determine the level of service related to time window, fuzzy functions has been used. In this article the multi-depot vehicle routing problem with fuzzy time windows (MDVRPFTW) has been solved as a multi-level model. This essay pursues its purposes to minimize the servicing time and distances passed by vehicles and also to maximize the level of service. In order to solve the multi-level model, a three-section algorithm has been developed. In the first section, for reducing the servicing time, customers are assigned to distribution centers. In the next section, a single-depot vehicle routing problem with time windows (VRPTW-) is solved in order to reduce the distribution costs. The third section concerns solving the improvement problem. Consideration of designed tests in this article illustrates a huge reduction in servicing time and distribution costs and actually elucidates a remarkable increase in customers’ level of satisfaction.


Multi-depot vehicle routing problem, time window, service level, minimizing the distribution costs

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