A Multi-depot Vehicle Routing Problem with Time Windows and Load Balancing: A Real World Application

Document Type: Research Paper


1 School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran

2 School of Industrial Engineering, Iran University of Science & Technology, Tehran, Iran


This paper presents a mixed integer non-linear programming (MINLP) model for a bi-
objective and multi-depot vehicle routing problem with time windows. The main goals of the
paper are minimization of total cost and equitable distribution of commodities between
vehicles. Two types of vehicle including delivery and installation vehicles are utilized in the
network regarding customers’ needs. Satisfying all demands of the customers is not
obligatory and unmet demands are permitted which leads to extra cost. A presented model is applied for real life case study in different provinces of Iran. To tackle the small-size
problems, the augmented e-constraint method is utilized by linearization of the model.
Because of the NP-hard nature of the problem, as the size of the problem increases, so does the complexity. As such, we develop multi-objective simulated annealing (MOSA meta-heuristic) algorithm for large scale problems. Then, several numerical experiments and sensitivity analyses are conducted to validate the presented model and the solution method, which indicate the efficiency of our proposed approach.


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