NUMERICAL ALGEBRA, doi:10.3934/naco.2017026 CONTROL AND OPTIMIZATION Volume 7, Number 4, December 2017 pp. 417–433 A ROBUST MULTI-TRIP VEHICLE ROUTING PROBLEM OF PERISHABLE PRODUCTS WITH INTERMEDIATE DEPOTS AND TIME WINDOWS Erfan Babaee Tirkolaee ∗ Mazandaran University of Science and Technology Department of Industrial Engineering, Babol, Iran Alireza Goli Department of Industrial Engineering Yazd University, Yazd, Iran Mani Bakhsi Department of Industrial and System Engineering Isfahan University of Technology, Isfahan, Iran Iraj Mahdavi Department of Industrial Engineering Mazandaran University of Science and Technology, Babol, Iran Abstract. Distribution of products within the supply chain with the highest quality is one of the most important competitive activities in industries with perishable products. Companies should pay much attention to the distribution during the design of their optimal supply chain. In this paper, a robust multi- trip vehicle routing problem with intermediate depots and time windows is formulated to deals with the uncertainty nature of demand parameter. A mixed integer linear programming model is presented to minimize total traveled distance, vehicles usage costs, earliness and tardiness penalty costs of services, and determine optimal routes for vehicles so that all customers’ demands are covered. A number of random instances in different sizes (small, medium, and large) are generated and solved by CPLEX solver of GAMS to evaluate the robustness of the model and prove the model validation. Finally, a sensitivity analysis is applied to study the impact of the maximum available time for vehicles on the objective function value. 2010 Mathematics Subject Classification. Primary: 46-xx; Secondary: 46N10. Key words and phrases. Robust multi-trip VRP, perishable products, intermediate depots, time windows. This paper was prepared at the occasion of The 12th International Conference on Industrial Engineering (ICIE 2016), Tehran, Iran, January 25-26, 2016, with its Associate Editors of Nu- merical Algebra, Control and Optimization (NACO) being Assoc. Prof. A. (Nima) Mirzazadeh, Kharazmi University, Tehran, Iran, and Prof. Gerhard-Wilhelm Weber, Middle East Technical University, Ankara, Turkey. 417