Inventory Routing Problem with Vehicle Resource Sharing in the Two-depot and Multi-retailer System


Wisut Supithak Titirat Vivithkeyoonvong


        The research considers the problem of determining vehicle routes and replenishment intervals in the system composed of two depots supplying an inventory item to multiple retailers. Each transportation vehicle leaving a depot can end its route at any depot and, therefore, the vehicle route can be either close loop or open loop. However, the number of vehicles leaving any depot must equal to the number of vehicles arriving the depot. The objective is to minimize the sum of inventory holding cost, delivery setup cost, transportation cost, and vehicle owning cost. A genetic algorithm is developed in order to determine a good solution to the problem when there exists at most one delivery route for each depot. The chromosome representation is designed in such a way that, after decoding, a chromosome can represent both types of vehicle route. To determine the optimal replenishment interval, the concept of economic order interval with joint replenishment is inserted in the genetic algorithm structure.  Two numerical experiments are conducted for the performance evaluation. The first experiment is to compare the genetic algorithm solution with the optimal solution obtained from the enumerative search. The result shows that the proposed method can provide optimal solution for 27 out of 30 randomly generated problems. The maximum percentage deviation is 1.79 percent. The second experiment is to compare the genetic algorithm solution with the solution yielded from a three-step heuristic at different levels of number of retailers and vehicle owning costs. According to the experimental result, the proposed method can provide better solution for all 270 randomly generated problems with the average percentage deviation of 10.33 percent. As the number of retailers and the vehicle owning cost increase, the open vehicle route tends to yield better solution than the close vehicle route.

Keywords: Inventory Routing Problem, Open Vehicle Routing, Vehicle Sharing, Genetic Algorithm


Bertazzi, L., & Speranza, M. G. (2012). Inventory routing problems: an introduction. EURO Journal on Transportation and Logistics, 1(4), 307-326.
Braekers, K., Ramaekers, K., & Nieuwenhuyse I. V. (2016). The vehicle routing problem: State of the art classification and review. Computers & Industrial Engineering, 99, 300-313.
Campbell, A. M., & Savelsbergh, M. W. P. (2004). A decomposition approach for the inventory-routing problem. Transport Science, 38(4), 488-502.
Cheng, R., Gen, M., & Tosawa, T. (1995). Minmax earliness/tardiness scheduling in identical parallel machine system using genetic algorithms. 17th International Conference on Computers and Industrial Engineering, 29, 513–517.
Dantzig, G. B., & Ramser, J. H. (1959). The truck dispatching problem. Management Science, 6(1), 80-91.
Feiyue, L., Bruce, G., & Edward, W. (2007). The open vehicle routing problem: Algorithms, large-scale test problems, and computational results. Computers & Operations Research, 34(10), 2918-2930.
Gurpreet, S., & Vijay D. (2014). Open Vehicle Routing Problem by Ant Colony Optimization. International Journal of Advanced Computer Science and Applications, 5(3), 63-68.
Lenstra, J. K., & Rinnooy-Kan, A. H. G. (1981). Complexity of vehicle routing and scheduling problems. Networks, 11(2), 221-227.
Modhi, L. M., Burhanuddin, M. A., & Asaad, S. H. (2017). Review paper in vehicle routing problem and future research trend. International Journal of Applied Engineering Research, 12, 12279-12283.
Olivera, F. B., Enayatifar, R., Sadaei, S. J., Guimaraes, F. G., & Potvin, J. Y. (2016). A cooperative coevolutionary algorithm for the Multi-Depot Vehicle Routing Problem.Expert Systems with Applications, 43, 117-130.
Sariklis, D., & Powell, S. (2000). A heuristic method for the open vehicle routing problem. The Journal of the Operational Research Society, 51(5), 564-573.
Serna, M. D. A., Cortes J., & Daniela G. S. (2015). Modeling the inventory routing problem (IRP) with multiple depots with genetic algorithms. IEEE Latin America Transactions, 13(12), 3959-3965.
Supithak, A., & Supithak, W. (2018). Determination of inventory replenishment policy with the open vehicle routing concept in a multi-depot and multi-retailer distribution system. Engineering and Applied Science Research, 45(1), 23-31.
Supithak, W., & Plongon, K. (2011). Memetic algorithm for non-identical parallel machines scheduling problem with earliness and tardiness penalties. International Journal of Manufacturing Technology and Management, 22(1), 26-38.
Viswanathan, S., & Mathur, K. (1997). Integrating routing and inventory decisions in one-warehouse multi-retailer multiproduct distribution system. Management Science, 43(3), 294-312.

Research Articles


How to Cite
SUPITHAK, Wisut; VIVITHKEYOONVONG, Titirat. Inventory Routing Problem with Vehicle Resource Sharing in the Two-depot and Multi-retailer System. Naresuan University Journal: Science and Technology (NUJST), [S.l.], v. 30, n. 2, p. 99-109, aug. 2021. ISSN 2539-553X. Available at: <>. Date accessed: 18 jan. 2022.