A Mathematical Model Based on Capacitated Vehicle Routing Problem with Time Lapses for Garbage Collection

Document Type : Research Paper


1 Associate Prof. of Industrial Engineering, Persian Gulf University, Bushehr, Iran

2 MSc Student of Industrial Engineering, Persian Gulf University, Bushehr, Iran

3 Assistant Prof., Faculty of Science, Numerical Analysis, Persian Gulf University, Bushehr, Iran


Producing various types of waste and related environmental problems, has faced urban management with many problems in the areas like: collection, transportation and waste disposal. Applying a good way to reduce the costs of collecting waste seems necessary, because collection and transportation of the waste needs allocation of a significant part of garbage management budget. In the present study, a mathematical model is presented for waste collection by which we can reduce the costs of collecting the waste by minimizing the distance for the trucks. The model is flexible enough to manage collecting the waste of a node in different separate times.  Then, some small-scale issues were solved using CPLEX software and meta-heuristic algorithm and the results were compared. The data for the case study were collected and the meta-heuristic algorithm was used to determine the vehicle schedule. Finally, a mathematical model was used to decide about the number of vehicles required


Chalkias, A. & Lasarid, E. (2009). Optimizing municipal solid waste collection using GIS. Waste management, 47, 776- 790.
Chen, Y., Hwang Wang, C. & Lin, J. (2015). Amulti-objective geographic information system for route selectionof nuclearwaste transport. Omega, 36, 363-372.
Claassen, F. & Hendriks, T. (2007). An application of Special Ordered Sets to a periodic milk collection problem. European Journal of Operational Research, 180 (2), 754-769.
Dhahri, A., Zidi, K. & Ghedira, K. (2014). Variable Neighborhood Search Based Set covering ILP model for the Vehicle Routing Problem with time windows. Procedia Computer Science, 29, 844-854.
Faiz, S., Krichen, S. & Inoubli, W. (2014). A DSS based on GIS and Tabu search for solving the CVRP: The Tunisian case. The Egyptian Journal of Remote Sensing and Space Sciences, 17, 105-110.
Flavia, B., Guillermo, D., Larumbe, F. & Marenco, J. (2012). A Method for Optimizing Waste Collection Using Mathematical Programming: A Buenos Aires Case Study. Waste Management & Research, 30(3), 311-324.
Fooladi, S., Fazlollahtabar, H. & Mahdavi, I. (2013). Waste Collection Vehicle Routing Problem Considering Similarity Pattern of Trashcan. International Journal of Applied Operational Research, 3, 105-111.
Inghels, D., Dullaert, W. & Vigo, D. (2016). A service network design model for multimodal municipal solid waste transport. European Journal of Operational Research, 254(1), 68-79.
Mahdavi, I., Tavakoli Moghadam, R. & Ghazi zade Hashemi, S. (2010). Vehicle Routing Problem and determine the number of cars garbage collection using a meta-heuristic method (a case study). Journal of Transportation, 7(1), 95-101. (in Persian)
Majlesi, m. (2007). The role of public participation in a mechanized waste collection system. Third National Conference on Waste Management. Tehran,
(in Persian)
Majlesi, M., Zamani, A., Mahdipor, F., Shmsaei, V., Sharifi Maleksari, H. & Darvar, P. (2013). Analysis of the cost of collecting and transporting waste of area of Bandar Abbas city. Journal of Health in the field, 1(1), 37-45.
(in Persian)
Markov, I., Varone, S. & Bierlaire, M. (2016). Integrating a heterogeneous fixed fleet and a flexible assignment of destination depots in the waste collection VRP with intermediate facilities. Transportation Research Part B: Methodological, 84, 256-273.
Merikh Bayat, F. (2014). Optimization algorithms inspired by nature. Tehran: Nas.(in Persian)
Montoya-Torres, J., Franco, J., Isaza, S., Jiménez, H. F. & Herazo-Padilla, N. (2015). A literature review on the vehicle routing problem with multiple depots. Computers & Industrial Engineering, 79, 115-129.
Sbihi, A., & Eglese, R. (2010). Combinatorial optimization and Green Logistics. Annals of Operations Research, 125, 159-175.
Tavakoli Moghadam, R. & Alinaghiyan, M. (2009). Presentation and solving a new mathematical programming model for Competitive Vehicle Routing Problem: A case study. Journal of Transportation, 6(4), 311-323.
(in Persian)
Tavakoli Moghadam, R., Rabbani, M., Shariat, M. & Safaei, N. (2006). Solving Vehicle Routing Problem with soft time windows using a compilation meta-heuristic algorithm. Journal of Technical University of Tehran, 40(4), 469-476. (in Persian)
Toth, P. & Vigo, D. (2014). Vehicle Routing Problems, Methods, and Applications. The Society for Industrial and Applied Mathematics and the Mathematical Optimization Society. SIAM, Italy.
Wy, J. & Byung-In, k. (2013). A hybrid meta heuristic approach for the rollon–rolloff vehicle routin problem. Computers & Operations Research, 40, 1947-1952.