Vehicle Routing Problem (VRP) with time windows is a generalization of the classic VRP. Specifically, every customer must be met in a certain time window. Sometimes in the real life, it is not possible to carry different products simultaneously. In other words, these products are non-adjacent. This paper presents a comprehensive model for the vehicle routing problem with time windows and the possibility of delivery split of non-adjacent products. The proposed model is an extension of VRP considering the profit in a bi-objective optimization model.
Mohammad Hossein Sarbaghi Yazdi,
A Bi-objective VRPTW Model for Non-adjacent Products, American Journal of Science, Engineering and Technology.
Vol. 2, No. 1,
2017, pp. 1-5.
Dantzig, G. and Ramser, J. H. ‘The truck dispatching problem’, Management Science, Vol. 6, pp. 80-91.
Lenstra, J. and Rinnooy, K. ‘Complexity of vehicle routing and scheduling problems’, Networks, Vol.
Baños, R., Ortega, J., Gil, C., Fernández, A. and de Toro, F. (2013) ‘A Simulated Annealing-based parallel multi-objective approach to vehicle routing problems with time windows’, Expert Systems with Applications, Vol. 40, Issue 5, pp. 1696–1707.
Wang, C., Mu, D., Zhao, F. and Sutherland, J. W. (2015) ‘A parallel simulated annealing method for the vehicle routing problem with simultaneous pickup–delivery and time windows’. Computers & Industrial Engineering, Vol. 83, pp. 111–122.
Ursani, Z., Essam, D., Cornforth, D. and Stocker, R. (2011) ‘Localized genetic algorithm for vehicle routing problem with time windows’, Applied Soft Computing, Vol. 11, Issue 8, pp. 5375–5390.
Yang, B., Hu, Z.-H., Wei, C., Li, S.-Q., Zhao, L. and Jia, S. (2015) ‘Routing with time-windows for multiple environmental vehicle types’, Computers & Industrial Engineering, Vol. 89, pp. 150-161.
Belhaiza, S., Hansen, P. and Laporte, G. (2014) ‘A hybrid variable neighborhood tabu search heuristic for the vehicle routing problem with multiple time windows’. Computers & Operations Research, Vol. 52, pp. 269–281.
Li, X., Tian, P. and Leung, C. H. (2010) ‘Vehicle routing problems with time windows and stochastic travel and service times: Models and algorithm’, International Journal of Production Economics, Vol. 125, pp. 137–145.
Zare-Reisabadi, E. and Mirmohammadi, S. H. (2015) ‘Site dependent vehicle routing problem with soft time window: Modeling and solution approach’. Computers & Industrial Engineering, Vol. 90, pp. 177-185.
Yu, B., Yang, Z. Z. and Yao, B. Z. (2011) ‘A hybrid algorithm for vehicle routing problem with time windows’, Expert Systems with Applications, Vol. 38, pp. 435–441.
Küçükoglu, I., and Öztürk, N. (2015) ‘An advanced hybrid meta-heuristic algorithm for the vehicle routing problem with backhauls and time windows’, Computers & Industrial Engineering, Vol. 86, pp. 60-68.
Belfiore, P. and Yoshizaki, H. T. Y. (2013) ‘Heuristic methods for the fleet size and mix vehicle routing problem with time windows and split deliveries’, Computers & Industrial Engineering, Vol. 64, pp. 589–601.
Cherkesly, M., Desaulniers, G. and Laporte, G. (2015) ‘A population-based metaheuristic for the pickup and delivery problem with time windows and LIFO loading’, Computers & Operations Research, Vol. 62, pp. 23-35.
Dror, M. and Trudeau, P. (1989) ‘Savings by split delivery routing’, Transportation Science, Vol. 23, pp. 141–145.
Dror, M., Laporte, G. and Trudeau, P. (1994) ‘Vehicle routing with split deliveries’, Discrete Applied Mathematics, Vol. 50 (3), pp. 239–354.
El-Sherbeny, N. (2010) ‘Vehicle routing with time windows: An overview of exact, heuristic and metaheuristic methods’, Journal of King Saud University (Science), Vol. 22, pp. 123–131.
Dell’Amico, M., Maffioli, F. and Varbrand, P. (1995) ‘On prize-collecting tours and the asymmetric travelling salesman problem’, International Transactions in Operational Research, Vol. 2, pp. 297–308.
Keller, C. P. and Goodchild, M. (1988) ‘the multi objective vending problem: A generalization of the traveling salesman problem’, Environment and Planning B: Planning and Design, Vol. 15, pp. 447-460.
Feillet, D., Dejax, P. and Gendreau, M. (2005) ‘Traveling salesman problems with profits’, Transportation Science, Vol. 36, pp. 188–205.
Laporte, G. and Martello, S. (1990) ‘The selective traveling salesman problem’, Discrete Applied Mathematics, Vol. 26, pp. 193–207.
Ausiello, G., Bonifaci, V. and Laura, L. (2008) ‘The online Prize-Collecting Traveling Salesman Problem’, Information Processing Letters, Vol. 107, pp. 199–204.
Pedro, O., Saldanha, R. and Camargo, R. (2013) ‘A Tabu Search Approach for the Prize Collecting Traveling Salesman Problem’, Electronic Notes in Discrete Mathematics, Vol. 41, pp. 261–268.
Archetti, C., Feillet, D., Hertz, A. and Speranza, M. G. (2010) ‘The undirected capacitated arc routing problem with profits’, Computers & Operations Research, Vol. 37, pp. 1860–1869.
Chao, I., Golden, B. and Wasil, E. (1996) ‘The team orienteering problem’, European Journal of Operational Research, Vol. 88, pp. 464–474.
Lin, S.-W. and Yu., V. F. (2015) ‘A simulated annealing heuristic for the multiconstraint team orienteering problem with multiple time windows’, Applied Soft Computing, Vol. 37, p.p. 632-642.
Boussier, S., Feillet, D. and Gendreau, M. (2007) ‘An exact algorithm for team orienteering problems’, 4OR, Vol. 5, pp. 211–230.
Aráoz, J., Fernández, E. and Meza, O. (2009) ‘Solving the prize-collecting rural postman problem’, European Journal of Operational Research, Vol. 196, pp. 886–896.
Mavrotas, G. (2009) ‘Effective implementation of the e-constraint method in Multi Objective Mathematical Programming problems’, Applied Mathematics and Computation, Vol. 213, pp. 455–465.
Mavrotas, G. and Florios, K. (2013) ‘An improved version of the augmented ε-constraint method (AUGMECON2) for finding the exact pareto set in multi-objective integer programming problems’, Applied Mathematics and Computation, Vol. 219, pp. 9652–9669.