Document Type : Original Article

Authors

1 Science and Research Branch, Islamic Azad University, Tehran, Iran.

2 Department of Industrial Management, College of management and accounting, West Tehran Branch, Islamic Azad University, Tehran, Iran.

10.22116/jiems.2020.205786.1309

Abstract

Nowadays, environmental deterioration is one of the most noticeable issues in logistics, so that the organizations are required to control the triggers of environmental contaminations generation. One of the most effective steps in addressing this term is to design transportation network considering CO2 emission limitation. In this paper, a vehicle routing problem with simultaneous pickup and delivery with heterogeneous fleet and environmental measurement consideration is proposed. Introduced two objectives mathematical modeling, with the help of the weighted LP metric method has become to a combined dimensionless objective. The formulated optimization problem is solved in small dimensions using General Algebraic Modelling System (GAMS) approach and specifically BARON solver respect to the nature of the mathematical equations. The results obtained from simulations are discussed to confirm the effectiveness of the proposed method in dealing with the desired example. Because of NP-hardness, Discrete Invasive Weed Optimization (DIWO) meta-heuristic algorithm is applied.

Keywords

Archetti, C., Speranza, and M. G., Hertz, M., (2006). "A tabu search algorithm for the split delivery vehicle routing problem", Transportation Science, Vol. 40, No. 1, pp. 64-73.
Babaee Tirkolaei, E., Goli, A., and Malekalipour Kordestanizadeh, R., (2019). "A robust bi-objective multi-trip periodic capacitated arc routing problem for urban waste collection using a multi-objective invasive weed optimization", Waste Management & Research, pp. 1-13.
Bektas, I. and Laporte, G., (2011). "The Pollution-Routing Problem", Transportation Research Part B: Methodological, Vol. 45, No. 8, pp. 1232-1250.
Belgin, O., Karaoglan, I., and Altiparmak, F., (2018). "Two-echelon vehicle routing problem with simultaneous pickup and delivery: Mathematical model and heuristic approach", Computer & Industrial Engineering, Vol. 115, pp. 1-16.
Chen, J. F. and Wu, T. H., (2006). "Vehicle routing problem with simultaneous deliveries and pickups", Journal of the Operational Research Society, Vol. 57, No. 5, pp. 579-587.
Chen, Q., Li K., and Liu, Z., (2014). "Model and algorithm for unpaired pickup and delivery vehicle routing problem with split loads", Transportation Research Part E, Vol. 69, pp. 218-235.
Cheng, C., Yang, P., Qi, M., and Rousseau, L.M., (2017). "Modeling a green inventory routing problem with a heterogeneous fleet", Transportation Research Part E, Vol. 97, pp. 97-112.
Cruz, R. C., Silva, T. C. B., and Souza, M. J. F., (2012). "A heuristic approach for solving the vehicle routing problem with simultaneous pickup and delivery", Electronic Notes in Discrete Mathematics, Vol. 39, pp. 217-224.
Dror, M., and Trudeau, P., (1989). "Savings by split delivery routing", Transportation Science, pp. 141-145.
Goli, A., Babaee Tirkolaei, E., and Soltani, M., (2019). "A robust just-in-time flow shop scheduling problem with outsourcing option on subcontractors", Production & Manufacturing Research, Vol. 7, No. 1, pp. 294-315.
Goli, A., and Davoodi, M.R., (2018). "Coordination policy for production and delivery scheduling in the closed loop supply chain", Production Engineering, Vol. 12, No. 5, pp. 621-631.
Goli, A., and Davoodi, M.R., (2019). "An integrated disaster relief model based on covering tour using hybrid Benders decomposition and variable neighborhood search: Application in the Iranian context", Computers & Industrial Engineering, Vol. 130, pp. 370-380.
Goli, A., Khademi Zare, H., Tavakkoli Moghaddam, R., and Sadeghieh, A., (2019). "Application of robust optimization for product portfolio problem using an invasive weed optimization algorithm", Numerical Algebra, Control and Optimization, Vol. 9, No. 2.
Goli, A., Khademi Zare, H., Tavakkoli Moghaddam, R., and Sadeghieh, A., (2019). "Multiobjective fuzzy mathematical model for a financially constrained closed-loop supply chain with labor employment", Computational Intelligence, pp. 1–31.
Goli, A., Khademi Zereh, H., Tavakkoli-Moghaddam, R., and Sadeghieh, A., (2019). "Hybrid artificial intelligence and robust optimization for a multi-objective product portfolio problem Case study: The dairy products industry", Computers & Industrial Engineering, Vol. 137.
 Huang, Y., Zhao, L., Woensel, T.V., and Gross, J.P., (2017). "Time-dependent vehicle routing problem with path flexibility", Transportation Research Part B, Vol. 95, pp. 169-195.
Kalayci, C. B., and Kaya, C., (2016). "An ant colony system empowered variable neighborhood search algorithm for the vehicle routing problem with simultaneous pickup and delivery", Expert System with Applications, Vol. 66, pp. 163-175.
Koç, Ç., and Karaoglan, I., (2016). "The green vehicle routing problem: A heuristic based exact solution approach", Applied Soft Computing, Vol. 39, pp. 154-164.
Lin C., Choy K. L., Ho G. T. S., Chung S. H., Lam H. T., (2013). "Survey of Green Vehicle Routing Problem: Past and future trends", Expert Systems with Applications, Vol. 41, pp. 1118-1163.
Madankumar, S., and Rajendran, C., (2018). "Mathematical models for green vehicle routing problems with pickup and delivery: A case of semiconductor supply chain", Computer and Operation research, Vol. 89, pp. 183-192.
Mehrabian, A.R., and Lucas, C., (2006). "A novel numerical optimization algorithm inspired from weed colonization", Ecological Information, Vol. 1, pp. 355-366.
Nagy, G.,  Salhi, S., (2005). "A heuristic algorithms for single and multiple depot vehicle routing problems with pickups and deliveries", European Journal of Operational Research, Vol. 162, pp. 126-141.
Özyurt, Z., Aksen, D., and Aras, N., (2006). "OVRP with time deadlines: solution methods and applications", OR Proceedings 2005. Springer Berlin Heidelberg, pp. 73-78.
Pachauri, R.K., Allen, M.R., Barros, Broome, J., Cramer, W., Christ, R., et al., (2014). "Climate change 2014: Synthesis report", Contribution of working groups 1, 2 and 3 to the fifth assessment report of the intergovernmental panel on climate change.
Poonthalir, G., and Nadarajan, R., (2018). "A Fuel Efficient Green Vehicle Routing Problem with varying speed constraint (F-GVRP)", Expert Systems with Applications, Vol. 100, pp. 131-144.
Ramezani Ghalenoei, M., Hajimirsadeghi, H., and Lucas, C., (2009). "Discrete Invasive Weed Optimization Algorithm: Application to cooperative Multiple Task Assignment of UAV’s", 48th IEEE Conference on decision and control.
Sangaiah, A.K., Babaee Tirkolaei, E., Goli, A., and Dehvani-Arani, S., (2019). "Robust optimization and mixed-integer linear programming model for LNG supply chain planning problem", Soft Computing.
Soleimani, H.,  Chaharlang, Y., and Ghaderi, H., (2018). "Collection and distribution of returned-remanufactured products in a vehicle routing problem with pickup and delivery considering sustainable and green criteria", Journal of Cleaner Production, Vol. 172, pp. 960-970.
Subramanian, A., Drummond, L. M. A., and Bentes, C., (2010). "A parallel heuristic for the vehicle routing problem with simultaneous pickup and delivery", Computers & Operations Research, Vol. 37, No. 11, pp. 1899-1911.
Taguchi, G., Chowdhury, S., and Wu, Y., (2005). "Taguchi’s Quality Engineering Handbook", Volume 1736. Hoboken, NJ: John Wiley & Sons, Inc.
Tasan, A.S., Gen, M., (2012). "A genetic algorithm based approach to vehicle routing problem with simultaneous pick-up and deliveries", Computers & Industrial Engineering, Vol. 62, No. 3, pp. 755-761.
Thangiah, S., Vinayagamoorty, R., and Gubbi A., (1993). "Vehicle routing and time deadlines using genetic and loca algorithms", Proceedings of the 5th International Conference on Genetic Algorithms, pp. 506-515.
Turkensteen, M., and Hasle, G., (2017). "Combining pickups and deliveries in vehicle routing – An assessment of carbon emission effects", Transportation Research Part C: Emerging Technologies, Vol. 80, pp. 117-132.
Ubeda, S., Arcelus, F. J., and Faulin, J., (2011). "Green logistics of vehicle routing problem", Vehicle routing problem, Vol. 9, pp. 1-26.
Wang, X., and Li, X., (2018). "Carbon reduction in the location routing problem with heterogeneous fleet, simultaneous pickup-delivery and time windows", Procedia Computer Science, Vol. 112, pp. 1131-1140.
Xiao, Y., and Konak, A., (2016). "The heterogeneous green vehicle routing and scheduling problem with time varying traffic congestion", Transportation Research Part E, Vol. 88, pp. 146-166.
Xiao, Y., Zhao, Q., Kaku, I., and Xu, Y., (2012). "Development of a fuel consumption optimization model for the capacitated vehicle routing problem", Computers and Operations Research, Vol. 39, Vol. 7, pp. 1419-1431.
Zachariadis, E. E., Tarantilis, C. D., and Kiranoudis C. T., (2009). "A hybrid metaheuristic algorithm for the vehicle routing problem with simultaneous delivery and pick-up service", Expert Systems with Applications, Vol. 36, No. 2, pp. 1070-1081.
Zhang, S., Lee, C.K.M., Choy, K.L., Ho, W., and Ip, W.H., (2014). "Design and development of a hybrid artificial bee colony algorithm for the environmental vehicle routing problem", Transportation Research Part D, Vol. 31, pp. 85-99.