Abstract
Pollution emitted by a vehicle can be checked by reducing the distance traveled and through operational adjustments. Optimized route and simultaneous pickup and delivery in a vehicle routing problem (VRP) can achieve the same. This paper investigates a two-echelon pollution routing problem with simultaneous pickup and delivery by considering multiple time windows (2E-PRPSPD-MTW) for customers’ visit. The first echelon consists of depots and intermediate depots (called satellites), whereas the second echelon consists of the satellites and customers. Two fleets (one for each echelon) of heterogeneous vehicles accomplish pickup and delivery operations. The 2E-PRPSPD-MTW is developed in a bi-objective framework, focusing on minimization of both travel time and fuel consumption. The proposed bi-objective 2E-PRPSPD-MTW is an NP-hard problem. So, in order to optimize it, multi-objective variable neighborhood search (MOVNS) is modified and used. In this process, six operators are proposed in order to improve the neighborhood structure. The suggested operators explore the entire solution space to find the near optimal solution. With the aim of providing much richer insights, the efficacy of the proposed method and mathematical formulation is demonstrated through numerical experiment for a number of instances varying from small to large scale.
Similar content being viewed by others
References
Abad, H.K.E., Vahdani, B., Sharifi, M., Etebari, F.: A bi-objective model for pickup and delivery pollution-routing problem with integration and consolidation shipments in cross-docking system. J. Clean. Prod. 193, 784–801 (2018)
Abdelkhalek, O., Masri, H., Krichen, S.: An adaptive variable neighborhood search for solving the multi-objective node placement problem. Electron. Notes Discrete Math. 47, 189–196 (2015)
Al Chami, Z., Manier, H., Manier, M.A., Fitouri, C.: A hybrid genetic algorithm to solve a multi-objective pickup and delivery problem. IFAC-PapersOnLine 50(1), 14,656–14,661 (2017)
Arroyo, J.E.C., dos Santos, Ottoni R., de Paiva, Oliveira A.: Multi-objective variable neighborhood search algorithms for a single machine scheduling problem with distinct due windows. Electron. Notes Theor. Comput. Sci. 281, 5–19 (2011)
Avci, M., Topaloglu, S.: A hybrid metaheuristic algorithm for heterogeneous vehicle routing problem with simultaneous pickup and delivery. Expert Syst. Appl. 53, 160–171 (2016)
Barth, M., Boriboonsomsin, K.: Real-world carbon dioxide impacts of traffic congestion. Transp. Res. Rec. 2058(1), 163–171 (2008)
Barth, M., Younglove, T., Scora, G.: Development of a heavy-duty diesel modal emissions and fuel consumption model. Technical report UC Berkeley: California Partners for Advanced Transit and Highways (PATH), California, USA (2005). http://www.path.berkeley.edu/PATH/Publications/PDF/PRR/2005/PRR-2005-01.pdf. Accessed 6 Apr 2020
Bektaş, T., Laporte, G.: The pollution-routing problem. Transp. Res. Part B: Methodol. 45(8), 1232–1250 (2011)
Belgin, O., Karaoglan, I., Altiparmak, F.: Two-echelon vehicle routing problem with simultaneous pickup and delivery: mathematical model and heuristic approach. Comput. Ind. Eng. 115, 1–16 (2018)
Belhaiza, S., Hansen, P., Laporte, G.: A hybrid variable neighborhood tabu search heuristic for the vehicle routing problem with multiple time windows. Comput. Oper. Res. 52, 269–281 (2014)
Bravo, M., Rojas, L.P., Parada, V.: An evolutionary algorithm for the multi-objective pick-up and delivery pollution-routing problem. Int. Trans. Oper. Res. 26(1), 302–317 (2019)
Breunig, U., Schmid, V., Hartl, R.F., Vidal, T.: A large neighbourhood based heuristic for two-echelon routing problems. Comput. Oper. Res. 76, 208–225 (2016)
Breunig, U., Baldacci, R., Hartl, R.F., Vidal, T.: The electric two-echelon vehicle routing problem. Comput. Oper. Res. 103, 198–210 (2019)
Capelle, T., Cortés, C.E., Gendreau, M., Rey, P.A., Rousseau, L.M.: A column generation approach for location-routing problems with pickup and delivery. Eur. J. Oper. Res. 272(1), 121–131 (2019)
Crainic, T.G., Perboli, G., Mancini, S., Tadei, R.: Two-echelon vehicle routing problem: a satellite location analysis. Procedia-Soc. Behav. Sci. 2(3), 5944–5955 (2010)
Dellaert, N., Dashty Saridarq, F., Van Woensel, T., Crainic, T.G.: Branch-and-price-based algorithms for the two-echelon vehicle routing problem with time windows. Transp. Sci. 53(2), 463–479 (2018)
Demir, E., Bektaş, T., Laporte, G.: An adaptive large neighborhood search heuristic for the pollution-routing problem. Eur. J. Oper. Res. 223(2), 346–359 (2012)
Demir, E., Bektaş, T., Laporte, G.: The bi-objective pollution-routing problem. Eur. J. Oper. Res. 232(3), 464–478 (2014)
Favaretto, D., Moretti, E., Pellegrini, P.: Ant colony system for a vrp with multiple time windows and multiple visits. J. Interdiscip. Math. 10(2), 263–284 (2007)
Geiger, M.J.: Randomised variable neighbourhood search for multi objective optimisation (2008). arXiv preprint arXiv:08090271
Goksal, F.P., Karaoglan, I., Altiparmak, F.: A hybrid discrete particle swarm optimization for vehicle routing problem with simultaneous pickup and delivery. Comput. Ind. Eng. 65(1), 39–53 (2013)
Grangier, P., Gendreau, M., Lehuédé, F., Rousseau, L.M.: An adaptive large neighborhood search for the two-echelon multiple-trip vehicle routing problem with satellite synchronization. Eur. J. Oper. Res. 254(1), 80–91 (2016)
Guimarães, T.A., Coelho, L.C., Schenekemberg, C.M., Scarpin, C.T.: The two-echelon multi-depot inventory-routing problem. Comput. Oper. Res. 101, 220–233 (2019)
Hoogeboom, M., Dullaert, W., Lai, D., Vigo, D.: Efficient neighborhood evaluations for the vehicle routing problem with multiple time windows. Transp. Sci. 54, 400–416 (2020)
Hornstra, R.P., Silva, A., Roodbergen, K.J., Coelho, L.C.: The vehicle routing problem with simultaneous pickup and delivery and handling costs. Comput. Oper. Res. 115(104), 858 (2020)
Kalayci, C.B., Kaya, C.: An ant colony system empowered variable neighborhood search algorithm for the vehicle routing problem with simultaneous pickup and delivery. Expert Syst. Appl. 66, 163–175 (2016)
Karimi, H.: The capacitated hub covering location-routing problem for simultaneous pickup and delivery systems. Comput. Ind. Eng. 116, 47–58 (2018)
Kramer, R., Subramanian, A., Vidal, T., Lucídio dos Anjos, F.C.: A matheuristic approach for the pollution-routing problem. Eur. J. Oper. Res. 243(2), 523–539 (2015)
Kumar, R.S., Kondapaneni, K., Dixit, V., Goswami, A., Thakur, L.S., Tiwari, M.: Multi-objective modeling of production and pollution routing problem with time window: a self-learning particle swarm optimization approach. Comput. Ind. Eng. 99, 29–40 (2016)
Li, H., Wang, L., Hei, X., Li, W., Jiang, Q.: A decomposition-based chemical reaction optimization for multi-objective vehicle routing problem for simultaneous delivery and pickup with time windows. Memet. Comput. 10(1), 103–120 (2018)
Lu, E.H.C., Yang, Y.W.: A hybrid route planning approach for logistics with pickup and delivery. Expert Syst. Appl. 118, 482–492 (2019)
Majidi, S., Hosseini-Motlagh, S.M., Ignatius, J.: Adaptive large neighborhood search heuristic for pollution-routing problem with simultaneous pickup and delivery. Soft. Comput. 22(9), 2851–2865 (2018)
Min, H.: The multiple vehicle routing problem with simultaneous delivery and pick-up points. Transp. Res. Part A: Gen. 23(5), 377–386 (1989)
Mu, D., Wang, C., Zhao, F., Sutherland, J.W.: Solving vehicle routing problem with simultaneous pickup and delivery using parallel simulated annealing algorithm. Int. J. Ship. Transp. Logist. 8(1), 81–106 (2016)
Noh, J., Kim, J.S.: Cooperative green supply chain management with greenhouse gas emissions and fuzzy demand. J. Clean. Prod. 208, 1421–1435 (2019)
Polat, O., Kalayci, C.B., Kulak, O., Günther, H.O.: A perturbation based variable neighborhood search heuristic for solving the vehicle routing problem with simultaneous pickup and delivery with time limit. Eur. J. Oper. Res. 242(2), 369–382 (2015)
Poonthalir, G., Nadarajan, R.: A fuel efficient green vehicle routing problem with varying speed constraint (f-gvrp). Expert Syst. Appl. 100, 131–144 (2018)
Qian, J., Eglese, R.: Fuel emissions optimization in vehicle routing problems with time-varying speeds. Eur. J. Oper. Res. 248(3), 840–848 (2016)
Rohmer, S., Claassen, G., Laporte, G.: A two-echelon inventory routing problem for perishable products. Comput. Oper. Res. 107, 156–172 (2019)
Ropke, S., Pisinger, D.: An adaptive large neighborhood search heuristic for the pickup and delivery problem with time windows. Transp. Sci. 40(4), 455–472 (2006)
de Siqueira, E., Souza, M.J., de Souza, S.R.: A multi-objective variable neighborhood search algorithm for solving the hybrid flow shop problem. Electron. Notes Discrete Math. 66, 87–94 (2018)
Subramanian, A., Drummond, LMdA, Bentes, C., Ochi, L.S., Farias, R.: A parallel heuristic for the vehicle routing problem with simultaneous pickup and delivery. Comput. Oper. Res. 37(11), 1899–1911 (2010)
Tajik, N., Tavakkoli-Moghaddam, R., Vahdani, B., Mousavi, S.M.: A robust optimization approach for pollution routing problem with pickup and delivery under uncertainty. J. Manuf. Syst. 33(2), 277–286 (2014)
Vicente, S.A.: Laying the Foundations for Greener Transport. Term 2011: Transport Indicators Tracking Progress Towards Environmental Targets in Europe, EEA REPORT 7/2011. European Environment Agency, Copenhagen (2011)
Wang, C., Mu, D., Zhao, F., Sutherland, J.W.: A parallel simulated annealing method for the vehicle routing problem with simultaneous pickup-delivery and time windows. Comput. Ind. Eng. 83, 111–122 (2015)
Wang, J., Yu, Y., Tang, J.: Compensation and profit distribution for cooperative green pickup and delivery problem. Transp. Res. Part B: Methodol. 113, 54–69 (2018)
Wang, K., Lan, S., Zhao, Y.: A genetic-algorithm-based approach to the two-echelon capacitated vehicle routing problem with stochastic demands in logistics service. J. Oper. Res. Soc. 68(11), 1409–1421 (2017)
Wu, X., Che, A.: Energy-Efficient No-Wait Permutation Flow Shop Scheduling by Adaptive Multi-objective Variable Neighborhood Search, pp. 102–117. Omega, Thousand Oaks (2019)
Zhou, L., Baldacci, R., Vigo, D., Wang, X.: A multi-depot two-echelon vehicle routing problem with delivery options arising in the last mile distribution. Eur. J. Oper. Res. 265(2), 765–778 (2018)
Acknowledgements
The authors would like to acknowledge the support provided by the Mathematics Department, Indian Institute of Technology Kharagpur, yielding facilities for research. The first and third authors are grateful to Ministry of Human Resource Development for supporting their scientific studies with the Institute Research Assistantship
Author information
Authors and Affiliations
Contributions
AP: conceptualization; formal analysis; investigation; methodology; data curation; resources; software; validation; visualization; roles/writing—original draft; writing—editing. RSK: investigation; methodology; resources; software; roles/writing—original draft; writing—review and editing. CR: software; validation; visualization; roles/writing—original draft; writing—review and editing. AG: conceptualization; data curation; project administration; resources; software; supervision; validation; visualization; roles/writing—-original draft; writing—review and editing.
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Paul, A., Kumar, R.S., Rout, C. et al. A bi-objective two-echelon pollution routing problem with simultaneous pickup and delivery under multiple time windows constraint. OPSEARCH 58, 962–993 (2021). https://doi.org/10.1007/s12597-020-00481-6
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12597-020-00481-6