Abstract
The municipal solid waste system is a complex reverse logistic chain which comprises several optimisation problems. Although these problems are interdependent—i.e., the solution to one of the problems restricts the solution to the other—they are usually solved sequentially in the related literature because each is usually a computationally complex problem. We address two of the tactical planning problems in this chain by means of a Benders decomposition approach: determining the location and/or capacity of garbage accumulation points, and the design and schedule of collection routes for vehicles. Our approach manages to solve medium-sized real-world instances in the city of Bahía Blanca, Argentina, showing smaller computing times than solving a full MIP model.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
Mainly capacity, but could also be cost.
A similar consideration is performed in Hemmelmayr et al. (2013).
Making it, de facto, a no-good cut.
To the best of our knowledge, in Argentina the largest bin that allows rear-loading is about 1.1m\(^3\).
Converted using the official exchange rate of Argentina (Banco Central de la República Argentina, 2021).
Performing certain simplifications, the service time of the bin combinations can be estimated assuming that types of bin I, II, and III that are used in this article correspond to the systems S4, S1, and S2 used in Carlos et al. (2019), respectively.
That in reality is about five hours.
Instances can be retrieved from https://github.com/diegorossit/Set-of-instances-Mah-o-et-al.-2021---ANOR
References
Asefi, H., Lim, S., Maghrebi, M., & Shahparvari, S. (2019). Mathematical modelling and heuristic approaches to the location-routing problem of a cost-effective integrated solid waste management. Annals of Operations Research, 273(1), 75–110. https://doi.org/10.1007/s10479-018-2912-1
Banco Central de la República Argentina (2021) Reference retail exchange rate. http://www.bcra.gov.ar/publicacionesestadisticas/Tipo_de_cambio_minorista_2.asp. Accessed: 24 Jul 2021
Bányai, T., Tamás, P., Illés, B., Stankevičiūtė, Z., & Bányai, A. (2019). Optimization of municipal waste collection routing: Impact of industry 4.0 technologies on environmental awareness and sustainability. International Journal Of Environmental Research And Public Health, 16(4), 634. https://doi.org/10.3390/ijerph16040634
Benders, J. (1962). Partitioning procedures for solving mixed-variables programming problems. Numerische Mathematik, 4(1), 238–252. https://doi.org/10.1007/s10287-004-0020-y
Blazquez, C., & Paredes, G. (2020). Network design of a household waste collection system: A case study of the commune of Renca in Santiago, Chile. Waste Management, 116, 179–189. https://doi.org/10.1016/j.wasman.2020.07.027
Bonomo, F., Durán, G., 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. https://doi.org/10.1177/0734242X11402870
Bretthauer, K., & Shetty, B. (1995). The nonlinear resource allocation problem. Operations Research, 43(4), 670–683. https://doi.org/10.1287/opre.43.4.670
Brogaard, L. K., & Christensen, T. H. (2012). Quantifying capital goods for collection and transport of waste. Waste Management & Research, 30(12), 1243–1250. https://doi.org/10.1177/0734242X12462279
Broz, D., Rossit, D., Rossit, D., & Cavallin, A. (2018). The Argentinian forest sector: opportunities and challenges in supply chain management. Uncertain Supply Chain Management. https://doi.org/10.5267/j.uscm.2018.1.001
Campbell, A., Clarke, L., Kleywegt, A., & Savelsbergh, M. (1998). The inventory routing problem. In: Fleet management and logistics (pp 95–113). Springer. https://doi.org/10.1007/978-1-4615-5755-5_4
Carlos, M., Gallardo, A., Edo-Alcon, N., & Abaso, J. (2019). Influence of the municipal solid waste collection system on the time spent at a collection point: A case study. Sustainability, 11(22), 6481. https://doi.org/10.3390/su11226481
Cavallin, A., Rossit, D., Herrán, V., Rossit, D., & Frutos, M. (2020). Application of a methodology to design a municipal waste pre-collection network in real scenarios. Waste Management & Research, 38(1), 117–129. https://doi.org/10.1177/0734242X19894630
Chang, N., & Wei, Y. (1999). Strategic planning of recycling drop-off stations and collection network by multiobjective programming. Environmental Management, 24(2), 247–263. https://doi.org/10.1007/s002679900230
Chang, N., & Wei, Y. (2000). Siting recycling drop-off stations in urban area by genetic algorithm-based fuzzy multiobjective nonlinear integer programming modeling. Fuzzy Sets and Systems, 114(1), 133–149. https://doi.org/10.1016/S0165-0114(98)00192-4
Crainic, T., Hewitt, M., & Rei, W. (2014). Partial decomposition strategies for two-stage stochastic integer programs. https://www.cirrelt.ca/documentstravail/cirrelt-2014-13.pdf
Cubillos, M., & Wøhlk, S. (2020). Solution of the maximal covering tour problem for locating recycling drop-off stations. Journal of the Operational Research Society. https://doi.org/10.1080/01605682.2020.1746701
D’Onza, G., Greco, G., & Allegrini, M. (2016). Full cost accounting in the analysis of separated waste collection efficiency: A methodological proposal. Journal of Environmental Management, 167, 59–65. https://doi.org/10.1016/j.jenvman.2015.09.002
Dror, M., Laporte, G., & Trudeau, P. (1994). Vehicle routing with split deliveries. Discrete Applied Mathematics, 50(3), 239–254. https://doi.org/10.1016/0166-218X(92)00172-I
Fattahi, M. (2020). A data-driven approach for supply chain network design under uncertainty with consideration of social concerns. Annals of Operations Research. https://doi.org/10.1007/s10479-020-03532-9
Ghiani, G., Laganà, D., Manni, E., Musmanno, R., & Vigo, D. (2014). Operations research in solid waste management: A survey of strategic and tactical issues. Computers & Operations Research, 44, 22–32. https://doi.org/10.1016/j.cor.2013.10.006
Giel, R., & Dąbrowska, A. (2021). Estimating time spent at the waste collection point by a garbage truck with a multiple regression model. Sustainability, 13(8), 4272. https://doi.org/10.3390/su13084272
Gilardino, A., Rojas, J., Mattos, H., Larrea, G., & Vázquez, I. (2017). Combining operational research and life cycle assessment to optimize municipal solid waste collection in a district in Lima (Peru). Journal of Cleaner Production, 156, 589–603. https://doi.org/10.1016/j.jclepro.2017.04.005
Gultekin, C., Olmez, O., Balcik, B., Ekici, A., & Ozener, O. (2020). A decomposition-based heuristic for a waste cooking oil collection problem. In: Derbel, H., Jarboui, B., Siarry, P. (Eds.) Green transportation and new advances in vehicle routing problems (pp 159–176).Springer. https://doi.org/10.1007/978-3-030-45312-1_6
Han, H., & Ponce, E. (2015). Waste collection vehicle routing problem: Literature review. PROMET-Traffic &Transportation, 27(4), 345–358. https://doi.org/10.7307/ptt.v27i4.1616
Hemmelmayr, V. (2015). Sequential and parallel large neighborhood search algorithms for the periodic location routing problem. European Journal of Operational Research, 243(1), 52–60. https://doi.org/10.1016/j.ejor.2014.11.024
Hemmelmayr, V., Doerner, K., Hartl, R., & Vigo, D. (2013). Models and algorithms for the integrated planning of bin allocation and vehicle routing in solid waste management. Transportation Science, 48(1), 103–120. https://doi.org/10.1287/trsc.2013.0459
Hemmelmayr, V., Smilowitz, K., & De la Torre, L. (2017). A periodic location routing problem for collaborative recycling. IISE Transactions, 49(4), 414–428. https://doi.org/10.1080/24725854.2016.1267882
Hoornweg, D., & Bhada, P. (2012). What a waste: a global review of solid waste management. Urban development series 15. http://hdl.handle.net/10986/17388. Accessed: 20 Apr 2021.
Jammeli, H., Argoubi, M., & Masri, H. (2019). A bi-objective stochastic programming model for the household waste collection and transportation problem: Case of the city of sousse. Operational Research. https://doi.org/10.1007/s12351-019-00538-5
Kim, J., & Lee, D. (2015). A case study on collection network design, capacity planning and vehicle routing in reverse logistics. International Journal of Sustainable Engineering, 8(1), 66–76. https://doi.org/10.1080/19397038.2014.947393
Kim, J., & Lee, D. (2015). An integrated approach for collection network design, capacity planning and vehicle routing in reverse logistics. Journal of the Operational Research Society, 66(1), 76–85. https://doi.org/10.1057/jors.2013.168
Kŭdela, J., Šomplák, R., Nevrlỳ, V., Lipovskỳ, T., Smejkalová, V., & Dobrovskỳ, L. (2019). Multi-objective strategic waste transfer station planning. Journal of Cleaner Production, 230, 1294–1304. https://doi.org/10.1016/j.jclepro.2019.05.167
Kung, H., Luccio, F., & Preparata, F. (1975). On finding the maxima of a set of vectors. Journal of the ACM, 22(4), 469–476. https://doi.org/10.1145/321906.321910
Laporte, G., & Louveaux, F. (1993). The integer l-shaped method for stochastic integer programs with complete recourse. Operations Research Letters, 13(3), 133–142. https://doi.org/10.1016/0167-6377(93)90002-X
Lu, J., Chang, N., Liao, L., & Liao, M. (2015). Smart and green urban solid waste collection systems: advances, challenges, and perspectives. IEEE Systems Journal, 11(4), 2804–2817. https://doi.org/10.1109/JSYST.2015.2469544
Mahéo, A., Belieres, S., Adulyasak, Y., & Cordeau, JF. (2020). Unified branch-and-Benders-cut for two-stage stochastic mixed-integer programs. Les Cahiers du GERAD G-2020-54.
Mahéo, A., Rossit, D., & Kilby, P. (2020). A Benders Decomposition Approach for an Integrated Bin Allocation and Vehicle Routing Problem in Municipal Waste Management. In: 10th international conference of production research ICPR - Americas 2020, Springer, Bahía Blanca, Argentina, in press.
Musante C (2021) Indicadores logísticos países miembros de ALALOG. Tech. rep., Asociación Latinoamericana de Logística. https://www.alalog.org/es/studies
Nagy, G., & Salhi, S. (2007). Location-routing: Issues, models and methods. European Journal of Operational Research, 177(2), 649–672. https://doi.org/10.1016/j.ejor.2006.04.004
QGIS Development Team (2020) QGIS geographic information system. Open Source Geospatial Foundation. http://qgis.osgeo.org
Rossit, D., & Nesmachnow, S. (2022). Waste bins location problem: A review of recent advances in the storage stage of the municipal solid waste reverse logistic chain. Journal of Cleaner Production. https://doi.org/10.1016/j.jclepro.2022.130793 (in press).
Rossit, D., Toutouh, J., & Nesmachnow, S. (2020). Exact and heuristic approaches for multi-objective garbage accumulation points location in real scenarios. Waste Management, 105, 467–481. https://doi.org/10.1016/j.wasman.2020.02.016
Saif, Y., Rizwan, M., Almansoori, A., & Elkamel, A. (2019). Municipality solid waste supply chain optimization to power production under uncertainty. Computers & Chemical Engineering, 121, 338–353. https://doi.org/10.1016/j.compchemeng.2018.11.003
Sheriff, K., Subramanian, N., Rahman, S., & Jayaram, J. (2017). Integrated optimization model and methodology for plastics recycling: Indian empirical evidence. Journal of Cleaner Production, 153, 707–717. https://doi.org/10.1016/j.jclepro.2016.07.137
Toth, P., & Vigo, D. (2002). The vehicle routing problem. SIAM, 10(1137/1), 9780898718515.
Toutouh, J., Rossit, D., & Nesmachnow, S. (2020). Soft computing methods for multiobjective location of garbage accumulation points in smart cities. Annals of Mathematics and Artificial Intelligence, 88(1), 105–131. https://doi.org/10.1007/s10472-019-09647-5
Vidović, M., Ratković, B., Bjelić, N., & Popović, D. (2016). A two-echelon location-routing model for designing recycling logistics networks with profit: MILP and heuristic approach. Expert Systems with Applications, 51, 34–48. https://doi.org/10.1016/j.eswa.2015.12.029
Vázquez A (2018) Ruteo de alta perfomance con OSRM. Rpubs by RStudio. https://rpubs.com/HAVB/osrm
Yaakoubi, O., Benabdouallah, M., & Bojji, C. (2018). Heuristic approaches for waste containers location problem and waste collection routes optimisation in an urban area. International Journal of Environment and Waste Management, 21(4), 269–286. https://doi.org/10.1504/IJEWM.2018.093436
Acknowledgements
The second author was supported by the 2018 Australia-Americas PhD Research Internship Program, co-financed by the Australian Academy of Science, the Ministry of Foreign Affairs and Worship of Argentina and the Universidad Nacional del Sur.
Author information
Authors and Affiliations
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
Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Mahéo, A., Rossit, D.G. & Kilby, P. Solving the integrated bin allocation and collection routing problem for municipal solid waste: a Benders decomposition approach. Ann Oper Res 322, 441–465 (2023). https://doi.org/10.1007/s10479-022-04918-7
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-022-04918-7