Combined maintenance and routing optimization for large-scale sewage cleaning

  • John E. Fontecha
  • Oscar O. Guaje
  • Daniel Duque
  • Raha Akhavan-Tabatabaei
  • Juan P. Rodríguez
  • Andrés L. MedagliaEmail author
S.I.: CLAIO 2016


The rapid population growth and the high rate of migration to urban areas impose a heavy load on the urban infrastructure. Particularly, sewerage systems are the target of disruptions, causing potential public health hazards. Although sewer systems are designed to handle some sediment and solid transport, particles can form deposits that increase the flood risk. To mitigate this risk, sewer systems require adequate maintenance scheduling, as well as ad-hoc repairs due to unforeseen disruptions. To address this challenge, we tackle the problem of planning and scheduling maintenance operations based on a deterioration pattern for a set of geographically spread sites, subject to unforeseen failures and restricted crews. We solve the problem as a two-stage maintenance-routing procedure. First, a maintenance model driven by the probability distribution of the time between failures determines the optimal time to perform maintenance operations for each site. Then, we design and apply an LP-based split procedure to route a set of crews to perform the planned maintenance operations at a near-minimum expected cost per unit time. Afterward, we adjust this routing solution dynamically to accommodate unplanned repair operations arising as a result of unforeseen failures. We validated our proposed method on a large-scale case study for sediment-related sewer blockages in Bogotá (Colombia). Our methodology reduces the cost per unit time in roughly 18% with respect to the policy used by the city’s water utility company.


Maintenance models Sediment-related sewer blockages Sewer system maintenance planning Split procedure Vehicle routing 



We would like to thank EAAB for providing us with data. We thank Professor Jorge Mendoza at HEC Montréal (Canada), for his support with the Multi-space Sampling Heuristic (MSH) which was extensively used in this project. Also, we would like to thank Gurobi for providing us with an academic license of their linear optimizer. Last, but not least, we thank the comments of the anonymous referees that significantly improved our paper.

Supplementary material


  1. Abraham, D. M., Wirahadikusumah, R., Short, T., & Shahbahrami, S. (1998). Optimization modeling for sewer network management. Journal of Construction Engineering and Management, 124(5), 402–410.CrossRefGoogle Scholar
  2. Afshar-Nadjafi, B., & Afshar-Nadjafi, A. (2017). A constructive heuristic for time-dependent multi-depot vehicle routing problem with time-windows and heterogeneous fleet. Journal of King Saud University-Engineering Sciences, 29(1), 29–34.CrossRefGoogle Scholar
  3. Alrabghi, A., & Tiwari, A. (2015). State of the art in simulation-based optimisation for maintenance systems. Computers & Industrial Engineering, 82, 167–182.CrossRefGoogle Scholar
  4. Angel, S., Parent, J., Civco, D. L., & Blei, A. M. (2016). Atlas of urban expansion, volume 1: Areas and densities. Cambridge, MA: Lincoln Institute of Land Policy.Google Scholar
  5. Baldacci, R., Mingozzi, A., & Roberti, R. (2011). New route relaxation and pricing strategies for the vehicle routing problem. Operations Research, 59(5), 1269–1283.CrossRefGoogle Scholar
  6. Beasley, J. E. (1983). Route first-cluster second methods for vehicle routing. Omega, 11(4), 403–408.CrossRefGoogle Scholar
  7. Bertazzi, L., & Speranza, M. G. (2012). Inventory routing problems: An introduction. EURO Journal on Transportation and Logistics, 1(4), 307–326.CrossRefGoogle Scholar
  8. Bettinelli, A., Ceselli, A., & Righini, G. (2011). A branch-and-cut-and-price algorithm for the multi-depot heterogeneous vehicle routing problem with time windows. Transportation Research Part C: Emerging Technologies, 19(5), 723–740.CrossRefGoogle Scholar
  9. Blakeley, F., Argüello, B., Cao, B., Hall, W., & Knolmajer, J. (2003). Optimizing periodic maintenance operations for schindler elevator corporation. Interfaces, 33(1), 67–79.CrossRefGoogle Scholar
  10. Braekers, K., Ramaekers, K., & Van Nieuwenhuyse, I. (2016). The vehicle routing problem: State of the art classification and review. Computers & Industrial Engineering, 99, 300–313.CrossRefGoogle Scholar
  11. Bräysy, O., & Gendreau, M. (2005). Vehicle routing problem with time windows, part I: Route construction and local search algorithms. Transportation science, 39(1), 104–118.CrossRefGoogle Scholar
  12. Campbell, A., Clarke, L., Kleywegt, A., & Savelsbergh, M. (1998). The inventory routing problem. In Fleet management and logistics (pp. 95–113). Springer.Google Scholar
  13. Chen, X., Thomas, B. W., & Hewitt, M. (2016). The technician routing problem with experience-based service times. Omega, 61, 49–61.CrossRefGoogle Scholar
  14. Chen, X., Thomas, B. W., & Hewitt, M. (2017a). Multi-period technician scheduling with experience-based service times and stochastic customers. Computers & Operations Research, 82, 1–14.CrossRefGoogle Scholar
  15. Chen, Y., Cowling, P., Polack, F., Remde, S., & Mourdjis, P. (2017b). Dynamic optimisation of preventative and corrective maintenance schedules for a large scale urban drainage system. European Journal of Operational Research, 257(2), 494–510.CrossRefGoogle Scholar
  16. Dantzig, G. B., & Ramser, J. H. (1959). The truck dispatching problem. Management Science, 6(1), 80–91.CrossRefGoogle Scholar
  17. Dekker, R. (1996). Applications of maintenance optimization models: A review and analysis. Reliability Engineering & System Safety, 51(3), 229–240.CrossRefGoogle Scholar
  18. Desaulniers, G. (2010). Branch-and-price-and-cut for the split-delivery vehicle routing problem with time windows. Operations Research, 58(1), 179–192.CrossRefGoogle Scholar
  19. Edgar, T. F., Himmelblau, D. M., Lasdon, L. S., et al. (2001). Optimization of chemical processes (Vol. 2). New York: McGraw-Hill.Google Scholar
  20. Empresa de Acueducto y Alcantarillado de Bogotá (2015) Delimitación por zonas de servicio.
  21. Fletcher, T. D., Andrieu, H., & Hamel, P. (2013). Understanding, management and modelling of urban hydrology and its consequences for receiving waters: A state of the art. Advances in Water Resources, 51, 261–279.CrossRefGoogle Scholar
  22. Fontecha, J. E., Akhavan-Tabatabaei, R., Duque, D., Medaglia, A. L., Torres, M. N., & Rodríguez, J. P. (2016). On the preventive management of sediment-related sewer blockages: A combined maintenance and routing optimization approach. Water Science and Technology, 74(2), 302–308.CrossRefGoogle Scholar
  23. Fukasawa, R., Longo, H., Lysgaard, J., de Aragão, M. P., Reis, M., Uchoa, E., et al. (2006). Robust branch-and-cut-and-price for the capacitated vehicle routing problem. Mathematical Programming, 106(3), 491–511.CrossRefGoogle Scholar
  24. Gendreau, M., Potvin, J.-Y., Bräumlaysy, O., Hasle, G., & Løkketangen, A. (2008). Metaheuristics for the vehicle routing problem and its extensions: A categorized bibliography. In The vehicle routing problem: latest advances and new challenges (pp. 143–169). Springer.Google Scholar
  25. Goodson, J. C., Ohlmann, J. W., & Thomas, B. W. (2013). Rollout policies for dynamic solutions to the multivehicle routing problem with stochastic demand and duration limits. Operations Research, 61(1), 138–154.CrossRefGoogle Scholar
  26. Goodson, J. C., Thomas, B. W., & Ohlmann, J. W. (2017). A rollout algorithm framework for heuristic solutions to finite-horizon stochastic dynamic programs. European Journal of Operational Research, 258(1), 216–229.CrossRefGoogle Scholar
  27. Gurobi Optimization, LLC (2019). Gurobi Optimizer Reference Manual.
  28. Jardine, A. K., & Tsang, A. H. (2013). Maintenance, replacement, and reliability: Theory and applications. Boca Raton: CRC Press.CrossRefGoogle Scholar
  29. Kek, A. G., Cheu, R. L., & Meng, Q. (2008). Distance-constrained capacitated vehicle routing problems with flexible assignment of start and end depots. Mathematical and Computer Modelling, 47(1–2), 140–152.CrossRefGoogle Scholar
  30. Korving, H., Clemens, F. H., & van Noortwijk, J. M. (2006). Statistical modeling of the serviceability of sewage pumps. Journal of Hydraulic Engineering, 132(10), 1076–1085.CrossRefGoogle Scholar
  31. Kumar, S. N., & Panneerselvam, R. (2012). A survey on the vehicle routing problem and its variants. Intelligent Information Management, 4(03), 66.CrossRefGoogle Scholar
  32. Lai, K., Leung, K., Tao, B., & Wang, S. (2001). A sequential method for preventive maintenance and replacement of a repairable single-unit system. Journal of the Operational Research Society, 52(11), 1276–1283.CrossRefGoogle Scholar
  33. L’Ecuyer, P. (2016). Ssj: Stochastic simulation in java, software library.Google Scholar
  34. L’Ecuyer, P., Meliani, L., & Vaucher, J. (2002). Ssj: Ssj: A framework for stochastic simulation in java. In Proceedings of the 34th conference on Winter simulation: Exploring new frontiers, Winter Simulation Conference (pp. 234–242).Google Scholar
  35. López-Santana, E., Akhavan-Tabatabaei, R., Dieulle, L., Labadie, N., & Medaglia, A. L. (2016). On the combined maintenance and routing optimization problem. Reliability Engineering & System Safety, 145, 199–214.CrossRefGoogle Scholar
  36. Mendoza, J. E., & Villegas, J. G. (2013). A multi-space sampling heuristic for the vehicle routing problem with stochastic demands. Optimization Letters, 7(7), 1503–1516.CrossRefGoogle Scholar
  37. Pessoa, A., De Aragão, M. P., & Uchoa, E. (2008). Robust branch-cut-and-price algorithms for vehicle routing problems. In The vehicle routing problem: Latest advances and new challenges (pp. 297–325). Springer.Google Scholar
  38. Pillac, V., Gendreau, M., Guéret, C., & Medaglia, A. L. (2013a). A review of dynamic vehicle routing problems. European Journal of Operational Research, 225(1), 1–11.CrossRefGoogle Scholar
  39. Pillac, V., Guéret, C., & Medaglia, A. L. (2013b). A parallel matheuristic for the technician routing and scheduling problem. Optimization Letters, 7(7), 1525–1535.CrossRefGoogle Scholar
  40. Pillac, V., Guéret, C., & Medaglia, A. L. (2018). A fast reoptimization approach for the dynamic technician routing and scheduling problem (pp. 347–367). New York: Springer.Google Scholar
  41. Prins, C. (2004). A simple and effective evolutionary algorithm for the vehicle routing problem. Computers & Operations Research, 31(12), 1985–2002.CrossRefGoogle Scholar
  42. Prins, C., Lacomme, P., & Prodhon, C. (2014). Order-first split-second methods for vehicle routing problems: A review. Transportation Research Part C: Emerging Technologies, 40, 179–200.CrossRefGoogle Scholar
  43. Rodríguez, J. P., McIntyre, N., Díaz-Granados, M., & Maksimović, Č. (2012). A database and model to support proactive management of sediment-related sewer blockages. Water Research, 46(15), 4571–4586.CrossRefGoogle Scholar
  44. Rodríguez, M. (2008). Informe de evaluación de alternativas de tratamiento y manejo de lodo de alcantarillado sanitario y pluvial. EAAB-UniAndes: Tech. rep.Google Scholar
  45. Ross, S. M. (2014). Introduction to probability models. Cambridge: Academic Press.Google Scholar
  46. Santry Jr, I. W. (1972). Sewer maintenance costs. Journal (Water Pollution Control Federation), 44(7), 1425–1432.Google Scholar
  47. Shirmohammadi, A. H., Love, C., & Zhang, Z. G. (2003). An optimal maintenance policy for skipping imminent preventive maintenance for systems experiencing random failures. Journal of the Operational Research Society, 54(1), 40–47.CrossRefGoogle Scholar
  48. Soriano-Pulido, E., Valencia-Arboleda, C., & Rodríguez-Sánchez, J. P. (2019). Study of the spatiotemporal correlation between sediment-related blockage events in the sewer system in Bogotá (Colombia). Water Science & Technology, 79(9), 1727–1738. Scholar
  49. Torres, M. N., Rodríguez, J. P., & Leitao, J. P. (2017). Geostatistical analysis to identify characteristics involved in sewer pipes and urban tree interactions. Urban Forestry & Urban Greening, 25, 36–42.CrossRefGoogle Scholar
  50. UN General Assembly (2015). Transforming our world: The 2030 agenda for sustainable development. New York: United Nations (1).Google Scholar
  51. United Nations. (2016). Global sustainable development report 2016. Department of Economic and Social Affairs.Google Scholar
  52. Vammen, K. (2015). Desafios del agua urbana en las americas: Perspectivas de las academias de ciencias. Agricultura, sociedad y desarrollo, 12(3), 475–478.CrossRefGoogle Scholar
  53. Vidal, T., Crainic, T. G., Gendreau, M., & Prins, C. (2013). Heuristics for multi-attribute vehicle routing problems: A survey and synthesis. European Journal of Operational Research, 231(1), 1–21.CrossRefGoogle Scholar
  54. Vidal, T., Crainic, T. G., Gendreau, M., & Prins, C. (2014). A unified solution framework for multi-attribute vehicle routing problems. European Journal of Operational Research, 234(3), 658–673.CrossRefGoogle Scholar
  55. Wang, C. H., Yeh, R. H., & Wu, P. (2006). Optimal production time and number of maintenance actions for an imperfect production system under equal-interval maintenance policy. Journal of the Operational Research Society, 57(3), 262–270.CrossRefGoogle Scholar
  56. Wang, H. (2002). A survey of maintenance policies of deteriorating systems. European Journal of Operational Research, 139(3), 469–489.CrossRefGoogle Scholar
  57. Worldatlas. (2018). The 150 largest cities in the World.
  58. Yang, M. D., & Su, T. C. (2007). An optimization model of sewage rehabilitation. Journal of the Chinese Institute of Engineers, 30(4), 651–659.CrossRefGoogle Scholar
  59. Zhang, S., Ohlmann, J. W., & Thomas, B. W. (2014). A priori orienteering with time windows and stochastic wait times at customers. European Journal of Operational Research, 239(1), 70–79.CrossRefGoogle Scholar
  60. Zhang, S., Ohlmann, J. W., & Thomas, B. W. (2018). Dynamic orienteering on a network of queues. Transportation Science, 52(3), 691–706.CrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Group for Applied Mathematical Modeling and Analytics (GAMMA), Industrial and Systems EnginneringUniversity at BuffaloBuffaloUSA
  2. 2.Departamento de Ingeniería Industrial, Centro para la Optimización y Probabilidad Aplicada (COPA)Universidad de los AndesBogotáColombia
  3. 3.Industrial Engineering and Management SciencesNorthwestern UniversityEvanstonUSA
  4. 4.School of ManagementSabanci UniversityIstanbulTurkey
  5. 5.Departamento de Ingeniería Civil y Ambiental, Centro de Investigaciones en Ingeniería Ambiental (CIIA)Universidad de los AndesBogotáColombia

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