# Combined maintenance and routing optimization for large-scale sewage cleaning

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## Abstract

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.

## Keywords

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

### Acknowledgements

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

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