### Topology-informed resource allocation for infrastructure systems: integrating network clustering and exact optimization

**Contact**: Camilo Gomez

**Contact**: Camilo Gomez

**Contact**: Camilo Gomez

Bus rapid transit (BRT) systems such as TransMilenio (in Bogota) have become a real alternative to more expensive rail-based public transportation systems. However, once the BRT system infrastructure is operational, its success often depends on the routes offered to the population. One of the challenges that planners face is the estimation of the origin-destination (OD) matrix that is the key driver to the set of routes and frequencies that need to be offered to the population. This matrix captures how people move in the city from each origin to each destination throughout the day. The estimation of the OD matrix is challenged by the lack of complete information. In many BRT systems it is known where passengers board buses, but not where they leave the system. Based on a vast amount of (partial) data and the use of modern analytics techniques this research line is focused on estimating the OD matrix of public transportation systems. Once the OD matrix is estimated, the problem of finding a set of routes (services) and frequencies that minimizes the operational and passenger costs (travel time) while simultaneously satisfying the system’s technical constraints (e.g., demands for trips, bus frequencies, and lane capacities). Our approach to the problem is based on a mathematical formulation that exploits the underlying network structure. However, because of the vast number of routes, solving the problem directly is out of reach for most practical instances. Thus, our approach is based on decomposition strategies (e.g., simultaneous column-and-row generation and matheuristics) that break the problem into manageable parts. | |

Photo by mariordo59/ CC BY-SA 2.0 |

**Contact**: Andrés L. Medaglia

**Related work:**:

- Walteros, J. L., Medaglia, A. L., and Riaño, G. (2015). Hybrid algorithm for route design on bus rapid transit systems. Transportation Science. 49(1):66-84.
- Feillet, D., Gendreau, M., Medaglia, A. L., Walteros, J. L. (2010). A note on branch-and-cut-and-price. Operations Research Letters. 38(5):346-353.

There are a vast amount of tactical and operational problems in transportation and logistics systems that rely on solving shortest paths (and variants) as a building block. The pulse algorithm can be seen as a general framework that can be extended to solve a wide range of routing problems. The idea behind the pulse algorithm is very simple, almost naive. The algorithm is based on the idea of recursively propagating pulses through a network from a start node to an end node. As a pulse traverses the network from node to node, it builds a partial path including the nodes already visited and some attributes associated with that path, such as the cumulative cost or resource consumption. Each pulse that reaches the final node contains all the information for a feasible path from the start to the end node. If nothing prevents the pulses from propagating, the algorithm completely enumerates all possible paths, ensuring that the optimal path is always found. At the core of the algorithm lies the ability to (effectively and aggressively) prune pulses as soon as there is enough evidence that the partial path will not lead to a feasible or improved solution. We have developed variants of the pulse algorithm to solve the Constrained Shortest Path Problem (CSP), the Elementary Shortest Path Problem with Resource Constraints (ESPPRC), the Biobjective Shortest Path Problem (BSP), the Orienteering Problem with Time Windows (OPTW), the Weight Constrained Shortest Path Problem with Replenishment (WCSPP-R), and a variant of the Robust Shortest Path Problem. Also, the pulse algorithm has been used as a module to solve more complex transportation and logistics problems such as the Multi-activity Shift Scheduling Problem and the Bus Rapid Transit Route Design Problem. Other authors have applied it to variants of routing problems for electric vehicles and interdiction problems. |

Photo by sjcockell/ CC BY |

**Contact**: Andrés L. Medaglia

**Related work:**:

- Lozano, L., Duque, D., and Medaglia, A. L. (2016). An exact algorithm for the elementary shortest path problem with resource constraints. Transportation Science. 50(1):348–357.
- Duque, D., Lozano, L. and Medaglia, A. L. (2015). An exact method for the biobjective shortest path problem for large-scale road networks. European Journal of Operational Research. 242:788-797.
- Duque, D., Lozano, L. and Medaglia, A. L. (2015). Solving the Orienteering Problem with Time Windows via the Pulse Framework. Computers & Operations Research. 54:168-176.
- Bolívar, M. A., Lozano, L. and Medaglia, A. L. (2014). Acceleration Strategies for the Weight Constrained Shortest Path Problem with Replenishment. Optimization Letters. 8(8): 2155-2172.
- Lozano, L. and Medaglia, A. L. (2013). On an exact method for the constrained shortest path problem. Computers & Operations Research. 40 (1):378-384.
- Restrepo, M. I., Lozano, L., and Medaglia, A. L. (2012). Constrained network-based column generation for the multi-activity shift scheduling problem. International Journal of Production Economics. 140(1):466-472

**Contact**: Andrés L. Medaglia and Jorge A. Huertas

A problem setting where strategic network design is of foremost importance, is the preparedness for wildfire events. Once a wildfire starts, pre-positioned resources (e.g., tools) are delivered to operation centers where tactical decisions are made by firefighters. One of the key drivers for allocating the resources are the fire ignition points and the fire spread, which are stochastic in nature. By using simulated scenarios and a two-stage stochastic program, we have been able to decide upon strategic decisions related to locating facilities and their inventory levels; along with the tactical transportation and distribution decisions within a time-space network that allows for realistic size problems such as those arising in Bogotá. |
Photo by usfwshq / CC BY |

**Contact**: Andrés L. Medaglia and Camilo Gómez

At a strategic level, optimizing the resilience of any given system requires optimizing decisions for diminishing vulnerability and increasing efficient response. We have worked on devising a comprehensive optimization framework that incorporates resilience and uncertainty of interconnected networks. The methodologies devised in this line of research help decision makers to plan where to invest in the networks (e.g., road network, supply chain, gas network, power network), so that after an uncertain and shocking (e.g., disaster or low-demand) event, the system is able to recover and perform well as early as possible. |

**Contact**: Andrés L. Medaglia

**Related work**:

González, A., Dueñas-Osorio, L., Sánchez-Silva, M., and Medaglia, A. L. (2016). The interdependent network design problem for optimal infrastructure system restoration. Computer-Aided Civil and Infrastructure Engineering. 31(5):334–350.

COPA supports the decision making process at organizations via the analysis, design and application of operations research (OR) and statistical computer-based techniques. Our purpose is to contribute to the scientific and technological development of Colombia, becoming a leading group in R&D.