# Supporting station idea…

By Suzan Afacan

As the end of the semester is approaching, we will start our final presentations as a class. One of the papers I will present is “A supporting station model for reliable infrastructure location design under interdependent disruptions” by Li et al (2013).

Infrastructure systems are important for society and the economy. The definition of infrastructure systems is pretty wide including transportation, communication, energy and more. The systems have high interdependency. In the models that study infrastructure systems it is not easy to include these interdependencies. Dependency between facility failures is one such instance. Even though independent failure of the facilities can be modeled without trouble, when we want to include the connections between facility failures, it is not that easy to model all the dependent failure scenarios.

With the supporting station idea, this paper explores the network location design problem under dependent facility failure with this connected supporting stations, which have independent and identical failure probabilities.

Each supporting station has a set of facilities to support. So a facility is operational if at least one of its supporting stations does not fail.

In this example customer “i” can be served by the facilities “A”, “B” and “C” with the given distances from “i” respectively 10, 20 and 30. With the supporting station idea, this system will turn into the next figure.

This figure shows the same customer with the same possible stations to serve it, but this time supporting stations show the failure dependency between facilities. To be more specific, if supporting stations “a” and “b” fail then facility “A” cannot be operational anymore and the failure of supporting station effects failure probabilities of facility “A” and facility “B”.

The integer formulation of the model is as follows:

The objective of the model is to minimize the expected total cost of the fixed facility and supporting station investment cost in addition to the expected total transportation and penalty cost.

The paper presents a sensitivity analysis and also a case study for the model with different failure probabilities and penalty costs. For further details, I will refer you to the paper.

To conclude with, this paper has a different approach to the modeling of interdependent failure of the facilities while introducing the supporting station idea. As one of the suggested future research directions of the writer, it could be worthwhile to extend this model to other related models in the field to increase the reliability and resilience of the problems.

Reference

Li, Xiaopeng, Yanfeng Ouyang, and Fan Peng. “A supporting station model for reliable infrastructure location design under interdependent disruptions.” Transportation Research Part E: Logistics and Transportation Review 60 (2013): 80-93.