Analyzing the Vulnerabilities in a Transshipment Network: A Bilevel Programming Approach

As one of the most common types of networks, transshipment networks face certain risks in their daily operations. This risk either stems from a deliberate intervention in the process or from an unpredictable natural effect. The owner of the network normally aims to minimize the total cost of the transportation, while a rival or an opponent might attempt to intervene in the process and cause an increase in the costs. Unpredictable natural setbacks, on the other hand, can also have a negative impact on the network necessitating decision-makers to be more vigilant, especially for the worst-case consequences of network disruptions. The problem can be designed as a bilevel mathematical model. In this study, we develop a bilevel max-min model considering that the arcs in a transshipment network are liable to a disruption imposed by an intervenor. We present an original model with a novel solution approach to identify vulnerabilities in the arcs of a given transshipment network. The results reveal the most vulnerable arcs in the network, which have the highest negative impact on transportation costs when a disruption occurs. The decision-makers can use such results to analyze the risk in distribution networks such as electrical grids and develop associated measures to decrease the cost and increase the flexibility of the distribution systems. The model also enables decision makers with a methodical understanding of worst cases if the distribution network is interrupted for some reason.