Streamlining emergency response: A K-adaptable model and a column-and-constraint-generation algorithm

Emergency response refers to the systematic response to an unexpected, disruptive occurrence such as a natural disaster. The response aims to mitigate the consequences of the occurrence by providing the affected region with the necessary supplies. A critical factor for a successful response is its timely execution, but the unpredictable nature of disasters often prevents quick reactionary measures. Preallocating the supplies before the disaster takes place allows for a faster response, but requires more overall resources because the time and place of the disaster are not yet known. This gives rise to a trade-off between how quickly a response plan is executed and how precisely it targets the affected areas. Aiming to capture the dynamics of this trade-off, we develop a $K$-adjustable robust model, which allows a maximum of $K$ second-stage decisions, i.e., response plans. This mitigates tractability issues and allows the decision-maker to seamlessly navigate the gap between the readiness of a proactive yet rigid response and the accuracy of a reactive yet highly adjustable one. The approaches we consider to solve the $K$-adaptable model are twofold: Via a branch-and-bound method as well as a static robust reformulation in combination with a column-and-constraint generation algorithm. In a computational study, we compare and contrast the different solution approaches and assess their potential.