A distributionally robust optimisation with joint chance constraints approach for location-routing problem in urban search and rescue operations

This paper examines a multi-period location-routing problem with uncertain demand and travel times in the context of disaster management. We propose an optimisation model that integrates strategic location decisions with multi-period routing decisions to navigate search-and-rescue teams in the aftermath of a disaster within an uncertain environment. To model this problem, we apply a distributionally robust optimisation approach with joint chance constraints. We enhance computational tractability by reformulating the problem using Bonferroni's inequality and approximating the chance constraints. The proposed methodology is evaluated in a hypothetical case study of Santa Cruz County, California, USA, a region highly susceptible to earthquakes. We tested multiple instances of this case study to demonstrate the effectiveness of the proposed method compared to the sample average approximation approach. Numerical experiments reveal that the methodology developed in this paper aids decision-makers in strategically locating facilities to deploy search-and-rescue teams and efficiently directing them towards affected sites, achieving a maximal rescue rate.