A Dynamic Facility Location Problem with Random Demand and the Restoration of Transportation Networks in Disaster Relief

This paper considers a multi-period facility location problem in disaster relief and introduces a scenario-based stochastic programming model that accounts for demand uncertainty. To better respond to the restoration of transportation networks and the varying demand situation, location strategies can be dynamically adjusted by establishing new facilities and closing old facilities. For the proposed large-scale mixed-integer model, we first decrease the number of integer variables by proving the totally unimodularity of several constraints and then implement a branch-and-Benders-cut method with several acceleration techniques to improve the computational efficiency. Extensive numerical results based on the randomly generated data and a case study under the pandemic threat shed light on a better location configuration with the deterministic model, especially in terms of the trade-off between nominal operational cost and system reliability, and the insights are validated through an out-of-sample performance analysis