Planning reliable service facility location against disruption risks and last-mile congestion in a continuous space

This paper proposes a methodological framework that incorporates probabilistic facility disruption risks, last-mile customers travel path choices, and the induced traffic congestion near the facilities into the consideration of service facility location planning. The customers can be pedestrians, drones, or any autonomous vehicles that do not have to travel via fixed channels to access a service facility. Analytical models are developed to evaluate the expected performance of a facility location design across an exponential number of facility disruption scenarios. In each of these scenarios, customers travel to a functioning facility through a continuous space, and their destination and path choices under traffic equilibrium are described by a class of partial differential equation (PDE). A closed-form solution to the PDE is derived in an explicit matrix form, and this paper shows how the traffic equilibrium patterns across all facility disruption scenarios can be evaluated in a polynomial time. These new analytical results are then incorporated into continuous and discrete optimization frameworks for facility location design. Numerical experiments are conducted to test the computational performance of the proposed modeling framework.