Reliable emergency service facility location under facility disruption, en-route congestion and in-facility queuing

The planning of emergency service facility location, especially for those expecting high demand and severe conditions, requires consideration of victims' en-route travel, in-facility service quality, and reliability of these service facilities themselves. This paper first presents a scenario-based stochastic mixed-integer non-linear program (MINLP) model that integrates facility disruption risks, en-route traffic congestion and in-facility queuing delay into an integrated facility location problem. We derive lower and upper bounds to this highly complex problem by approximating the expected total system costs across the normal and all probabilistic facility disruption scenarios. This allows us to develop a more tractable approximate MINLP formulation and a Lagrangian Relaxation (LR) based solution approach. The relaxed sub-problem for location and service allocation decisions is further reformulated into a second-order conic program. Numerical experiments show that the approximate model and LR solution approach are capable of overcoming the computational difficulties associated with the problem. Interesting findings and managerial insights are obtained from a series of sensitivity analyses, e.g., regarding the importance of considering in-facility queuing in location design, and the significance of resource pooling on the optimal facility deployment.