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This paper presents an extension of Naor’s analysis on the join-or-balk problem in observable M/M/1 queues. Although all other Markovian assumptions still hold, we explore this problem assuming uncertain arrival rates under the distributionally robust settings. We first study the problem with the classical moment ambiguity set, where the support, mean, and mean-absolute deviation of the underlying distribution are known. Next, we extend the model to the data-driven setting, where decision makers only have access to a finite set of samples. We develop three optimal joining threshold strategies from the perspectives of an individual customer, a social optimizer, and a revenue maximizer such that their respective worst-case expected benefit rates are maximized. Finally, we compare our findings with Naor’s original results and the traditional sample average approximation scheme. Funding: This research was supported by the National Science Foundation [Grants 2342505 and 2343869]. 

We propose a rigorous modeling and methodological effort that integrates statistical implementation of hydrology models in predicting inland and coastal flood scenarios due to hurricanes and a scenario-based stochastic integer programming model which suggests resource and staging area decisions in the first stage and the evacuation decisions in the second stage. This novel study combines physics-based flood prediction models and stochastic optimization for large- scale multi-facility coordination of hospital and nursing home evacuations before impending hurricanes. The optimization model considers scenario-dependent evacuation demand, transport vehicles with varying capacities, and both critical and non-critical patients. Utilizing Hurricane Harvey of 2017 as a case study and actual healthcare facility locations in southeast Texas, we explore various evacuation policies, demonstrating the impact of routing strategies, staging area decisions, flood thresholds, and receiving facility capacities on evacuation outcomes. One of the findings is that choosing staging area(s) and deploying evacuation vehicles optimally considering the uncertainty of the hurricane’s path at the time of decision making could have significant effect on the total cost of the operation and evacuation time experienced by the evacuees. We also show the non-negligible value of the scenario-based staging and routing solution conservatively calculated in relation to a single scenario solution using the concept of value of stochastic solution. 

Hurricanes often induce catastrophic flooding due to both storm surge near the coast, and pluvial and fluvial flooding further inland. In an effort to contribute to uncertainty quantification of impending flood events, we propose a probabilistic scenario generation scheme for hurricane flooding using state-of-art hydrological models to forecast both inland and coastal flooding. The hurricane scenario generation scheme incorporates locational uncertainty in hurricane landfall locations. For an impending hurricane, we develop a method to generate multiple scenarios by the predicated landfall location and adjusting corresponding meteorological characteristics such as precipitation. By combining inland and coastal flooding models, we seek to provide a comprehensive understanding of potential flood scenarios for an impending hurricane. To demonstrate the modeling approach, we use real-world data from the Southeast Texas region in our case study. 

This paper proposes a two-stage stochastic mixed integer programming framework for patient evacuation. While minimizing the expected total cost of patient evacuation operations, the model determines the location of staging areas and the number of emergency medical service (EMS) vehicles to mobilize in the first stage, and the EMS vehicle routing assignments in the second stage. A real-world data from Southeast Texas region is used to demonstrate our modeling approach. To provide a more pragmatic solution to the patient evacuation problem, we attempt to create comprehensive hurricane instances by integrating the publicly available state-of-art hydrology models for surge, Sea, Lake Ocean and Overland Surge for Hurricanes (SLOSH), and for streamflow, National Water Model (NWM), prediction. The surge product captures potential flooding in coastal region while the streamflow product predicts inland flooding. The results exhibit the importance of the integrated approach in patient evacuation planning, provide guidance on flood mapping and prove the potential benefit of comprehensive approach in scenario generation. 

The total cost for weather-related disasters in the US increases over time, and hurricanes usually create the most damage. One of the challenges, which is present in almost every major hurricane event, is the patient evacuation mission. We propose a comprehensive modeling and methodological framework for a large-scale patient evacuation problem when an area is faced with a forecasted disaster such as a hurricane. In this work, we integrate a hurricane scenario generation scheme using publicly available surge level forecasting software and a scenario-based stochastic integer program to make decisions on patient movements, staging area locations and positioning of emergency medical vehicles with an objective of minimizing the total expected cost of evacuation and the setup cost of staging areas. The hurricane scenario generation scheme incorporates the uncertainties in the hurricane intensity, direction, forward speed and tide level. To demonstrate the modeling approach, we apply real-world data from the Southeast Texas region in our experiments. We highlight the importance of operation time limits, the number of available resources and an accurate forecast on forthcoming hurricanes in determining the locations of staging areas and patient evacuation decisions.