A robust multi-objective model for healthcare resource management and location planning during pandemics

In this study, we consider the problem of healthcare resource management and location planning problem during the early stages of a pandemic/epidemic under demand uncertainty. Our main ambition is to improve the preparedness level and response effectiveness of healthcare authorities in fighting pandemics/epidemics by implementing analytical techniques. Building on lessons from the Chinese experience in the COVID-19 outbreak, we first develop a deterministic multi-objective mixed integer linear program (MILP) which determines the location and size of new pandemic hospitals (strategic level planning), periodic regional health resource re-allocations (tactical level planning) and daily patient-hospital assignments (operational level planning). Taking the forecasted number of cases along a planning horizon as an input, the model minimizes the weighted sum of the number of rejected patients, total travel distance, and installation cost of hospitals subject to real-world constraints and organizational rules. Next, accounting for the uncertainty in the spread speed of the disease, we employ an across scenario robust (ASR) model and reformulate the robust counterpart of the deterministic MILP. The ASR attains relatively more realistic solutions by considering multiple scenarios simultaneously while ensuring a predefined threshold of relative regret for the individual scenarios. Finally, we demonstrate the performance of proposed models on the case of Wuhan, China. Taking the 51 days worth of confirmed COVID-19 case data as an input, we solve both deterministic and robust models and discuss the impact of all three level decisions to the quality and performance of healthcare services during the pandemic. Our case study results show that although it is a challenging task to make strategic level decisions based on uncertain forecasted data, an immediate action can considerably improve the response effectiveness of healthcare authorities. Another important observation is that, the installation times of pandemic hospitals have significant impact on the system performance in fighting with the shortage of beds and facilities.