Disruption Management in the (Post-)Pandemic World

Coronavirus Disease 2019 (COVID-19) is a contagious illness caused by the SARS-CoV-2 virus. The first documented case emerged in Wuhan, China, in December 2019, leading to the global spread of the disease and the declaration of the COVID-19 pandemic. This unprecedented global health crisis presents significant challenges to both healthcare and supply chain systems. In my thesis, I delve into the analysis of various transient systems in the pandemic and post-pandemic world. Specifically, my thesis investigates disease transmission dynamics and addresses the optimal allocation of limited healthcare resources, such as testing kits and vaccines of different doses. Additionally, I explore the effects of the disruption in a circulatory transportation system and we identify the whiplash and whipsaw effect in this transient system. My thesis aims to bridge the gap in studying the disruption management of transient systems across diverse domains, encompassing healthcare management and supply chain resilience, and devising optimal control and mitigation strategies for such systems. In Chapter 1, in order to better capture the dynamics of the COVID-19 outbreak, I extend the SIR model to incorporate limited testing capacity and account for asymptomatic individuals. This extended framework enables me to analyze both first- and second-order structural properties of a key metric--the fraction of uninfected individuals--with respect to testing capacity, accuracy, delay, turnaround time, and contact tracing effectiveness. From these analyses, I derive qualitative managerial insights into how these parameters influence the total number of infections, as well as quantitative policies for managing testing capacity at the operational level. Specifically, I show how to optimally allocate limited testing resources over time and between symptomatic and asymptomatic individuals. Counterintuitively, I find that under certain conditions, policymakers may want to allocate testing resources equally between these two groups instead of prioritizing the symptomatic. Moreover, I demonstrate that reserving testing capacity for later periods can, in some cases, reduce the total number of infections. To guide policymakers in prioritizing testing methods, I also propose a testing index based on capacity, accuracy, and turnaround time. Using COVID-19 data, I fit with my model and apply a sliding-window method to account for non-stationarity in model parameters and predict future infections. My study's analytical findings provide insights for managing testing capacities at both strategic and operational levels, while the estimation results highlight the strong predictive power of this parsimonious model. In Chapter 2, I investigate the optimal vaccine allocation policy in scenarios where the vaccine supply is scarce. By exploring the trade-offs between administering fractional and full dosages, I formulate the problem as an optimal control problem under disease transmission dynamics to minimize the total number of infections over a planning horizon. Specifically, I extend the SIR model by introducing two new compartments for partially and fully vaccinated individuals. Under mild conditions, I demonstrate that an attainable optimal vaccine allocation policy exhibits a ``bang-bang'' structure, suggesting that either the ``Partial Doses First'' (PDF) or the ``Full Doses First'' (FDF) allocation policy achieves optimality at any time. Furthermore, I compare the committed PDF and FDF policies for the entire planning horizon and identify a critical threshold on the fractional-dose vaccine efficacy, such that when the efficacy is above (resp., below) this threshold, choosing the committed PDF (resp., FDF) policy is better. Using COVID-19 vaccination data, I calculate thresholds for different countries in January 2021 to recommend to governments whether the priority should be given to allocating the first dose or to prioritizing the allocation of both first and second doses to the population. I also illustrate the versatility of our proposed scarce capacity allocation model in addressing a broad spectrum of resource allocation problems under diffusion dynamics, for which partial resource allocation can still yield some, though not full, benefits, and the optimal allocation decision involves balancing the coverage and protection level. The (post-)pandemic time witnessed many disruptions at ports, leading to delays and rising costs for shippers. In Chapter 3, I build a fluid model in transient states to investigate how disruptions at one port can affect the disrupted port and its counterpart in another country in a circulatory container shipping system where a stream of fleets moves goods back and forth between the two ports. Port disruption leads to two types of congestion: the inbound backlogs, which occur when ships are unable to enter the port, and the outbound backlogs, which arise when goods are unable to be loaded onto ships for transport to other ports. I characterize the recovery time of the system of two ports (from when the disruption ends to when the system goes back to normal) in closed form and the dynamics of inbound and outbound backlogs during the recovery process. I identify a whiplash and whipsaw effect in the outbound backlog process at both ports in which ports take turns being whipsawed by outbound backlogs that may go up and down. This counterintuitive phenomenon is due to the uneven spatial distribution of ships on the routes caused by the disruption. Furthermore, using the base two-port model as a building block, I obtain more general results in characterizing the recovery process of those bipartite port networks. I also extend the fluid model to a diffusion model to capture the second-order effect of the real-life system. Finally, I use our model prediction as a feature and apply machine learning techniques to predict the time that vessels spend in the Shanghai port after a typhoon disruption and show that using our model predictor, alongside all relevant vessel and voyage attributes as raw features, significantly reduces prediction errors by 10% to 30% on average compared to not using it.

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