Aggressive overlapping of stochastic activities during phases of vaccine development has been critical to making effective vaccines for COVID‐19 available to the public, at “pandemic” speed. In cyclical projects wherein activities can be overlapped, downstream tasks may need rework on account of having commenced prior to receiving requisite information that is only available upon completion of upstream task(s). We provide a framework to understand the interplay between stochastic overlap duration and rework due to overlap, and its impact on minimizing expected completion time for a cyclical project. We motivate the problem using the new paradigm for planning vaccine development projects. It best exemplifies features and scenarios in our model that were not considered and are also not apparent in the examples for cyclical development projects in the literature focused on engineered and manufactured products. We find that planning overlapping in scenarios that may be deemed ineffective with an assumption of deterministic tasks, can actually be beneficial when analyzed using stochastic task duration. We determine optimal planned start times for stochastic tasks as a function of a parameter that proxies for the extent of net gain/loss from overlap to minimize expected completion time for the project. We show that in situations with a net gain from overlap it is optimal to start the downstream task concurrently unless the downstream task does not stochastically dominate the upstream task and the net gain from overlap is not low enough. However, in situations with a net loss from overlap it is always optimal to have some degree of overlap in a stochastic task environment. We find that project rescheduling flexibility is always beneficial in a scenario with net loss from overlap and only beneficial in a scenario with net gain from overlap when the downstream task does not stochastically dominate the upstream task and the net gain from overlap is high enough. Our results on overlapping in 1‐to‐1, 1‐to‐ n , and n ‐to‐1 stochastic task configurations guide the development of an effective heuristic. Our heuristic offers good solution quality and is scalable to large networks as its computational complexity is linear in the number of tasks.

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The COVID-19 pandemic has forced governments to impose crippling restrictions on the day-to-day activities of citizens. To contain the virus and lift these restrictions safely, policymakers need to know quickly where the virus is spreading. This has been possible only through widespread testing. Not long after starting largescale testing in the early stages of the pandemic and more recently with a surge of new variants, countries hit a roadblock—the shortage of swabs used in the testing kits due to disruptions in the supply chain caused by COVID-19. This disruption translates to a variable production capacity of the swab suppliers. As a result, when countries order swabs from a swab supplier, their order might not be fully satisfied. Hence, adopting a proper swab inventory management model can help countries better manage COVID-19 testing and avoid widespread shortages of testing supplies. By considering two different swab demand patterns (i.e., stationary and stochastic) and two different production capacity scenarios for the swab supplier (i.e., ample and variable production capacity), we develop four analytical models, in which we consider all combinations of the above demand and capacity scenarios, to derive the optimal swab-procurement policy for a country. Given the rapid change of COVID-19 infection cases and the limited planning period, countries should aim for reactive scheduling. Through a comprehensive numerical study, we also provide guidelines on how countries should optimally react to these changes in the supply and demand of swabs. The research implications for managing inventory with stochastic supplier capacity and uncertain demand in a finite time horizon extend well beyond the application to COVID-19 testing. Supplementary Information The online version contains supplementary material available at 10.1007/s12063-022-00308-1.

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