Managing concurrency in cyclical projects under stochastic task environments: Vaccine development projects during pandemics.

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.