We study mechanisms for reopening economic activities that explore the trade off between containing the spread of COVID-19 and maximizing economic impact. This is of current importance as many organizations, cities, and states are formulating reopening strategies. Our mechanisms, referred to as group scheduling, are based on partitioning the population into groups and scheduling each group on appropriate days with possible gaps (when all are quarantined). Each group interacts with no other group and, importantly, any person who is symptomatic in a group is quarantined. Specifically, our mechanisms are characterized by three parameters $(g,d,t)$, where $g$ is the number of groups, $d$ is the number of days a group is continuously scheduled, and $t$ is the gap between cycles. We show that our mechanisms effectively trade off economic activity for more effective control of the COVID-19 virus. In particular, we show that the $(2,5,0)$ mechanism, which partitions the population into two groups that alternatively work for five days each, flat lines the number of COVID-19 cases quite effectively, while still maintaining economic activity at 70% of pre-COVID-19 level. We also study mechanisms such as $(2,3,2)$ and $(3,3,0)$ that achieve a somewhat lower economic output (about 50%) at the cost of more aggressive control of the virus; these could be applicable in situations when the disease spread is more rampant in the population. We demonstrate the efficacy of our mechanisms by theoretical analysis and extensive experimental simulations on various epidemiological models. Our mechanisms prove beneficial just by regulating human interactions. Moreover, our results show that if the disease transmission (reproductive) rate is made lower by following social distancing, mask wearing, and other public health guidelines, it can further increase the efficacy of our mechanisms.