Faced with the daunting task of parceling out a limited supply of coronavirus vaccines, Trump administration officials came up with a seemingly simple formula last year to streamline distribution of the shots.

First, federal administrators would run an automated algorithm to divide vaccine doses nationwide, based on the size of each state’s adult population. Then each state would decide how to dole out the shots to local hospitals, nursing homes and clinics.

But rather than streamline vaccine distribution, public health experts say, the algorithm has increased the burden for many states. It requires them to come up with multiple delivery plans for their weekly quotas of Pfizer and Moderna shots, even if the different shipments are destined for the same clinics and hospitals.