“3rd Panzer Division’s quartermaster described the supply situation for the division as “very critical””
3rd Panzer is also WAY out in front of everyone else, too, south of, and already past Minsk.
They have already outrun the logistics train, and it was only the refueling done with stocks captured on the 26th when they overran a huge Russian fuel dump that has allowed them to keep moving East to the river.
The logistics on the Eastern Front was a major issue from the word go. It goes beyond just the fact that there were different rail gauges between the Russians and the rest of Europe. The larger Russian trains required fewer service points and as a result, the ones that were not destroyed as the Russians retreated were too far apart for German locomotives.
Traveling from the far away (and getting further by the day) rail heads were the motorized supply system which consisted mostly of captured vehicles (Guderian’s motorized support were all French vehicles). Many of these vehicles were not suited for the poor Russian roads and fell into disrepair very quickly. The rest of the logistics, and honestly the bulk of the effort to get supplies to the front were handled by horse drawn supply wagons. Even this was problematic since the German horses were used to a more hearty diet than what could be provided on the Soviet frontier. The oat supply for these horses were often far short of what they were conditioned to handle and the horses fell weak and began dying off faster than they could be replaced by captured Russian horses or horses from Germany.