When I was taking AP World History in high school, my teacher told us that the mere cost of the bullets needed to execute all of the "undesirables" was calculated to be ruinously expensive, nearly bankrupting Germany. Moreover, thousands of soldiers, billions of Reichsmarks, and much of the SS's manpower were solely devoted to guarding, rounding up, and hunting Jews and other minorities. Is there any truth to the idea that the Final Solution and Holocaust were a significant waste of resources that harmed the German war effort in WWII?
In short, no. Under a normal functioning economy, the Final Solution would have absolutely done significant harm to Germany's ability to fight a multi-front world war however, given the "free" labor and raw materials Nazi Germany enjoyed, they were able to basically accomplish both. In other words, I have not seen any evidence that suggests Germany lost the war because of their Final Solution efforts. To the contrary, they were efficient in how they "evacuated" the Jews and others and even used them to aid the war effort.
The Nazi's knew exactly who and where the "undesirables" were in Germany and each country they invaded. Their system for finding and rounding them up into ghettos became very efficient. For a current reference, it would be similar to serving warrants on fugitives by US Marshals. They know names, addresses, same for close family members, occupation, etc. Plus, many of the conquered countries had anti-Semitic parties/factions that were all to eager to help the Nazi's complete their final solution. So yes, a large undertaking but they had a lot of help and were very efficient.
Most necessary for the Final Solution were getting people from the ghettos to the concentration or death camps. The Nazi's were very smart in that they built the camps in areas with significant rail access from many directions. Once at the death camps, Zyklon B gas was used to murder and than industrial ovens used to destroy the bodies. On the whole, this was their preferred method of "evacuating" the undesirables. The USHMM estimates 2.7million Jews were killed in these death camps {1}. In addition, many others were killed by firing squad and buried in mass graves. Generally, these would have taken place on the front lines in an ad hoc manner. Again, the Nazi's were efficient.
Finally, keep in mind while the Nazi's were simultaneously imprisoning and exterminating the Jews and others, German industry used those same people as forced labor in their factories and instead of paying the worker, the SS was paid their wage {2}. In addition, many of the raw materials were mined using forced labor in conquered countries. As almost all industry in Germany turned their production towards aiding the war effort, the Nazi's had plenty of armaments to fight a multi-front war however as they would later find out, they were no match for the U.S.
{1} https://www.ushmm.org/wlc/en/article.php?ModuleId=10007327
{2} https://www.ushmm.org/wlc/en/article.php?ModuleId=10007326