Is VCG mechanism applicable in reverse auction? If so, how?
In general, VCG is also applicable to reverse auction settings. VCG is not even restricted to auction settings and can be used quite generally, see wikipedia for an introduction. If you want a deeper treatment, I recommend Tilman Börger's book (it used to be fully online, maybe there are still copies flying around). In reality, there are often problems associated with VCG, see, e.g., Ausubel and Milgrom writing about &quot;The Lovely but Lonely Vickrey Auction.&quot;
The general idea of VCG is that each agent's transfer is their own externality.  In your setting, you cannot simply do that because there is a budget restriction on transfers. Papers with such a knapsack constraint in economics are Ensthaler &amp;Giebe and Jarman &amp;Meisner (JET 2017), who use clock auctions as in Milgrom &amp; Segal (JPE 2020).