usually there's a block on the online travel request form where you can enter your rationale for not accepting the lowest fare; the travel request goes into the system normally, and if the approving supervisor/manager doesn't have an issue with your rationale they just approve and send on ... if anyone rejects the request, the system should automatically send it back to you; alternatively, that individual may call or email you directly to discuss before rejecting or approving

a succinct statement ("lowest cost route was 2 connections and 38 hours vs 1 connection and 26 hours") should generally be sufficient