My friend works for a company that opted for the lowest possible fare and used software to find it. The result was that everywhere he went, he had to make stops..sometimes 2 or 3 layovers. Over time, this meant more missed connections which meant more lost work and more expenses. I am not sure if that outweighed the costs saved in flights or not, but the work enviroment became so unpleasant for he and his co-workers that within 2 years most had left the company and turn over increased significantly.
Sometimes it's cheaper in the long run to spend more to protect yourself against intangible, uncontrollable costs.