The current structure does not provide any incentive for reducing travel expense by finding a hotel under the per diem rate. If the rate in a city is $90 per night but there are hotels offered for $60, the traveler would not select the lesser expensive hotel.
There should be a system in place to split the savings between both the traveler and government. 50/50 would suffice, but this could be adjusted. Using the above room rates, on a four night trip, the total savings would be $120 for one traveler ($240 vs $360). The traveler would pocket $60 and the government would save this same amount. Factoring in how many people travel, the savings from this program would be incredible.