Sometimes measurements taken to increase resource efficiency do not reach the estimated magnitude, as part of the reduction vanishes due to the reaction of entities to the changed environment. This so-called rebound effect is intensively discussed in the energy sector literature. Surprisingly, little is found for transportation, and the question arises whether rebound effects occur in logistics as well. In this paper, we fill this gap by examining a Traveling Purchaser Problem (TPP) transport network. The implementation, which is a generalization of the TSP, will serve as a decision space in which the procurement of various quantities of products inside a logistics network will be optimized in regard to total costs while the consumption of fuel is monitored. Different parameterizations of the environment will be analyzed and tested to determine factors for the occurrence and magnitude of rebound effects. We present an upper bound on the number of rebound effects and we prove that smaller steps in fuel efficiency increase let each rebound effect become a backfire.