In this work we present a simple local search based approach to solve the Vehicle Routing Problem with Cross-docks. The problem is based on the classic Vehicle Routing Problem, but incorporates cross-docks that allow transfer operations oriented to reduce travel costs. Our approach considers two main phases: construction and local search. The local search phase uses four movements. Our main focus here is to analyze how the design of the set of local search operators can influence the performance of the designed algorithm. For this, we analyze two basic design schemes: diversification and intensification oriented operators. Moreover, we compare two versions of the algorithm, a standard fixed rates approach and an adaptive selection operators approach from literature.We compare these approaches on two set of well known problem instances from literature that consider from 20 to 500 pair of nodes. From our results we can establish that it is not a clear relevance of the design scheme neither on the use of adaptive operator selection nor to the fixed rates schemes.