The notion of 'resource' plays an important role in the overall efficiency and performance of most cross-docks. The processing time can often be described in terms of the resources allocated to different trucks. Conversely, for a given processing time, different combinations of resources can be prescribed. We study the problem of truck scheduling and dock assignment in the presence of resource constraints. In the absence of a closed-form (or well-defined) linear formulation describing the processing times as a function of resources, expert' knowledge has been mobilised to enable modelling of the problem as an integer linear model. Two cases are taken into account: 1)the expert believes in his/her estimation of the processing time for every truck and only proposes a different combination of resources for his/her estimation, while 2)the expert proposes a limited number of resource deployment scenarios for serving trucks, each of which has a different combination of resources and different processing times. We propose a novel compact integer programming formulation for the problem, which is particularly designed with an embedded structure that can be exploited in dual decomposition techniques with a remarkably computationally efficient column generation approach in this case. The case in which a scenario with invariant processing time is considered and modelled as a special case of the proposed model. Since a direct application of commercial solvers such as CPLEX to solve instances of this problem is not realistic, we propose a branch-and-price framework and, moreover, several classes of valid inequalities are also introduced to improve the mathematical formulation of the problem. Our extensive computational experiments confirm that the proposed exact solution framework is very efficient and viable in solving real-size instances of the practice, in a reasonable amount of time.