Cross-docking provides benefits such as facilitating fast and direct unloading, consolidation, and reloading of goods from inbound to outbound trucks. The vehicle routing problem with cross-docking (VRPCD) is an extension of the vehicle routing problem with an additional constraint in which the depot has a role as cross-dock. The current paper provides a mixed-integer linear programming model for the VRPCD that considers multiple products, multiple vehicle types, and split pickups and delivery. Based on the literature, we generated two sets of instances, one with a homogenous vehicle and one with heterogeneous vehicles. The instances are then solved using the Gurobi Solver. Results show that instances with heterogeneous vehicles provide better results but require an increase in computation time (median of 37.3% for a 10-node instance with five types of vehicles). Split pickups and deliveries can produce lower objective values and generate solutions previously infeasible. The computational results also show that smaller instances of 10 nodes can be solved in a reasonable amount of time. However, larger instances of 30 nodes are not optimally solved given a limited computation time of 1 hour.