Operational problems in agri-food supply chains usually show characteristics that are scarcely addressed by traditional academic approaches. These characteristics make an already NP-hard problem even more challenging; hence, this problem requires the use of tailor-made algorithms in order to solve it efficiently. This work addresses a rich vehicle routing problem in a real-world agri-food supply chain. Different types of animal food products are distributed to raising-pig farms. These products are incompatible, i.e., multi-compartment heterogeneous vehicles must be employed to perform the distribution activities. The problem considers constraints regarding visit priorities among farms, and not-allowed access of large vehicles to a subset of farms. Finally, a set of flat tariffs are employed to formulate the cost function. This problem is solved employing a reactive savings-based biased-randomized heuristic, which does not require any time-costly parameter fine-tuning process. Our results show savings in both cost and traveled distance when compared with the real supply chain performance.