A Milk Collection Problem with Incompatibility Constraints

The milk collection problem is well known in rural areas of the world. This paper considers this real-life problem for an Italian dairy company that collects raw milk from farmers. In our milk collection problem, we address the constraint that some farms are small and inaccessible by large vehicles; moreover, these farmers produce different milk types, and the tank trucks used for transporting the milk have multiple compartments. This generates the additional constraint that at most one milk type can be assigned to a tank compartment. The goal of this paper is to show how operations research techniques helped the company to improve its daily performance. In particular, we present a solution approach based on two mathematical formulations and local search, all embedded within a multiple-restart mechanism. The first mathematical formulation minimizes the number of vehicles to be routed in the network; the second minimizes the tour length. We also discuss experiments we conducted as part of our case study and compare our solution with the process that the company used previously.