A milk collection problem with blending

•We present the milk collection problem with blending, inspired on practice.•Milk of different qualities is collected from rural farms and blended in the trucks.•Blending decreases revenues, but more significantly reduces transportation costs.•We solve medium size instances optimally and a real, large instance, heuristically.

A milk collection problem with blending is introduced. A firm collects milk from farms, and each farm produces one out of three possible qualities of milk. The revenue increases with quality, and there is a minimum requirement at the plant for each quality. Different qualities of milk can be blended in the trucks, reducing revenues, but also transportation costs, resulting in higher profit. A mixed integer-programming model, a new cut, and a branch-and-cut algorithm are proposed to solve medium-sized instances. A three-stage heuristic is designed for large instances. Computational experience for test instances and a large-sized real case is presented.