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.