The milk collection problem with blending and collection points

- A collection of different qualities of milk from rural farms is proposed.
- The solution approach incorporates milk blending and pickup from collection points.
- The blended milk is classified as its lowest quality component.
- A branch-and-cut algorithm and a heuristic procedure are proposed.
- A real case study involving 500 farms and 112 possible collection points is solved.

A novel problem for the collection of raw milk from a network of farms supplying a dairy is specified and solved. The proposed approach incorporates milk blending and the delivery of production to collection points by small, distant farms. The milk is collected by, and blended in, a homogeneous fleet of trucks and classified according to the lowest quality product included in the blend. Optimization criteria are used to determine where the collection points should be located and which producers are allocated to them for delivery, with all other production picked up directly at the farms. The approach is built around an integer programming model and two implementation strategies, one using a branch-and-cut algorithm for small instances and the other a heuristic procedure combining both exact and approximated methods to handle large instances within a reasonable computation time. A real case study involving 500 farms and 112 possible collection points is solved and the results compared. The impact on the solutions of dividing the real instance into zones is also explored.