Game theory is widely used to model how individualistic players may decide to join forces and cooperate in order to increase their own benefits. When such agents belong to the same level of a given supply chain, such collaboration is called horizontal.

Given the high costs involved in the wine grape harvesting operations, horizontal collaboration seems to be a key factor for wine producers to stay competitive by sharing workers and machinery.

The wine grape harvesting problem consists of deciding when and where to harvest, while taking into account several operational constraints such as labor allocation, routing decisions and operations time windows. The way how producers may decide to collaborate highly depends, however, on how the benefits obtained from cooperation are split among partners. To this end, the authors study three different allocation methods leading to different linear and nonlinear mathematical optimization models.

Artelys Knitro is employed to solve the proposed nonlinear mathematical models, and their numerical analysis show that the nonlinear allocation method provides solutions that have, on average, a more equitable behavior when compared to the two other linear models. Such results illustrate the fact that taking into account nonlinear behaviors can be of great importance when conceiving a mathematical model.