Collaborative job scheduling in the wine bottling process

This paper proposes a horizontal collaborative approach for the wine bottling scheduling problem. The opportunities for collaboration in this problem are due to the fact that many local wine producers are usually located around the same region and that bottling is a standard process. Collaboration among wineries is modeled as a cooperative game, whose characteristic function is derived from a mixed integer linear programming model. Real world instances of the problem are, however, unlikely to be solved to optimality due to its complex combinatorial structure and large dimension. This motivates the introduction of an approximated version of the original game, where the characteristic function is computed through a heuristic procedure. Unlike the exact game, the approximated game may violate the subadditivity property. Therefore, it turns relevant not only to find a stable cost allocation but also to find a coalition structure for selecting the best partition of the set of firms. We propose a maximum entropy methodology which can address these two problems simultaneously. Numerical experiments illustrate how this approach applies, and reveal that collaboration can have important positive effects in wine bottling scheduling decreasing delay by 33.4 to 56.9% when improvement heuristic solutions are used. In contrast to the exact game in which the grand coalition is always the best outcome, in the approximated game companies may be better forming smaller coalitions. We also devise a simple procedure to repair the characteristic function of the approximated game so that it recovers the subadditivity property.