The Migratory Beekeeping Routing Problem: Model and an Exact Algorithm

Apiculture has gained worldwide interest because of its contributions to economic incomes and environmental conservation. In view of these, migratory beekeeping, as a high-yielding technique, is extensively adopted. However, because of the lack of an overall routing plan, beekeepers who follow the experiential migratory routes frequently encounter unexpected detours and suffer losses when faced with problems such as those related to nectar source capacities and the production of bee products. The migratory beekeeping routing problem (MBRP) is proposed based on the practical background of the commercial apiculture industry to optimize the global revenue for beekeepers by comprehensively considering nectar source allocation, migration, production and sales of bee products, and corresponding time decisions. The MBRP is a new variant of the vehicle routing problem but with significantly different production time decisions at the vertices (i.e., nectar sources). That is, only the overlaps between residence durations and flowering periods generate production benefits. Different sales visits cause different gains from the same products; in turn, these lead to different production time decisions at previously visited nectar source locations and even change the visits for production. To overcome the difficulty resulting from the complicated time decisions, we utilize the Dantzig–Wolfe decomposition method and propose a revised labeling algorithm for the pricing subproblems. The tests, performed on instances and a real-world case, demonstrate that the column generation method with the revised labeling algorithm is efficient for solving the MBRP. Compared with traditional routes, a more efficient overall routing schedule for migratory beekeepers is proposed.