176 / 2024-04-22 16:25:45

The Bilevel Migratory Beekeeping Routing Problem with Pollination Subsidy

migratory beekeeping,productive routing,timing decision,government subsidy,bilevel programming

The apiculture industry provides not only direct benefits for human society in the production of bee products but also significant externalities such as crop yield increase, especially in the production mode of migratory beekeeping. Nevertheless, its externalities are not fully utilized since production yield, in most areas of developing countries, is the sole concern for beekeepers. This study incorporates the role of government in the migratory beekeeping industry, where the pollination subsidy is introduced to induce beekeepers to follow the migratory routes that can contribute more externalities. Due to the inconsistent objectives of respectively the government and beekeepers, a bilevel programming (BLPP) model is proposed to reflect the leader-follower game relationship between them. Thereinto, the upper-level model with the social welfare (consisting of the bee product yields and pollination externalities) pursuit of government and the lower of the production-service-mixed-oriented routing problem with comprehensive revenue (from both production and pollination) are well established. The game and optimization mechanisms, especially the selection of vertices (nectar sources) and time decisions thereon, make the problem difficult to solve. On the basis of the model transformation and decomposition, an implicit enumeration algorithm with the tailored branch-price-and-cut (B&P&C), routes pooling, and non-dominated subsidy tabu list embedded is proposed to solve the problem. The numerical study, with a real-world case included, shows the efficient performance of the proposed solution method in solving and coordinating the pursuits of social welfare for the government and economic revenue for beekeepers; moreover, managerial implications for the subsidies in the migratory beekeeping industry are also provided.