Description:
Companies frequently offer wholesale prices for their products that decrease with the number of purchased items. However, single buyers may not be willing or able to purchase large quantities of a single item. Nevertheless, consumers can form groups to purchase at wholesale prices, obtaining bargaining power. This practice can be extended from single products to bundles. We propose a mathematical model to create groups of buyers wishing to purchase product bundles optimally. Mixed-integer programming formulations are presented for the cases of non-increasing price and step price functions. A Benders decomposition formulation is proposed for step price functions to solve large instances. Computational experiments show the performance of the method for synthetic instances