A Mixed-Integer Optimization Formulation for Buyers Formation

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