A mixed-integer optimization formulation for buyer formation

Abstract

Companies frequently offer wholesale prices for their products that decrease with the number of items purchased. However, individual buyers may not be willing or able to purchase large quantities of a single item. To address this consumers can form groups to purchase at wholesale prices and gain bargaining power. This practice can be extended from single products to product bundles. This paper proposes a combinatorial coalition formation problem to create groups of buyers who wish to optimally purchase product bundles. We propose a generic mathematical model and present mixed-integer programming formulations for nonincreasing price and step price functions. To handle large instances, a Benders decomposition method is proposed for step price functions. Computational experiments conducted on a large set of synthetic instances illustrate the performance of the method.