Combinatorial reverse auction algorithm for group buying

Group buying is an important business model. From the perspective of buyers, quantity based discounts provide a huge incentive to form coalitions and take advantage of lower prices without ordering more than their actual demand. By forming a coalition, buyers can also improve their bargaining power and negotiate more advantageously with sellers to purchase at a lower price. In this paper, we study coalition formation problem in group buying. We formulate this problem as a combinatorial reverse auction with multiple buyers and multiple sellers. We propose the concept of proxy buyer to deal with this problem. The proxy buyer consolidates the demands from the buyers and then holds a reverse auction to try to obtain the goods from a set of sellers who can provide the goods. The main results include: (1) a problem formulation for the combinatorial reverse auction problem; (2) a solution methodology based on Lagrangian relaxation and (3) analysis of numerical results based on our solution algorithms.