An inventory model for group-buying auction
  Group-buying auction has become a popular marketing strategy in the last decade. In this paper, a stochastic model is developed for an inventory system subjects to demands from group-buying auctions. The model discussed here takes into the account of the costs of inventory, transportation, dispatching and re-order as well as the penalty cost of non-successful auctions. Since a new cycle begins whenever there is a replenishment of products, the long-run average costs of the model can be obtained by using the renewal theory. A closed form solution of the optimal replenishment quantity is also derived. 
Allen H. Tai
math.OC cs.GT math.PR