Optimal Procurement Management by Reverse Auctions for a Price-Setting Newsvendor

In this paper, we study the optimal procurement management by reverse auctions for a price-setting newsvendor(retailer) in a single period setting. The retailer facing price-dependent stochastic demand first designs a procurement contract and then invites the suppliers to bid for this contract in the reverse auction. The winning supplier produces and delivers the demanded quantity.The retailer obtains the procurement quantity and simultaneously determines the retail price. By using the price elasticity of the lost-sales rate, we show that the retailer’s expected profit(excluding the procurement cost) is a concave function of the purchased quantity, which can be used to obtain the optimal procurement and retail pricing decisions for the retailer. Further, when the underlying random term of demand function is normally distributed under left-truncation(at 0), we get the analytical expressions of the purchased quantity and expected profit function for the retailer. Moreover, some numerical examples are given.