Dynamic procurement management by reverse auctions with fixed setup costs and sales levers

In this paper, we study a dynamic procurement problem for a retailer with fixed setup costs and sales levers (such as pricing, advertising, etc.). The retailer runs a reverse auction with a procurement contract in each period. A number of potential suppliers bid for this contract, and the winner is the supplier with the highest bid and is given the decision right for the quantity produced and delivered. The demand is either realized by selling via Internet auctions and unmet demand is lost, or is a price-sensitive nonnegative random variable and all shortages are backlogged. We show the existence of the retailer's optimal procurement contract, under which the suppliers' Bayesian-Nash equilibrium bidding strategy is (q(·),Q(·)), similar to the classic (s, S) policy for the retailers in dynamic inventory control problems. However, the (q(·),Q(·)) strategy here is for the suppliers and is realized through the suppliers' marginal production costs and so consists of two random variables for the retailer.