On optimal bidding and inventory control in sequential procurement auctions: the multi period case

In this paper we consider the problem of a firm the that builds inventory of identical items that it acquires by participating in auctions in order to satisfy its own market demand. The objective of the firm is to have a procurement strategy that maximizes the expected present value of the profit, both for finite and infinite planning horizons. We present an MDP formulation of the problem. Under a few additional assumptions, such as excess demand is lost and stationary data, we establish monotonicity properties for the value function and the optimal dynamic procurement (bidding) strategy for the firm.