Robust optimization strategies for seller based on uncertainty sets in context of sequential auction

Different sequence of selling the diverse goods (used cars) in sequential auction, which is different sequential strategy, collides risk of price uncertainty that leads uncertain revenue. To find the optimal solutions for seller facing revenue uncertainty, a robust optimization method is proposed to overcome the inherent uncertainty of price. In this way, the traditional maximum revenue model is extended into four corresponding robust models according to the different forms of uncertainty sets, the robustness and conservativeness of the solutions are compared. Moreover, these results can be shown by corollaries and numerical examples: (1) the greater uncertain level parameter is, the less revenue is; (2) revenue in model without considering uncertainty is too high, and revenues in robust models are less than it; (3) the revenue does not always increase with total auction sequence increases; (4) value strategies are not optimal for auctioneer in despite of whether to consider uncertainty.