The Distributionally Robust Inventory Strategy of the Overconfident Retailer under Supply Uncertainty

To factor in the retailer's overconfidence when dealing with the inventory problem with supply uncertainty, this paper develops a distributionally robust optimization model by only considering the mean and variance of the yield rate distribution. We first show that overconfidence would prompt the retailer to order more under low-profit conditions, whereas it reduces the order quantity under high-profit conditions. The analysis results imply that the pull-to-center effect still exists when only supply uncertainty applies, and the asymmetry that the deviation is higher under low-profit conditions is proved. The performance of overconfidence is also characterized in the expected profits of both retailer and supplier. Numerical studies show that even though the retailer may suffer losses, the supplier can benefit from the retailer's overconfidence in the low-profit case, which would positively increase the joint expected profit of the supply chain. Two extensions to the base model are also considered, including the scenario with both demand and supply uncertainties and an overconfident multi-product problem with budget constraints. This research provides tractable results to predict how the decision-maker is biased, and such insights would help the applications of de-biasing techniques in practice.