Events & Seminars

When only the moments of the underline distribution are known, many max-min optimization models can be interpreted as zero-sum games, in which the firm chooses actions to maximize her expected profit while Nature chooses a distribution subject to the moment conditions to minimize the firm’s expected profit. For single-period models, we reformulate the zero-sum game as a robust moral hazard, in which Nature chooses both the distribution and actions to minimize the firm’s expected profit subject to incentive compatibility (IC) constraints. Under quasi-concavity, these IC constraints are replaced by the firm’s first-order conditions, which give rise to additional moment constraints and an extended reformulation of the dual problem in a higher dimensional space, facilitating the search for the closed-form solution. In the equilibrium, the additional moment constraints are binding but have zero Lagrangian multipliers. This property enables us to derive closed-form solutions for several distributionally robust inventory models that the extant literature is unable to solve. For multi-period models, we apply subgame perfect conditions to eliminate Nature’s dominated strategies so that we can conveniently compute the firm’s time-average cost under Adverse Nature’s undominated strategy. We then solve the robustly optimal base-stock level with positive lead time and lost sales (or backorder). The theme of this ambitious research program is to combine both zero-sum games and semi-infinite programming tools.

We explore a new model of bandit experiments where a potentially nonstationary sequence of contexts influences arms' performance. Context-unaware algorithms risk confounding while those that perform correct inference face information delays. Our main insight is that an algorithm we call deconfounted Thompson sampling strikes a delicate balance between adaptivity and robustness. Its adaptivity leads to optimal efficiency properties in easy stationary instances, but it displays surprising resilience in hard nonstationary ones which cause other adaptive algorithms to fail.

We study an assortment optimization problem under a multi-purchase choice model in which customers choose a bundle of up to one product from each of two product categories. Different bundles have different utilities and the bundle price is the summation of the prices of products in it. For the uncapacitated setting where any set of products can be offered, we prove that this problem is strongly NP-hard. We show that an adjusted-revenue-ordered assortment provides a 1/2-approximation. Furthermore, we develop an approximation framework based on a linear programming relaxation of the problem and obtain a 0.74-approximation algorithm. This approximation ratio almost matches the integrality gap of the linear program, which is proven to be at most 0.75. For the capacitated setting, we prove that there does not exist a constant-factor approximation algorithm assuming the Exponential Time Hypothesis. The same hardness result holds for settings with general bundle prices or more than two categories. Finally, we conduct numerical experiments on randomly generated problem instances. The average approximation ratios of our algorithms are over 99%.

We consider a platform marketplace with both third-party and platform-owned sellers. The platform charges commissions to third-party sellers and buyers for their transactions in the marketplace. Meanwhile, it also directly determines the transaction prices for platform-owned sellers in their sales to buyers. Sellers and buyers are divided into different types with their compatibility captured by a bipartite network. Different types of sellers and buyers are heterogeneous in their cost and utility functions. Given the platform's choices of prices and commissions, third-party sellers/buyers maximize their own payoffs from supplying/demanding products, and market-clearing conditions are satisfied in the networked market. Facing the complexity with non-convex equilibrium constraints in the network, we develop a method of determining the platform's price-commission vector for profit maximization purposes. Based on the characterization of the platform's profit-optimal equilibrium, we investigate three other aspects of the revenue management problem. First, under fairness consideration between the platform and its market participants, we develop an efficient approximation algorithm to obtain a price-commission vector such that an allocation of surplus with a fairness level between the platform and its market participants is guaranteed in the equilibrium trades. Next, we shed light on how the platform should determine the optimal mixture of third-party sellers and platform-owned ones in the networked market. Lastly, we establish how the platform's profit-optimal price-commission decision depends on the network structure and demonstrate the impact of network structure on the platform's optimal profit.