On Policies for Single-leg Revenue Management with Limited Demand Information

In this paper we study the single-item revenue management problem, with no information given about the demand trajectory over time. When the item is sold through accepting/rejecting different fare classes, Ball and Queyranne (2009) have established the tight competitive ratio for this problem using booking limit policies, which raise the acceptance threshold as the remaining inventory dwindles. However, when the item is sold through dynamic pricing instead, there is the additional challenge that offering a low price may entice high-paying customers to substitute down. We show that despite this challenge, the same competitive ratio can still be achieved using a randomized dynamic pricing policy. Our policy incorporates the price-skimming technique from Eren and Maglaras (2010), but importantly we show how the randomized price distribution should be stochastically-increased as the remaining inventory dwindles. A key technical ingredient in our policy is a new "valuation tracking" subroutine, which tracks the possible values for the optimum, and follows the most "inventory-conservative" control which maintains the desired competitive ratio. Finally, we demonstrate the empirical effectiveness of our policy in simulations, where its average-case performance surpasses all naive modifications of the existing policies

Decision Forest: A Nonparametric Approach to Modeling Irrational Choice

Customer behavior is often assumed to follow weak rationality, which implies that adding a product to an assortment will not increase the choice probability of another product in that assortment. However, an increasing amount of research has revealed that customers are not necessarily rational when making decisions. In this paper, we propose a new nonparametric choice model that relaxes this assumption and can model a wider range of customer behavior, such as decoy effects between products. In this model, each customer type is associated with a binary decision tree, which represents a decision process for making a purchase based on checking for the existence of specific products in the assortment. Together with a probability distribution over customer types, we show that the resulting model -- a decision forest -- is able to represent any customer choice model, including models that are inconsistent with weak rationality. We theoretically characterize the depth of the forest needed to fit a data set of historical assortments and prove that with high probability, a forest whose depth scales logarithmically in the number of assortments is sufficient to fit most data sets. We also propose two practical algorithms -- one based on column generation and one based on random sampling -- for estimating such models from data. Using synthetic data and real transaction data exhibiting non-rational behavior, we show that the model outperforms both rational and non-rational benchmark models in out-of-sample predictive ability.Comment: The paper is forthcoming in Management Science (accepted on July 25, 2021

Follow Your Star: New Frameworks for Online Stochastic Matching with Known and Unknown Patience

We study several generalizations of the Online Bipartite Matching problem. We consider settings with stochastic rewards, patience constraints, and weights (both vertex- and edge-weighted variants). We introduce a stochastic variant of the patience-constrained problem, where the patience is chosen randomly according to some known distribution and is not known until the point at which patience has been exhausted. We also consider stochastic arrival settings (i.e., online vertex arrival is determined by a known random process), which are natural settings that are able to beat the hard worst-case bounds of more pessimistic adversarial arrivals. Our approach to online matching utilizes black-box algorithms for matching on star graphs under various models of patience. In support of this, we design algorithms which solve the star graph problem optimally for patience with a constant hazard rate and yield a 1/2-approximation for any patience distribution. This 1/2-approximation also improves existing guarantees for cascade-click models in the product ranking literature, in which a user must be shown a sequence of items with various click-through-rates and the user's patience could run out at any time. We then build a framework which uses these star graph algorithms as black boxes to solve the online matching problems under different arrival settings. We show improved (or first-known) competitive ratios for these problems. Finally, we present negative results that include formalizing the concept of a stochasticity gap for LP upper bounds on these problems, bounding the worst-case performance of some popular greedy approaches, and showing the impossibility of having an adversarial patience in the product ranking setting.Comment: 43 page