23 research outputs found
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