Paat Rusmevichientong

Dynamic Assortment Optimization with a Multinomial Logit Choice Model and Capacity Constraint

We consider an assortment optimization problem where a retailer chooses an assortment of products that maximizes the profit subject to a capacity constraint. The demand is represented by a multinomial logit choice model. We consider both the static and dynamic optimization problems. In the static problem, we assume that the parameters of the logit model are known in advance; we then develop a simple algorithm for computing a profit-maximizing assortment based on the geometry of lines in the plane and derive structural properties of the optimal assortment. For the dynamic problem, the parameters of the logit model are unknown and must be estimated from data. By exploiting the structural properties found for the static problem, we develop an adaptive policy that learns the unknown parameters from past data and at the same time optimizes the profit. Numerical experiments based on sales data from an online retailer indicate that our policy performs well.

An analysis of belief propagation on the turbo decoding graph with Gaussian densities

Motivated by its success in decoding turbo codes, we provide an analysis of the belief propagation algorithm on the turbo decoding graph with Gaussian densities. In this context, we are able to show that, under certain conditions, the algorithm converges and that-somewhat surprisingly-though the density generated by belief propagation may differ significantly from the desired posterior density, the means of these two densities coincide. Since computation of posterior distributions is tractable when densities are Gaussian, use of belief propagation in such a setting may appear unwarranted. Indeed, our primary motivation for studying belief propagation in this context stems from a desire to enhance our understanding of the algorithms dynamics in a non-Gaussian setting, and to gain insights into its excellent performance in turbo codes. Nevertheless, even when the densities are Gaussian, belief propagation may sometimes provide a more efficient alternative to traditional inference methods.

A Nonparametric Approach to Multiproduct Pricing

Developed by General Motors (GM), the Auto Choice Advisor website (http://www.autochoiceadvisor.com) recommends vehicles to consumers based on their requirements and budget constraints. Through the website, GM has access to large quantities of data that reflect consumer preferences. Motivated by the availability of such data, we formulate a nonparametric approach to multiproduct pricing. We consider a class of models of consumer purchasing behavior, each of which relates observed data on a consumers requirements and budget constraint to subsequent purchasing tendencies. To price products, we aim at optimizing prices with respect to a sample of consumer data. We offer a bound on the sample size required for the resulting prices to be near-optimal with respect to the true distribution of consumers. The bound exhibits a dependence of O(n log n) on the number n of products being priced, showing thatin terms of sample complexitythe approach is scalable to large numbers of products. With regards to computational complexity, we establish that computing optimal prices with respect to a sample of consumer data is NP-complete in the strong sense. However, when prices are constrained by a price ladderan ordering of prices defined prior to price determinationthe problem becomes one of maximizing a supermodular function with real-valued variables. It is not yet known whether this problem is NP-hard. We provide a heuristic for our price-ladder-constrained problem, together with encouraging computational results. Finally, we apply our approach to a data set from the Auto Choice Advisor website. Our analysis provides insights into the current pricing policy at GM and suggests enhancements that may lead to a more effective pricing strategy.

A Nonparametric Asymptotic Analysis of Inventory Planning with Censored Demand

We study stochastic inventory planning with lost sales and instantaneous replenishment where, contrary to the classical inventory theory, knowledge of the demand distribution is not available. Furthermore, we observe only the sales quantity in each period and lost sales are unobservable, that is, demand data are censored. The manager must make an ordering decision in each period based only on historical sales data. Excess inventory is either perishable or carried over to the next period. In this setting, we propose nonparametric adaptive policies that generate ordering decisions over time. We show that the T-period average expected cost of our policy differs from the benchmark newsvendor cost---the minimum expected cost that would have incurred if the manager had known the underlying demand distribution---by at most O(1/T0.5).

Dynamic Pricing Under a General Parametric Choice Model

We consider a stylized dynamic pricing model in which a monopolist prices a product to a sequence of T customers who independently make purchasing decisions based on the price offered according to a general parametric choice model. The parameters of the model are unknown to the seller, whose objective is to determine a pricing policy that minimizes the regret, which is the expected difference between the sellers revenue and the revenue of a clairvoyant seller who knows the values of the parameters in advance and always offers the revenue-maximizing price. We show that the regret of the optimal pricing policy in this model is

Robust Assortment Optimization in Revenue Management Under the Multinomial Logit Choice Model

\Theta(\sqrt T)

Adaptive Data-Driven Inventory Control with Censored Demand Based on Kaplan-Meier Estimator

, by establishing an

A structured multiarmed bandit problem and the greedy policy

\Omega(\sqrt T)

Linearly Parameterized Bandits

lower bound on the worst-case regret under an arbitrary policy, and presenting a pricing policy based on maximum-likelihood estimation whose regret is

The d-Level Nested Logit Model: Assortment and Price Optimization Problems

\cal{O}(\sqrt T)