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Intertemporal Pricing via Nonparametric Estimation: Integrating Reference Effects and Consumer Heterogeneity
with Junyu Cao, Zuo-Jun Max Shen
Manufacturing & Service Operations Management 26.1 (2024): 28-46.
abstract
ssrn
slides
code
real data
journal
🏆 Finalist, 2020 MSOM Data-Driven Research Challenge
📺 Media: ORAI_China
We consider intertemporal pricing in the presence of reference effects and consumer heterogeneity. Our research question encompasses how to estimate heterogeneous consumer reference effects from data and how to efficiently compute the optimal pricing policy. Understanding reference effects is essential for designing pricing policies in modern retailing. Our work contributes to this area by incorporating consumer heterogeneity under arbitrary distributions. We propose a mixed logit demand model that allows arbitrary joint distributions of valuations, responsiveness to prices, and responsiveness to reference prices among consumers. We use a nonparametric estimation method to learn consumer heterogeneity from transaction data. Further, we formulate the pricing optimization as an infinite horizon dynamic programming problem and solve it by applying a modified policy iteration algorithm. Moreover, we investigate the structure of optimal pricing policies and prove the sub-optimality of constant pricing policies even when all consumers are loss-averse according to the classical definition. Our numerical studies show that our estimation and optimization framework improves the expected revenue of retailers via accounting for heterogeneity. We validate our model using real data from JD.com, a large E-commerce retailer, and find empirical evidence of consumer heterogeneity. In practice, ignoring consumer heterogeneity may lead to a significant loss of revenue. Furthermore, heterogeneous reference effect offers a strong motive for promotions and price fluctuations.
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A Nonparametric Maximum Likelihood Approach to Mixture of Regression
with Adityanand Guntuboyina
Under revision for resubmission to Journal of the American Statistical Association
abstract
arxiv
slides
code
🏆 Winner, 2020 IISA Best Student Paper (Theory/Methodology Category)
Mixture of regression models are useful for regression analysis in heterogeneous populations where a single regression model may not be appropriate for the entire population. We study the nonparametric maximum likelihood estimator (NPMLE) for fitting these models. The NPMLE is based on convex optimization and does not require prior specification of the number of mixture components. We establish existence of the NPMLE and prove finite-sample parametric (up to logarithmic multiplicative factors) Hellinger error bounds for the predicted density functions. We also provide an effective procedure for computing the NPMLE without ad-hoc discretization and prove a theoretical convergence rate under certain assumptions. Numerical experiments on simulated data for both discrete and non-discrete mixing distributions demonstrate the remarkable performance of our approach. We also illustrate the approach on two real data sets.
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Multi-Product Dynamic Pricing with Reference Effects Under Logit Demand
with Mengzi Amy Guo, Zuo-Jun Max Shen
Major revision at Manufacturing & Service Operations Management
abstract
ssrn
We consider an infinite-horizon multi-product dynamic pricing problem with reference effects in a monopolistic setting, where the reference price is an exponentially weighted average of historical prices. In each period, the demand follows the multinomial logit (MNL) model, where the utility depends on both the current price and the reference price, and consumers can have product-differentiated sensitivities to the price and the reference price. We conduct thorough analyses of the myopic pricing policy, including its solution, long-run convergence behavior, and performance guarantee compared to the long-term discounted revenue of the optimal pricing policy. Furthermore, we establish the structural properties of the optimal pricing policy. When consumers are loss-neutral towards all products, we explicitly characterize the optimal pricing policy if it converges to a steady state, and based on our characterization we show that the steady state price can be computed efficiently by a binary search. Interestingly, we find that such a convergence behavior of the optimal pricing policy heavily relies on the upper bound of the admissible price range, and a low price upper bound facilitates the policy to converge. In contrast, when consumers are gain-seeking towards all products, we prove that the optimal pricing policy admits no steady state regardless of the price range. Nevertheless, if consumers are only gain-seeking towards certain but not all products, the optimal pricing policy can potentially be convergent. In addition, our numerical experiments show that loss-aversion over all products does not rule out price fluctuations. This finding is at odds with the classic belief on loss-averse consumers and hence, highlights the significance of accounting for cross-product effects through the MNL demand.
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Learning While Repositioning in On-Demand Vehicle Sharing Networks
with Shunan Jiang, Zuo-Jun Max Shen, Chunlin Sun (alphabetical order)
Under 2nd-round review at Management Science after R&R
abstract
ssrn
🏆 Winner, YinzOR Student Conference Flash Talk Competition 2022
We consider the vehicle repositioning problem for a one-way on-demand vehicle sharing service with a fixed number of rental units distributed across the network. Due to uncertainty in both customer arrivals and vehicle returns, the service provider needs to periodically reposition the vehicles to match the supply with the demand while minimizing the total costs of repositioning labor and lost sales. The repositioning problem is critical in the successful management of on-demand one-way vehicle sharing services, and it is challenging both analytically and computationally. The optimal repositioning policy under a general $n$-location network is intractable without knowing the optimal value function. We define the best base-stock repositioning policy as a generalization of the popular inventory control policy to the vehicle repositioning problem, and we establish its asymptotic optimality in two different limiting regimes under general network structures. We develop learning methods to dynamically reposition vehicles to find the best base-stock policy with censored demand. By establishing a tight concentration inequality, we show that the one-time learning algorithm achieves a regret of $\widetilde{\bigo}\left(T^{\frac{2}{3}}\right)$, which is independent of the number of locations in the network. We furthermore develop an online stochastic gradient descent algorithm using only censored demand and prove that it achieves a regret of $\widetilde{\bigo}\left(T^{\frac{1}{2}}\right)$ under a cost structure assumption. Crucially, our online algorithm is based on a novel decomposition of cumulative costs and linear programming reformulation of the offline problem. Numerical experiments illustrate the effective performance of our approaches.
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Smoothness-Adaptive Dynamic Pricing with Nonparametric Demand Learning
with Zeqi Ye
International Conference on Artificial Intelligence and Statistics (AISTATS) 2024.
abstract
arxiv
proceeding
We study the dynamic pricing problem where the demand function is nonparametric and H\"older smooth, and we focus on adaptivity to the unknown H\"older smoothness parameter $\beta$ of the demand function. Traditionally the optimal dynamic pricing algorithm heavily relies on the knowledge of $\beta$ to achieve a minimax optimal regret of $\widetilde{O}(T^{\frac{\beta+1}{2\beta+1}})$. However, we highlight the challenge of adaptivity in this dynamic pricing problem by proving that no pricing policy can adaptively achieve this minimax optimal regret without knowledge of $\beta$. Motivated by the impossibility result, we propose a self-similarity condition to enable adaptivity. Importantly, we show that the self-similarity condition does not compromise the problem's inherent complexity since it preserves the regret lower bound $\Omega(T^{\frac{\beta+1}{2\beta+1}})$. Furthermore, we develop a smoothness-adaptive dynamic pricing algorithm and theoretically prove that the algorithm achieves this minimax optimal regret bound without the prior knowledge $\beta$.
Supply Chain Forecast Sharing Under Asymmetric Forecast Preferences
with Lin Zhao, Mengshi Lu, Zuo-Jun Max Shen, Kemal Guler
Under revision at Production and Operations Management
abstract
ssrn
Forecast sharing has been widely adopted to coordinate capacity planning in supply chains. However, the effectiveness of forecast sharing can be hindered by forecast inflation caused by the forecaster's asymmetric preferences toward underforecasts or overforecasts. In this paper, we study how suppliers can benefit from knowing the asymmetric preferences in forecasts shared by their customers. We employ a multi-period Bayesian repeated newsvendor model to depict the impact of forecast preferences on how a supplier updates its demand information and prepares its production capacity based on the shared forecast. We characterize the value of the forecast preference information, which is the increase in the supplier's expected profit through improved capacity planning enabled by considering asymmetric forecast preferences. We show that firms can benefit from the forecast preference information, and the benefit is more substantial under higher degrees of preference asymmetry, lower estimation error, and more profitable operations. We also show that it may not be optimal for the supplier to know the exact forecast preference. In the presence of estimation errors, the supplier may benefit from overestimating or underestimating the forecast preference. We further study the impact of the forecast preference information on the supplier's expected profit and derive a finite-sample bound on its regret. We apply the model in a numerical study with data from a real-world forecast sharing practice in a PC manufacturing supply chain. The results show that there exists significant forecast inflation in the shared forecasts. Furthermore, the preference toward overforecast is higher when the forecast horizon is shorter or when the product family's total demand is lower. Using forecast preferences reflected in the data set, we quantify the value of forecast preference information, which is shown to be significant and increasing in the manufacturer's estimation accuracy and the supplier's profitability.
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Quantum Computing Methods for Supply Chain Management
with Zuo-Jun Max Shen, Junyu Liu
Proceedings of 2022 IEEE/ACM 7th Symposium on Edge Computing (SEC)
abstract
arxiv
proceeding
Quantum computing is expected to have transformative influences on many domains, but its practical deployments on industry problems are underexplored. We focus on applying quantum computing to operations management problems in industry, and in particular, supply chain management. Many problems in supply chain management involve large state and action spaces and pose computational challenges on classic computers. We develop a quantized policy iteration algorithm to solve an inventory control problem and demonstrative its effectiveness. We also discuss in-depth the hardware requirements and potential challenges on implementing this quantum algorithm in the near term. Our simulations and experiments are powered by the IBM Qiskit and the qBraid system.
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Potential Energy Advantage of Quantum Economy
with Junyu Liu, Zuo-Jun Max Shen
Working paper
abstract
arxiv
Energy cost is increasingly crucial in the modern computing industry with the wide deployment of large-scale machine learning models and language models. For the firms that provide computing services, low energy consumption is important both from the perspective of their own market growth and the government's regulations. In this paper, we study the energy benefits of quantum computing vis-a-vis classical computing. Deviating from the conventional notion of quantum advantage based solely on computational complexity, we redefine advantage in an energy efficiency context. Through a Cournot competition model constrained by energy usage, we demonstrate quantum computing firms can outperform classical counterparts in both profitability and energy efficiency at Nash equilibrium. Therefore quantum computing may represent a more sustainable pathway for the computing industry. Moreover, we discover that the energy benefits of quantum computing economies are contingent on large-scale computation. Based on real physical parameters, we further illustrate the scale of operation necessary for realizing this energy efficiency advantage.