lifetime-value pricing

This paper addresses dynamic pricing under completely unknown demand functions, aiming to eliminate restrictive parametric assumptions and enhance practical applicability. We propose a nonparametric Bayesian optimization framework based on Gaussian processes (GPs), unifying treatment of both infinite- and finite-horizon inventory settings. The method performs sequential price decisions to balance exploration and exploitation, and—crucially—provides the first theoretical regret bound for this nonparametric setting. Demand uncertainty is modeled via a GP prior, and adaptive price updates are guided by an acquisition function, requiring no assumption on the functional form of demand. Experiments demonstrate that our approach significantly outperforms state-of-the-art reinforcement learning algorithms in cumulative revenue, robustness to demand misspecification, and sample efficiency, validating its effectiveness and practicality in highly uncertain environments.

This study addresses the limitation of conventional e-commerce A/B tests, which often overlook the long-term impact of interventions on profitability across an inventory item’s full lifecycle due to short experimental windows. To overcome this, the authors propose Stock Lifetime Value (SLV), a novel metric that aggregates the expected profit of current inventory over its entire sales horizon within short-term experiments, thereby enabling more accurate assessment of long-term profitability. SLV uniquely integrates inventory constraints and seasonal lifecycle dynamics into the A/B testing framework, combining causal inference with financial mapping to support both item-level and user-level experimentation while aligning with annual financial reporting. Empirical validation at Zalando demonstrates that SLV effectively predicts actual profits over an 18-month horizon, enhances pricing algorithm performance, and delivers interpretable estimates of annual financial impact.

This study addresses the challenges of extreme demand volatility, delayed pricing responses, and misalignment between short-term revenue and long-term profitability during major fashion e-commerce promotions. To tackle these issues, the authors propose a high-frequency “predict–optimize” automated pricing system that breaks away from traditional weekly decision cycles by operating at a minute-level granularity. The system achieves the first industrial-scale deployment of daily multi-objective dynamic pricing in large-scale e-commerce settings, combining gradient-boosted tree models for daily demand forecasting with a multi-objective optimization framework to generate real-time pricing strategies that jointly maximize long-term profit and net merchandise value. Evaluated across 23 A/B tests in 12 Zalando markets from 2023 to 2024, the system delivered approximately 6% higher profit while maintaining sales volume and has since been fully deployed for promotional pricing.

This paper addresses the bi-objective optimization of static threshold-based pricing in price-sensitive queueing systems: simultaneously approximating the maximum average revenue rate and minimizing the average queue length under a fixed-price + truncation admission policy. Motivated by practical constraints that limit dynamic pricing implementation, we establish—for the first time—theoretical bi-objective approximation guarantees for static threshold pricing, thereby challenging the conventional assumption that optimal performance necessitates dynamic pricing. Leveraging stochastic analysis frameworks—Poisson arrivals, exponential service times, and FIFO discipline—we derive performance bounds for the revenue–delay trade-off within M/M/1 and extended models (multi-class customers, multi-server systems). For the M/M/1 system, we achieve joint approximation ratios such as (0.5, 1) and (0.8, 2) for revenue and queue length, respectively, and successfully generalize these results to broader settings.

This paper addresses the Combinatorial Pricing Problem (CPP), a canonical combinatorial bilevel programming problem where a leader sets item tolls to maximize revenue, while a follower solves a combinatorial optimization subproblem subject to the induced cost constraints. To overcome the scalability limitations of conventional value-function-based approaches, we propose the first single-level dual formulation that embeds CPP into a dynamic programming framework. Specifically, we reformulate the follower’s problem as a longest-path problem on a directed acyclic graph and introduce a novel “Selection Diagram” structure—a compact decision diagram encoding feasible follower choices. We further pioneer the integration of decision diagrams with cutting-plane methods for efficient solution. Our approach significantly outperforms state-of-the-art algorithms on three CPP variants and the knapsack interdiction problem, substantially expanding the scale of combinatorial bilevel programs solvable to provable optimality.

This study investigates the performance trade-offs of data-driven approaches in finite-horizon dynamic pricing, with a focus on complex settings involving high-dimensional multi-product offerings, heterogeneous demand structures, and intertemporal revenue constraints. By systematically comparing Fitted Dynamic Programming (Fitted DP) against several reinforcement learning algorithms—integrating demand estimation, trajectory sampling, and expectation-based optimization—the work comprehensively evaluates their relative strengths in terms of revenue generation, stability, constraint satisfaction, and computational scalability. The findings reveal that Fitted DP exhibits superior scalability in structured, complex environments, whereas reinforcement learning demonstrates greater flexibility and adaptability. These insights provide both theoretical grounding and empirical evidence to inform method selection for real-world dynamic pricing systems.

This study addresses the design of optimal pricing mechanisms for data markets under budget-constrained rational buyers. Focusing on scenarios where buyers aim to maximize predictive accuracy by selecting data bundles within a fixed budget, the work proposes a class of monotone continuous pricing functions to maximize total market revenue. Theoretical analysis reveals that the optimal pricing function exhibits a piecewise-linear convex structure, with the number of breakpoints bounded by the number of buyers. While general nonlinear pricing can be solved in polynomial time, linear pricing—despite its apparent simplicity—is shown to be APX-hard, highlighting a striking computational dichotomy. To address this challenge, the paper develops an online 2-approximation algorithm and an offline $(1-1/e)^{-1}$-approximation algorithm, providing foundational insights for pricing theory in data markets.

This work addresses dynamic pricing under capacity constraints, where prediction errors can lead to irreversible inventory loss. Focusing on a setting with linear demand, stochastic noise, and finite inventory, the paper introduces a demand prediction model with bounded error and a proxy model to stabilize pricing through a boundary-attracting mechanism—without requiring non-degeneracy assumptions. Theoretically, it establishes a sharp phase transition: when the prediction error $\varepsilon \lesssim T^{-1/4}$, the regret drops abruptly from $O(\sqrt{T})$ to $O(\log T)$, and this threshold is tight. Furthermore, by integrating control variates, the proxy model reduces estimation variance by a factor of $(1-\rho^2)$. Extensive experiments confirm the algorithm’s robustness and effectiveness across diverse scenarios.