Solving Data-Driven Newsvendor Pricing Problems with Decision-Dependent Effect

TL;DR

This paper develops an Approximate Gradient Descent algorithm to solve complex data-driven newsvendor pricing problems with decision-dependent effects, demonstrating convergence and effectiveness through numerical experiments.

Contribution

It introduces the concept of approximate gradients and an AGD algorithm for decision-dependent pricing models, extending solutions to non-convex and real-world scenarios.

Findings

AGD converges to local maxima when approximation is effective

Decision-dependent effects are crucial for accurate modeling

Model is distribution-free and applicable to various decision-dependent problems

Abstract

This paper investigates the data-driven pricing newsvendor problem, which focuses on maximizing expected profit by deciding on inventory and pricing levels based on historical demand and feature data. We first build an approximate model by assigning weights to historical samples. However, due to decision-dependent effects, the resulting approximate model is complicated and unable to solve directly. To address this issue, we introduce the concept of approximate gradients and design an Approximate Gradient Descent (AGD) algorithm. We analyze the convergence of the proposed algorithm in both convex and non-convex settings, which correspond to the newsvendor pricing model and its variants respectively. Finally, we perform numerical experiment on both simulated and real-world dataset to demonstrate the efficiency and effectiveness of the AGD algorithm. We find that the AGD algorithm can converge to the local maximum provided that the approximation is effective. We also illustrate the significance of two characteristics: distribution-free and decision-dependent of our model. Consideration of the decision-dependent effect is necessary for approximation, and the distribution-free model is preferred when there is little information on the demand distribution and how demand reacts to the pricing decision. Moreover, the proposed model and algorithm are not limited to the newsvendor problem, but can also be used for a wide range of decision-dependent problems.