Interpretable Price Bounds Estimation with Shape Constraints in Price Optimization

TL;DR

This paper proposes a comprehensive framework for estimating and adjusting interpretable price bounds in price optimization, incorporating shape constraints to ensure practical applicability in real-world scenarios.

Contribution

It introduces a novel method combining historical data-based estimation with shape-constrained optimization for realistic price bounds.

Findings

Effective price bounds estimation from historical data

Shape constraints improve interpretability and practicality

Numerical experiments validate the approach

Abstract

This study addresses the interpretable estimation of price bounds in the context of price optimization. In recent years, price-optimization methods have become indispensable for maximizing revenue and profits. However, effective application of these methods to real-world pricing operations remains a significant challenge. It is crucial for operators responsible for setting prices to utilize reasonable price bounds that are not only interpretable but also acceptable. Despite this necessity, most studies assume that price bounds are given constant values, and few have explored reasonable determinations of these bounds. Therefore, we propose a comprehensive framework for determining price bounds that includes both the estimation and adjustment of these bounds. Specifically, we first estimate price bounds using three distinct approaches based on historical pricing data. Then, we adjust the estimated price bounds by solving an optimization problem that incorporates shape constraints. This method allows the implementation of price optimization under practical and reasonable price bounds suitable for real-world applications. We report the effectiveness of our proposed method through numerical experiments using historical pricing data from actual services.