The New Era of Dynamic Pricing: Synergizing Supervised Learning and Quadratic Programming

TL;DR

This paper addresses dynamic pricing for car rentals by integrating supervised learning with quadratic programming to maximize margins under demand and elasticity uncertainty. It builds a simulation environment where baseline price $P_b = \frac{1}{N} \sum p_i$ and features $F$ drive forecasts via LSTM and elasticity models, using price randomization to address endogeneity. Elasticity forecasts feed a QP with objective $\max_{\Delta P} \mathbb{E}[M] - \lambda \mathrm{Var}[M]$ under capacity and price-change constraints, incorporating explicit risk terms. The approach yields a transparent, scalable framework with daily re-optimization and potential margin gains in volatile markets.

Abstract

In this paper, we explore a novel combination of supervised learning and quadratic programming to refine dynamic pricing models in the car rental industry. We utilize dynamic modeling of price elasticity, informed by ordinary least squares (OLS) metrics such as p-values, homoscedasticity, error normality. These metrics, when their underlying assumptions hold, are integral in guiding a quadratic programming agent. The program is tasked with optimizing margin for a given finite set target.

Figures (1)

• Figure 1: utilization risk as an area under the normal pdf.