Approximate Dynamic Programming for Delivery Time Slot Pricing: a Sensitivity Analysis

TL;DR

This paper compares approximate dynamic programming algorithms for delivery time slot pricing, demonstrating that gradient-bounded dynamic programming outperforms others in efficiency and profit, especially under parameter uncertainty, based on real-world data.

Contribution

The study introduces and evaluates three approximate dynamic programming algorithms for delivery slot pricing, highlighting the superior performance of gradient-bounded dynamic programming.

Findings

Gradient-bounded dynamic programming outperforms other algorithms in computation time.

It generates higher profit margins in delivery slot pricing.

Uncertainty in model parameters enhances the algorithm's profit advantages.

Abstract

We consider the revenue management problem of finding profit-maximising prices for delivery time slots in the context of attended home delivery. This multi-stage optimal control problem admits a dynamic programming formulation that is intractable for realistic problem sizes due to the so-called "curse of dimensionality". Therefore, we study three approximate dynamic programming algorithms both from a control-theoretical perspective and in a parametric numerical case study. Our numerical analysis is based on real-world data, from which we generate multiple scenarios to stress-test the robustness of the pricing policies to errors in model parameter estimates. Our theoretical analysis and numerical benchmark tests show that one of these algorithms, namely gradient-bounded dynamic programming, dominates the others with respect to computation time and profit-generation capabilities of the delivery slot pricing policies that it generates. Finally, we show that uncertainty in the estimates of the model parameters further increases the profit-generation dominance of this approach.