A practical approach to multi-day dynamic pricing in attended home delivery

This paper proposes a sampling-based dynamic pricing approach for attended home delivery (AHD), utilizing approximation methods to improve both calculation efficiency and profitability. First, the pricing mechanism is formulated as a choice-based optimization to reflect individual customer preferences. To account for the sequential arrival of multiple customers, the problem is extended to a Markov decision process (MDP) framework. For practical use, a logistics platform must determine prices within 100 milliseconds to ensure a seamless experience for each customer. However, the computational complexity of vehicle routing combined with future uncertainty regarding multi-day customer choices leads to the curse of dimensionality, making real-time application computationally infeasible. To address these challenges, we introduce area-based (Continuous Approximation and Regression-based) and route-based (Cheapest Insertion) approximation methods. Crucially, a sampling-based approximation is developed to mitigate future uncertainty across multi-day delivery options, thereby overcoming the computational barriers of the MDP framework. The performance of each method is evaluated via simulation, incorporating a nested logit model estimated from large-scale stated choice data to reflect realistic delivery timing preferences. The results show that dynamic pricing outperforms fixed pricing, with all methods meeting the required speed limitations (100 milliseconds). After integrating the sampling-based model, profits increase across all approximation methods. Additionally, we evaluate the model under different cost-scaling factors, slot capacities, and customer preferences. The results show that sampling-based policies generally improve profit, with route-based approximation maintaining the highest average profit across the tested settings. This efficient approach provides a scalable and robust solution for dynamic time slot pricing in real-world logistics platforms.