Convexity and Feedback in Approximate Dynamic Programming for Delivery Time Slot Pricing

We consider the revenue management problem of finding profit-maximizing prices for delivery time slots in the context of attended home delivery. This multistage optimal control problem admits a dynamic programming (DP) formulation that is intractable for realistic problem sizes due to the so-called “curse of dimensionality.” We therefore study three approximate DP algorithms both from a numerical and control-theoretical perspective. Our 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 indicate that one of these algorithms, namely gradient-bounded DP, dominates the others with respect to computation time and profit-generation capabilities of the pricing policies that it generates.