Convexity and feedback in approximate dynamic programming for delivery time slot pricing

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 socalled “curse of dimensionality”. Therefore, we study three approximate dynamic programming algorithms both from a control-theoretical perspective and numerically. 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 dynamic programming, dominates the others with respect to computation time and profit-generation capabilities of the pricing policies that it generates