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We consider the revenue management problem of finding profit-maximisingprices for delivery time slots in the context of attended home delivery. Thismulti-stage optimal control problem admits a dynamic programming formulationthat is intractable for realistic problem sizes due to the so-called "curse ofdimensionality". Therefore, we study three approximate dynamic programmingalgorithms both from a control-theoretical perspective and in a parametricnumerical case study. Our numerical analysis is based on real-world data, fromwhich we generate multiple scenarios to stress-test the robustness of thepricing policies to errors in model parameter estimates. Our theoreticalanalysis and numerical benchmark tests show that one of these algorithms,namely gradient-bounded dynamic programming, dominates the others with respectto computation time and profit-generation capabilities of the delivery slotpricing policies that it generates. Finally, we show that uncertainty in theestimates of the model parameters further increases the profit-generationdominance of this approach.

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