An approximate dynamic programming approach to attended home delivery management

We propose a new method of controlling demand through delivery time slot pricing in attended home delivery management with a focus on developing an approach suitable for industry-scale implementation. To this end, we exploit a relatively simple yet effective way of approximating delivery costs by decomposing the overall delivery problem into a collection of smaller, area-specific problems. These cost estimations serve as inputs into an approximate dynamic programming method that provides estimates of the opportunity cost associated with having a customer from a specific area book delivery in a specific time slot. These estimates depend on the area and on the delivery time slot under consideration. Using real, large-scale industry data, we estimate a demand model including a multinomial logit model of customers’ delivery time slot choice, and show in simulation studies that we can improve profits by over two percent in all tested instances relative to using a fixed-price policy commonly encountered in e-commerce. These improvements are achieved despite making strong assumptions in estimating delivery cost. These assumptions allow us to reduce computational run-time to a level suitable for real-time decision making on delivery time slot feasibility and pricing. Our approach provides quantitative insight into the importance of incorporating expected future order displacement costs into opportunity cost estimations alongside marginal delivery costs.