AdONE Seminar: Prof. Willem van Jaarsveld (TU Eindhoven)

Fulfilling online orders quickly is increasingly vital in e-commerce, with many companies offering same-day shipment services to meet rising customer expectations. However, companies risk overpromising these services when shipment options and fees are not aligned with their fulfillment capabilities, which can lead to delays and customer dissatisfaction. To address this issue, shipment options and fees should be adapted based on the time remaining for the fulfillment center to collect and ship orders.
We develop a parsimonious model of a fulfillment center operating under such a transparent, time-dependent shipment policy. In our model, utility-maximizing customers arrive according to a Poisson process, and processing capacity is stochastic. We present an exact steady-state performance analysis based on the underlying periodic Markov chain and establish structural properties of the optimal shipment policy. Our results show that expected profit increases when introducing a cutoff point for the same-day shipment option and when switching from a constant fee to a time-dependent fee that rises as the shipping deadline approaches. We prove that an optimal policy exists with monotonically increasing fees for same-day shipment. By transforming the problem domain to analyze shipment fees through the lens of cumulative demand profiles, we further demonstrate that expected profit is supermodular, which enables us to compute the optimal shipment policy in polynomial time.
Motivated by its practical appeal, we propose a two-level time-dependent shipment policy that differentiates between two fees for same-day shipment. Numerical experiments show that this policy achieves near-optimal performance and substantially outperforms benchmark policies currently used in practice, which rely on time-independent fees.
From a managerial perspective, our findings highlight that e-commerce companies can better manage demand for same-day and next-day shipment by implementing transparent time-dependent policies. Such policies not only align with operational constraints but also provide a simple and customer-friendly approach to balancing capacity and service quality.