Same-day or next-day? Transparent time-dependent shipment pricing for e-fulfillment

Abstract

We develop a parsimonious model of an e-commerce fulfillment center that offers time-dependent shipment options and corresponding fees to utility-maximizing customers arriving according to a Poisson process. For any such policy, we provide an exact steady-state analysis using the underlying periodic Markov chain to characterize system performance. Because shipment fees shape both the volume and timing of same-day demand, direct optimization over the price domain is analytically intractable. To enable structural and computational insights, we introduce a transformation that maps each shipment-fee policy to its induced cumulative demand profile. This reformulation reveals that the optimal policy features a cutoff time and monotonically increasing fees, and it yields a supermodular profit function that can be optimized in polynomial time. We also propose a simple two-level time-dependent fee structure that is intuitive for customers and achieves near-optimal performance. Numerical experiments show that introducing a cutoff time substantially improves profits under static fees, and that using time-dependent fees produces further significant gains. Overall, transparent time-dependent shipment policies help firms align same-day demand with fulfillment capacity while maintaining transparency and fairness for customers.