We study a system in which a common delivery fleet provides service to both same-day delivery (SDD) and next-day delivery (NDD) orders placed by e-retail customers who are sensitive to delivery prices. We develop a model of the system and optimize with respect to two separate objectives. First, empirical research suggests that fulfilling e-retail orders ahead of promised delivery days increases a firm's long-run market share. Motivated by this phenomenon, we optimize for customer satisfaction by maximizing the quantity of NDD orders fulfilled one day early given fixed prices. Next, we optimize for total profit by setting prices in a two-level scheme with discounts for early-ordering customers. Our analysis relies on continuous approximation techniques to capture the interplay between NDD and SDD orders, and particularly the effect one day's operations have on the next, a novel modeling component not present in SDD-only models; a key technical result is establishing the model's convergence to a steady state using dynamical systems theory. We derive structural insights and efficient algorithms for both objectives. In particular, we show that, under certain conditions, the total profit is a piecewise-convex function with polynomially-many breakpoints that can be efficiently enumerated. We validate our model's results via simulation on a case study derived from real-world data.
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