Who has access to e-commerce and when? Time-varying service regions in same-day delivery

We study the design of same-day delivery (SDD) systems under the assumption that service regions are allowed to vary over the course of the day; equivalently, that customers in different locations may have access to SDD for different lengths of time over the service day or may have no access at all. This contrasts with the bulk of the literature, in which a service region is defined in advance and all customers in the service region can place SDD orders during the same time window. Leveraging continuous approximation techniques to capture average-case system behavior, we derive optimal service region areas and corresponding SDD order cutoff times to maximize the expected number of orders served per day. We quantify the benefit of allowing the service regions to vary, both theoretically and empirically, and discuss related equity issues in SDD systems. We illustrate and validate our results with a case study set in the Phoenix, Arizona metropolitan area.