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Electric vehicle routing problems can be particularly complex when recharging must be performed mid-route. In some applications such as the e-commerce parcel delivery truck routing, however, mid-route recharging may not be necessary because of constraints on vehicle capacities and maximum allowed time for delivery. In this study, we develop a mixed-integer optimization model that exactly solves such a time-constrained capacitated vehicle routing problem, especially of interest to e-commerce parcel delivery vehicles. We compare our solution method with an existing metaheuristic and carry out exhaustive case studies considering four U.S. cities -- Austin, TX; Bloomington, IL; Chicago, IL; and Detroit, MI -- and two vehicle types: conventional vehicles and battery electric vehicles (BEVs). In these studies we examine the impact of vehicle capacity, maximum allowed travel time, service time (dwelling time to physically deliver the parcel), and BEV range on system-level performance metrics including vehicle miles traveled (VMT). We find that the service time followed by the vehicle capacity plays a key role in the performance of our approach. We assume an 80-mile BEV range as a baseline without mid-route recharging. Our results show that BEV range has a minimal impact on performance metrics because the VMT per vehicle averages around 72 miles. In a case study for shared-economy parcel deliveries, we observe that VMT could be reduced by 38.8\% in Austin if service providers were to operate their distribution centers jointly.