This paper shows how distribution problems with delivery time constraints can be modeled approximately with just a few variables. Its objective is neither to develop a scheduling algorithm nor an exact predictive method; rather, it is to illustrate some trade-offs and principles that can be used for planning and algorithm development. A workday is divided into time periods. Time windows are modeled by specifying the period in which a vehicle should visit each customer. (The companion paper explores scenarios where many customers do not specify a time window, and thus, it is advantageous not to allocate all the customers to periods.) Travel distance expressions are provided for a “cluster-first, route-second” strategy, similar to some routing methods currently in use. Travel distance expressions are also provided for refinements of the strategy, including one in which tours are systematically staggered, overlapping. The consequent reductions in travel distance can be quite significant. We suggest here that more attention should be paid to the clustering part of algorithm construction, and point to ways in which the customers served by one vehicle should be selected.