Abstract: A computer-implemented method includes receiving a list of items in a purchase order and accessing inventories of items available at each location. The functioning of the computer is improved by reducing the number of combinations of locations and items that must be considered to find a combination of locations and items that provides a lowest total fulfillment cost through steps that begin with identifying all combinations of the items in the list of items. For each combination, a location that can ship that combination at a lowest fulfillment cost is identified. A fulfillment superset is selected that is formed from one or more combinations, provides all of the items in the list of items and has a lowest total fulfillment cost.