Inventory mirroring in a heterogeneous fulfillment network

A method being implemented via execution of computing instructions configured to run at one or more processors and stored at one or more non-transitory computer-readable media, the method comprising:

• in a fulfillment network, the fulfillment network comprising a plurality of distribution centers, determining, by solving an integer programming formulation, a solution value for a number of clusters (k), wherein each cluster of the number of clusters (k) comprises two or more distribution centers (f) of the plurality of distribution centers, wherein the solution value for the number of clusters (k) is configured to minimize a sum of a total shipping cost (ci) of each distinct item (i), subject to a total distinct item capacity (M) of the plurality of distribution centers in the fulfillment network, wherein the two or more distribution centers (f) are heterogeneous such that the two or more distribution centers (f) have one or more different capacities, and wherein the integer programming formulation is solved using the one or more processors by:
• obtaining a first set of rules using a binary variable to determine whether to mirror the each distinct item (i) of a set of distinct items in the number of clusters (k);
• obtaining a second set of rules to determine a size (N) of the set of distinct items;
• obtaining a third set of rules capping a maximum number of slots available in the number of clusters (k);
• generating a shipping cost resulting from stocking the each distinct item (i) at the number of clusters (k);
• and
• applying the shipping cost to minimize the total shipping cost (ci) for the each distinct item (i);
• determining a probability for each distribution center of the two or more distribution centers (f) to be selected from within the each cluster of the number of clusters (k), wherein the each distribution center is associated with a particular SKU of the each distinct item (i), wherein the probability that a particular one of the two or more distribution centers (f), is selected is a function of a SKU capacity of the two or more distribution centers (f) in a particular cluster of the number of clusters (k), and wherein determining the probability of the each distribution center being associated with the particular SKU of the each distinct item (i) is based on dividing a particular SKU capacity of the each distribution center by a capacity of the each cluster of the two or more distribution centers (f);
• and
• stocking the plurality of distribution centers based at least in part on the probability determined for the each distribution center as a function of the SKU capacity of the two or more distribution centers (f).