At first glance the Interdistrict shipping problem resembles a transportation problem. N sources with M destinations with k Stock keeping units (SKU’s); however, we want to solve for the optimal shipping frequency between each node while determining the flow of each SKU across the network. As the replenishment quantity goes up, the shipping frequency goes down and the inventory holding cost goes up (AWI = Replenishment Qty/2 + SS). Safety stock also increases as frequency decreases. The relationship between replenishment quantity and shipping frequency is non-linear (frequency = annual demand/replenishment qty). The trucks which are used to transfer the product have finite capacity and the cost to drive the truck between 2 locations is constant regardless of how many containers are actually on the truck up to the max capacity. Each product can have a different footprint of truck capacity. Cross docking is allowed. (i.e. a truck may travel from Loc A to loc B carrying products X and Y. At loc B, the truck unloads product X, picks up product Z, and continues to location C. The key here is that product Y does not incur any handling costs at Loc B while products X and Z do.)
The objective function seeks to minimize the total costs ( distribution + handling + inventory holding costs) for all locations, for all SKU’s, while determining how much of each product should flow across each arc such that all demand is satisfied.