Lot-sizing algorithm for a coordinated multi-item, multi-source distribution problem

Consider a distribution problem consisting of several warehouses or production facilities. A production facility produces one or more items distributed to several retailers. A retailer may receive supplies from any number of production facilities. External demands for items are constant, continuous, and deterministic. Each facility has a fixed set-up cost, and incurs echelon holding cost for any unused stock. A product-nested replenishment policy whose cost is less than 2% above the cost of all feasible policies is determined. The complexity of the solution algorithm is shown to be O(ℝWℝ⁴ℝDℝlogℝDℝ) where ℝWℝ and ℝDℝ are the number of warehouses and items, respectively.