Amrani, Hadar; Khmelnitsky, Eugene Optimal division of inventory between depot and bases. (English) Zbl 1411.90010 Nav. Res. Logist. 64, No. 1, 3-18 (2017). Summary: We consider a problem of optimal division of stock between a logistic depot and several geographically dispersed bases, in a two-echelon supply chain. The objective is to minimize the total cost of inventory shipment, taking into account direct shipments between the depot and the bases, and lateral transshipments between bases. We prove the convexity of the objective function and suggest a procedure for identifying the optimal solution. Small-dimensional cases, as well as a limit case in which the number of bases tends to infinity, are solved analytically for arbitrary distributions of demand. For a general case, an approximation is suggested. We show that, in many practical cases, partial pooling is the best strategy, and large proportions of the inventory should be kept at the bases rather than at the depot. The analytical and numerical examples show that complete pooling is obtained only as a limit case in which the transshipment cost tends to infinity. Cited in 5 Documents MSC: 90B05 Inventory, storage, reservoirs 90B06 Transportation, logistics and supply chain management Keywords:inventory control; optimization; supply chain management; transshipments PDFBibTeX XMLCite \textit{H. Amrani} and \textit{E. Khmelnitsky}, Nav. Res. Logist. 64, No. 1, 3--18 (2017; Zbl 1411.90010) Full Text: DOI