Technical Note–A Simple Heuristic Policy for Stochastic Distribution Inventory Systems with Fixed Shipment Costs

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Original languageEnglish
Pages (from-to)1651–1659
Journal / PublicationOperations Research
Issue number6
Online published25 Mar 2021
Publication statusPublished - Nov 2021


We study a continuous-review, two-echelon inventory system with one central warehouse, multiple local facilities, and each facility facing random demand. Local facilities replenish their stock from the central warehouse (or distribution center), which in turn places orders at an outside supplier with ample supply. Inventory replenishment at each location incurs a fixed-plus-variable cost for each shipment. The optimal policy remains unknown, and even if it exists, such a policy must be extremely complicated. Instead, we evaluate a class of easy-to-implement heuristics, called modified echelon (r, Q) policies. The parameters for such a heuristic are obtained by solving a set of independent single-stage systems. We show that the proposed policy is asymptotically optimal, as pairs of system primitives, such as the ratios of the fixed cost of the central facility to those of the local facilities, are scaled up. We also show that as the number of retailers grows, the performance bound of the heuristic converges to a primitive-dependent constant.

Research Area(s)

  • multi-echelon, distribution system, stochastic demand, performance bound, (r, Q) policy