A Simple Heuristic Policy for Stochastic Distribution Inventory Systems with Fixed Shipment Costs
56 Pages Posted: 23 Feb 2017 Last revised: 21 Feb 2019
Date Written: February 15, 2019
We study a continuous-review, two-echelon inventory system with one central warehouse and multiple local facilities, with each facility facing random demand. This is known as the classic one-warehouse multi-retailer distribution system, and becomes more prevalent, as e-retailers are setting up urban facilities, replenished from a distribution center, to fulfill orders from urban consumers more rapidly. Local facilities (retailers or urban facilities) replenish their stock from the central facility (warehouse or distribution center), which in turn places orders at an outside supplier with an unlimited supply. Inventory replenishment at each location incurs a fixed-plus-variable cost for each shipment and takes a constant lead time. 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, which do not require a nested integer-ratio property or a synchronized ordering property. 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 approaches infinity, a performance bound converges to a primitive-dependent constant. The numerical study demonstrates that our proposed heuristic is often near optimal and outperforms the echelon-stock $(r, Q)$ heuristic policy in the literature.
Keywords: Multi-echelon, Distribution system, Stochastic demand, Performance evaluation, (r, Q) policy
Suggested Citation: Suggested Citation