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

Abstract

We study a classic one-warehouse multi-retailer distribution system, in which any inventory replenishment at each location incurs a fixed-plus-variable cost and takes a constant lead time. The optimal policy is unknown and even if it exists, must be extremely complicated. The goal of this paper is to identify an easy-to-compute heuristic policy within the class of modified echelon (r, Q) policies that does not require an integer-ratio property or a synchronized, nested ordering property, yet has certain performance bounds. We first develop a cost upper bound for any given modified echelon (r, Q) policy. Computation of the bound does not require an exact evaluation of the system-wide cost, which is notoriously difficult. We next adopt parameters of the heuristic by minimizing the cost upper bound, which is equivalent to solving a set of independent single-stage (r, Q) systems. With a cost lower bound that has been established in the literature, we then develop easy-to-compute performance bounds for the heuristic policy. Finally, using those bounds, we show that the proposed modified echelon (r, Q) heuristic policy is asymptotically optimal as a pair of system parameters is scaled up, e.g., when the ratios of the fixed cost of the warehouse over those of the retailers become large. Numerical study demonstrates that our proposed heuristic performs well and tends to outperform the echelon-stock (r, nQ) heuristic policy studied in the literature.