Modified Echelon (r, Q) Policies with Guaranteed Performance Bounds for Stochastic Serial Inventory Systems

41 Pages Posted: 17 Jun 2012 Last revised: 19 Mar 2014

See all articles by Ming Hu

Ming Hu

University of Toronto - Rotman School of Management

Yi Yang

School of Management, Zhejiang University

Date Written: December 24, 2013

Abstract

We consider the classic continuous-review N-stage serial inventory system with a homogeneous Poisson demand arrival process at the most downstream stage (Stage 1). Any shipment to each stage, regardless of its size, incurs a positive fixed setup cost and takes a positive constant leadtime. The optimal policy for this system under the long-run average cost criterion is unknown. Finding a good worst-case performance guarantee for this problem remains an open problem. We tackle this problem by introducing a class of modified echelon (r, Q) policies that do not require Q_{i 1}/Q_i to be a positive integer: Stage i 1 ships to Stage i based on its observation of the echelon inventory position at Stage i; if it is at or below r_i and Stage i 1 has positive on-hand inventory, then a shipment is sent to Stage i to raise its echelon inventory position to r_i Q_i as close as possible. We construct a heuristic policy within this class of policies, which has the following features: First, it has provably primitive-dependent performance bounds. In a two-stage system, the performance of the heuristic policy is guaranteed to be within (1 K_1/K_2) times of the optimal cost, where K_1 is the downstream fixed cost and K_2 is the upstream fixed cost. We also provide an alternative performance bound, which depends on efficiently-computable optimal (r, Q) solutions to N single-stage systems, but tends to be tighter. Second, the heuristic is simple, efficiently computable and numerically performs well, likely to even outperform the optimal integer-ratio echelon (r,Q) policies when K_1 is dominated by K_2. Third, the heuristic is asymptotically optimal, as we take some dominant relationships, between the setup or holding cost primitives at an upstream stage and its immediate downstream stage, to the extreme, e.g., when h_2/h_1\rightarrow0, where h_1 is the downstream holding cost parameter and h_2 is the upstream holding cost parameter.

Keywords: Inventory, Multi-Echelon, Stochastic Demand, Performance Guarantee, Control Policy, (r,Q) Policy

Suggested Citation

Hu, Ming and Yang, Yi, Modified Echelon (r, Q) Policies with Guaranteed Performance Bounds for Stochastic Serial Inventory Systems (December 24, 2013). Available at SSRN: https://ssrn.com/abstract=2085156 or http://dx.doi.org/10.2139/ssrn.2085156

Ming Hu (Contact Author)

University of Toronto - Rotman School of Management ( email )

105 St. George st
Toronto, ON M5S 3E6
Canada
416-946-5207 (Phone)

HOME PAGE: http://ming.hu

Yi Yang

School of Management, Zhejiang University ( email )

38 Zheda Road
Hangzhou, Zhejiang 310058
China

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