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

56 Pages Posted: 23 Feb 2017 Last revised: 21 Feb 2019

See all articles by Han Zhu

Han Zhu

Desautels Faculty of Management, McGill University

Frank Chen

City Univ. of Hong Kong - Dept of Management Scienes; City University of Hong Kong - Dept of Management Sciences

Ming Hu

University of Toronto - Rotman School of Management

Yi Yang

School of Management, Zhejiang University

Date Written: February 15, 2019

Abstract

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

Zhu, Han and Chen, Frank Y. and Hu, Ming and Yang, Yi, A Simple Heuristic Policy for Stochastic Distribution Inventory Systems with Fixed Shipment Costs (February 15, 2019). Rotman School of Management Working Paper No. 2921743. Available at SSRN: https://ssrn.com/abstract=2921743 or http://dx.doi.org/10.2139/ssrn.2921743

Han Zhu

Desautels Faculty of Management, McGill University ( email )

1001 Sherbrooke St. West
Montreal, Quebec H3A1G5 H3A 2M1
Canada

Frank Y. Chen

City Univ. of Hong Kong - Dept of Management Scienes ( email )

Kowloon Tong
Hong Kong

City University of Hong Kong - Dept of Management Sciences ( email )

Kowloon Tong
Hong Kong

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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