LSMS2010 AND ICSEE 2010
A hybrid genetic algorithm for two-stage multi-item inventory
system with stochastic demand
Yuli Zhang
•
Shiji Song
•
Heming Zhang
•
Cheng Wu
•
Wenjun Yin
Received: 26 October 2010 / Accepted: 20 May 2011
Springer-Verlag London Limited 2011
Abstract We study a two-stage, multi-item inventory
system where stochastic demand occurs at stage 1, and
nodes at stage 1 replenish their inventory from stage 2. Due
to the complexity of stochastic inventory optimization in
multi-echelon system, few analytical models and effective
algorithms exist. In this paper, we establish exact stochastic
optimization models by proposing a well-defined supply–
demand process analysis and provide an efficient hybrid
genetic algorithm (HGA) by introducing a heuristic search
technique based on the tradeoff between the inventory cost
and setup cost and improving the initial solution. Monte
Carlo method is also introduced to simulate the actual
demand and thus to approximate the long-run average cost.
By numerical experiments, we compare the widely used
installation policy and echelon policy and show that when
variance of stochastic demand increase, echelon policy
outperforms installation policy and, furthermore, the pro-
posed heuristic search technique greatly enhances the
search capacity of HGA.
Keywords Multi-echelon inventory
Stochastic demand Heuristic search
Hybrid genetic algorithm Monte Carlo method
1 Introduction
Supply chain management, which is the approach to inte-
grate the material suppliers, manufacturers, wholesalers,
and retailers and control the material flow from the upstream
to the ultimate customers, has been a crucial technique to
minimize the total system-wide costs in practice. Inventory
control has been proved to be critical in determining the
profit of manufacturing firms, since inventory system
usually represents from 20 to 60% of the total assets [1]. In
production and distribution systems, items at different
stages, such as raw material, semi-product, and product, are
often distributed at different warehouses and flow from one
stage to the next. The objective of multi-stage inventory
control is to distribute the items at different stage at the right
quantities, to the right locations and at the right time, in
order to minimize the total costs while satisfying service-
level requirements.
Multi-stage inventory control problems have been
studies for decades, and modern information technology,
such as electronic data interchange (EDI), has created new
possibility for more sophisticated control polices. For
example, the echelon inventory policy, under which the
reorder point and order quantity of a warehouse are
determined by the whole inventory on its hand and at its
downstream stages, makes full use of the information
exchange between the members in the inventory system.
On the basis of network structure, the studies on the
multi-stage inventory control issues can be categorized into
several groups, such as series system, assembly system,
distribution system, tree system, and fully general net-
worked system. The simplest structure is the series system,
in which each location only supplies the next one, only the
first upstream stage receives supply from outside the
system and only the last one meets exogenous customer
Y. Zhang S. Song (&) H. Zhang C. Wu
Department of Automation, TNList, Tsinghua University,
Beijing 100084, China
e-mail: shijis@mail.tsinghua.edu.cn
Y. Zhang
e-mail: yl-zhang08@mails.tsinghua.edu.cn
W. Yin
IBM China Research Lab, Beijing 100084, China
123
Neural Comput & Applic
DOI 10.1007/s00521-011-0658-7