OPTIMIZED MULTI-ECHELON INVENTORY P

OPTIMIZED MULTI-ECHELON INVENTORY POLICIES IN ROBUST
DISTRIBUTION NETWORKS
Dr.-Ing. Katja Klingebiel Cong Li
Chair of Factory Organization Department of Supply Chain Engineering
Technical University of Dortmund Fraunhofer Institute for Material Flow and Logistics
Leonhard-Euler-Str. 5 Joseph-von-Fraunhofer Straße 2-4
44227 Dortmund, Germany 44227 Dortmund, Germany
katja.klingebiel@tu-dortmund.de cong.li@iml.fraunhofer.de
KEYWORDS
Supply Chain Management, Multi-Echelon Distribution
Networks, Inventory Policy, Robustness, Optimization,
Simulation
ABSTRACT
To cope with current turbulent market demands, more
robust inventory policies are needed for distribution
networks, to lower the inventory cost as well as
maintain high responsiveness. This paper analyzes the
inventory policies in the context of complex multiechelon distribution networks and proposes an
optimization and simulation integrating approach to
robust inventory policies selection for multi-echelon
distribution networks. Based on the existing
approximation approaches designed primarily for twoechelon inventory model, an analytical multi-echelon
inventory model with an efficient optimization
algorithm is presented. Through systematic parameter
adjustment, “optimal” inventory policies are suggested
by this model. In the next step, a simulation model is
applied to evaluate the proposed solutions under market
dynamics, so that the most favorable ones may be
selected. Finally, a case study is conducted and future
research directions are suggested.
1 INTRODUCTION
As collaboration between different supply chain
echelons gains attention, it is imperative to consider
inventory policies from a network perspective rather
than supposing each stage to be a single isolated player.
Moreover, under current market dynamics, the level of
customer demand uncertainty itself has significantly
increased, which immensely aggravates the difficulty of
demand forecasting. And product trends like larger
variety and shorter life cycles have intensified
uncertainty.
Yet, “optimal” inventory policies obtained through
traditional approaches are based on deterministic and
stable conditions. They are not capable of delivering the
desired results in real situation, or even greatly
deteriorate the performance of the entire supply chain,
leading to high stock levels or short sales. Thus, to cope
with current turbulent market demands, more robust
inventory policies are needed for distribution networks,
so as to lower the inventory cost as well as maintain
high responsiveness. In this paper we propose an
optimization and simulation integrating approach to
robust multi-echelon inventory policies selection.
The paper is organized as follows: Section 2 reviews the
important multi-echelon inventory models and
optimization solutions. Section 3 presents our integrated
approach, which integrates simulation into the
traditional analytical inventory model. The analytical
model is presented and discussed in detail in section 4,
including model formulation, model calculation and
optimization algorithm. The simulation model is
described in section 5. The proposed integrated
approach is then applied to an industrial case in section
6. Finally, section 7 concludes the current work and
provides directions for further research.
2 LITERATURE REVIEW
An overview of the fundamental ideas about problem
assumptions, model designs and solution approaches of
inventory policies for one- or multi- echelon logistic
networks has been presented by Zipkin (2000), Axsäter
(2006) and Tempelmeier (2006). For the inventory
models with stochastic lead time in multi-echelon
distribution networks, which is also our research
emphasis, Axsäter (2003b) has provided a quite
comprehensive review. Starting from the early famous
METRIC model presented by Sherbrooke (1968),
numerous literatures have been devoted to this research
area, among which pioneering research is conducted by
Graves (1985), Svoronos and Zipkin (1988), Axsäter
(1990, 1993, 1998, 2000) , Kiesmüller and Kok (2005).
Apart from the classical multi-echelon model, Dong and
Chen (2004) developed a network of inventory-queue
models for the performance modeling and analysis of an
integrated logistic network. Simchi-Levi and Zhao
(2005) derived recursive equations to characterize the
dependencies across different stages in the supply chain
network. Miranda and Garrido (2009) dealt inventory
decisions simultaneously with network design decisions
while Kang and Kim (2010) focused on the coordination
of inventory and transportation management.
Although great attention has been paid to the analytical
model of distribution networks, its application in the
optimization field is still strongly restricted because of
the modeling complexity and computational
Proceedings 25th European Conference on Modelling and
Simulation ©ECMS Tadeusz Burczynski, Joanna Kolodziej
Aleksander Byrski, Marco Carvalho (Editors)
ISBN: 978-0-9564944-2-9 / ISBN: 978-0-9564944-3-6 (CD)
requirement in large scale inventory networks.
Therefore, various approximation methods and heuristic
algorithms have been suggested by researchers for real
world applications.
Of note in this context is the work of Cohen et al.
(1990), who developed and implemented a system
called Optimizer that determined the inventory policies
for each part at each location in IBM’s complex
network with assumptions of deterministic lead time
and ample supply. Caglar et al. (2004) developed a
base-stock policy for a two-stage, multi-item spare part
inventory system and presented a heuristic algorithm
based on METRIC approximation and single-depot sub
problem to minimize the system-wide inventory cost
subject to a response time constraint at each field depot.
Al-Rifai and Rossetti (2007) formulated an iterative
heuristic optimization algorithm to minimize the total
annual inventory investment subject to annual ordering
frequency and backorder number constraints. Their
approach can be regarded as the further work of Hopp et
al. (1997), who utilized ሺܴǡ ܳሻ policies and presented
three heuristic algorithms based on simplified
representations of the inventory and service expressions
to optimize the same inventory problem in a single stage.
Axsäter (2003a) used normal approximations both for
the customer demand and retailer demand to solve the
general two-stage distribution inventory system. Axsäter
(2005) considered a different approach to decompose
the two-stage inventory problems. Through providing
an artificial unit backorder cost of the warehouse, its
optimal inventory policy can be solved first.
From the above analysis, it may be deduced that multiechelon inventory models have been analyzed
extensively in recent years. However, computational
scale, integrity and non-convexity make the
corresponding optimization problem intractable to exact
analysis and up till now no general approach is accepted,
which might also explain why two-echelon networks are
mostly dealt with. In response to such difficulties, an
efficient optimization solution procedure will be
presented in this paper, which optimizes inventory
policies in a general multi-item, multi-echelon
distribution network.
3 INTEGRATED APPROACH
It is one task to develop a multi-echelon inventory
model for distribution networks and solve
mathematically. We will present a model of that kind in
section 4. However, even the most delicate model forces
abstraction of reality and involves some kinds of
simplification or approximation. Besides, as mentioned
above, the computational efficiency decreases
dramatically with the complexity of the analytical
model, so the real world application of these
sophisticated models has been greatly limited in the past.
Fortunately, these deficiencies can be compensated to a
large extent by simulation models, as they allow to
reproduce and to test different decision-making
alternatives (e.g. inventory policies) upon several
anticipated supply chain scenarios (e.g. forecasted
demand development). This allows ascertaining the
level of optimality and robustness of a given strategy in
advance (Terzi and Cavalieri, 2004). Nevertheless,
simulation itself can provide only what-if analysis. Even
for a small-sized problem, there exist large numbers of
possible alternatives, making exhaustive simulation
impossible.
Thus, a simulation model can and should be integrated
with analytical models. Through systematic adjustment
of input parameters, a limited set of “optimal”
alternatives may be derived from the analytical model.
After simulating these inventory policies under realistic
environment (e.g. dynamic and stochastic volatile
customer demand), their performance level (e.g.
inventory cost, fill rate) can be evaluated and consulted
for decision making. The schematic diagram of such an
integrated approach is shown in Figure 1.
Figure 1: Integrated Approach to Inventory Policy
Selection
However, a problem arises when all the suggested
alternatives have not fulfilled the desired expectation.
One of our answers is to reconfigure the input
parameters of the analytical model based on the
simulation result (dotted line in Figure 1), and then to
restart the optimization process and simulation, so that a
closed feedback loop is formed. Such reconfigurations,
although feasible, is not quite easy to maintain, because
the analytical model is an abstraction of real world. No
matter how sophisticated, the “optimal” alternatives
obtained from it can act only as a reference or starting
point. Thus, it is not wise to look for robust inventory
policies merely through analytical optimization. Other
approaches, which integrate optimization and simulation
more closely, should be introduced to deal with this
problem, but are not discussed here.
4 ANALYTICAL MODEL
4.1 Model Formulation
The distribution network is represented as a multiechelon inventory model comprising several
warehouses in each stage and multiple stock points in
each warehouse. Each warehouse is supposed to sto