两阶段供应链动态分析：切换系统理论视角
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本文标题"Dynamic analysis of a two-stage supply chain—a switched system theory approach"探讨的是供应链动态分析的一个新颖视角，利用切换系统理论来研究一个包含一个零售商和一个分销商的两阶段供应链。该研究聚焦于订单管理策略中的订单-up-to-control政策（Order-Up-To Control, OUTC），即当库存达到预设阈值时，供应商才会进行补货。
作者Hongwei Wang、Huixin Liu 和 Jian-bo Yang在2007年2月提交了研究，并在同年7月29日接受，最终于2008年9月2日在线发表。文章发表在Springer-Verlag London Limited期刊上。研究的核心是构建了一个离散时间状态空间模型，将分销商的能力限制考虑在内，这使得整个供应链成为一个自主切换系统，其行为受分销商的发货策略影响。
论文的核心内容涉及对这种切换系统稳定性进行深入分析，运用了切换系统理论和离散系统控制理论，以便从实际操作角度理解供应链的动态行为。研究发现，由于系统内部的切换机制，系统的动态表现可以呈现出稳定、周期性和发散三种不同的模式，这取决于订单政策参数的选择。
此外，文中还探讨了供应链动态与其成本之间的关系，通过分析揭示了如何通过调整这些参数来优化控制策略，以降低成本并提高效率。关键词包括“供应链”、“库存控制”和“切换”，这些关键词突出了研究的重点和应用领域。
这篇文章不仅提供了一种创新的方法来理解和管理两阶段供应链的动态特性，还为供应链管理者提供了实用的洞察，帮助他们根据具体业务环境调整策略，实现更有效的运营。对于供应链管理和控制理论的发展具有重要意义。
systems and switched arrival systems are some of the
generalized models [23–27]. A more detailed description of
such applications could be found in Morse [28].
The stability of a switched system is a basic problem,
which is affected by two factors: the stability of its
subsystems and the switching rule. The supply chain
syste m investigated in this paper is considered as an
autonomous switched system, and its stability analysis is
decomposed into three parts: analysis of the dynamics of
the linear subsystems, analysis of switching rules, and
analysis of the stability of supply chain under the switching
rules. This analys is method can more easily handle the
stability and dynamics of the system than using t he
nonlinear system theory.
3 Basic dynamic model
3.1 System description
The system under study is a typical cascaded production–
distribution system consisting of two secto rs: a retailer and
a distributor (see Fig. 1 ). Customer demand is exogenous.
Given that stocks are available, each sector must supply the
amount requested by the next sector. If the stocks are
insufficient, surplus orders must be kept in backlog until
deliveries can be made. With the assumption that the
system is a periodic-reviewed supply chain, the sequenc e of
events during a period is, first, the member observes and
satisfies consumer demand if there is no backlog and then
receives goods; next, the member observes the new
inventory level and finally places an order on its supplier.
Based on this arrangement, there is a period from the time
the order is sent until the supplier receives it. Suppose it
takes the distributor l periods to transport goods to the
retailer. The total lead time is then given by L=l+1. To
simplify the model without loss of generality, we assume
that the outside supplier’s lead time is L as well. It is
assumed that the outside supplier has infinite inventory so
that the distributor’s order can be fully satisfied. Cap acity
of the distributor is assumed to be limited. Therefore, he
will satisfy the retailer’s demand based on his inventory
level.
3.2 Block diagram and difference equations of the system
Model notation Hereafter, let r, d,ands denote t he
retailer’s state variables, the distributor’s state variables,
and the outside supplier’s state variables, respectively.
t time period, t=1,2,...;
D(t) the outside demand at time period t
I
i
(t) inventory level of member i at the end of time
period t, i∈ {r,d}, and similarly below
BL
i
(t) backup orders of member i at the end of time
period t
O
i
(t) order quantity of member i at the end of time
period t
R
i
(t) quantity of goods that member i received at the
beginning of time period t
S
i
(t) shipments of mem ber i to its downstream
member at time period t
S
s
(t) shipments of outside supplier to the distributor at
time period t
WIP
i
(t) work in progress of member i at time period t
F
i
(t) forecasted demand of member i in period t
)(tD
)(tO
r
1
Z
l
Z
l
Z
1
Z
α
)(tS
d
1
1
1
z
L
1
1
1
z
0
r
I
β
1
Z
1
1
1
z
1
1
1
z
)(tI
r
)(tWIP
r
+
+
+
+
+
+
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-
-
-
-
-
-
-
-
+
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+
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+
+
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0
d
I
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1
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z
θ
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1
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)(tWIP
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)(tI
d
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d
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r
Distributor
Retailer
)(t
σ
_
_
_
_
_
_
_
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θ
β
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Fig. 2 The block diagram of the supply chain
Fig. 3 The states of the eigenvalues of subsystem 15
202 Int J Adv Manuf Technol (2009) 43:200–210
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