J. Service Science & Management, 2009, 2: 129-135
Published Online June 2009 in SciRes (www.SciRP.org/journal/jssm)
A Modeling Framework for the Planning of Strategic
Supply Chain Viewed from Complex Network
Jiangbo Zheng
School of management, Jinan University, Guangzhou, China.
Received February 18th, 2009; revised April 1st, 2009; accepted May 4th, 2009.
ABSTRACT
Based on the theory of complex network, this paper focuses on the planning of logistics nodes for strategic supply chain.
I propose a practical mathematical modeling framework that simultaneously captures many practical aspects but still
understated in the existing literatures of network planning problems. Moreover, capacity expansion and reduction sce-
narios are also analyzed as well as modular capacity shifts for the fluctuation of demands. So this paper is of impor-
tance for the research of network planning in strategic supply chain systems.
Keywords: strategic supply chain, logistics nodes, complex network
1. Introduction
With the increasingly competitive situation, enterprises
have to face the changes of their internal operation mode
and external supply chain mode for higher efficiency and
lower operational costs. Different from traditional supply
chains, a strategic supply chain emphasizes on the opti-
mization of all resources and the coordinate development
of the allies based on their core competences. What’s
more, a strategic supply chain is also different from the
integrated supply chain, which mainly emphasizes on the
overall control of the upstream and downstream of the
supply chain and unilaterally pursues the stability of the
chain. Therefore, strategic supply chain is a neutral
competitive mode which focuses on the integration of
allies’ core competences and is of such great features as
coordination, agility and difference. Under strategic sup-
ply chain mode, the coordination among the allies is
more intimate and more dynamic. So the whole supply
chain is of much more complexity and perhaps the tradi-
tional theories and methods can not give the further sup-
port for some relative research.
Complex network is a theory attempted to describe the
properties of an actual or virtual network and to establish
a model (for instance, mathematical model) to mirror
those properties. Based on this theory and from the view
of logistics nodes planning of a strategic supply chain,
this paper proposes a mathematical modeling framework
that captures many practical aspects of network design
problems which have not been received adequate atten-
tion in the relative literatures. Such aspects considered
include: dynamic planning horizon, generic supply chain
network structure, external supply of materials, inventory
opportunities for goods, distribution of commodities,
facility configuration, availability of capital for invest-
ments, and storage limitations. Therefore, the research of
this paper may provide some references for the mecha-
nism of a strategic supply chain.
2. The Significance for Strategic Supply
Chain Design Applying Complex
Network Theory
To better understand the significance for strategic supply
chain design, it is necessary to briefly review the back-
ground and the fundamental contents about complex
network theory. A network is a set of items, which are
called nodes, with connections between them, called
edges. Systems taking the form of networks (also called
graphs in some of mathematical literatures) abound in
the world. Typical examples of networks include the
World Wide Web, information networks of citations
between academic papers, technological networks, bio-
logical networks and social networks of acquaintance or
other connections between individuals, organizations and
business relations among companies, and supply chain
networks for sure. The study of networks, in the form of
mathematical graph theory, is one of the fundamental
pillars of discrete mathematics. Networks have also been
studied extensively in the social sciences and in the
1930s socialists realized the importance of the patterns of

JIANGBO ZHENG 130
connection between people to the understanding of the
function of human society [1]. From then on, typical
relevant researches address issues of centrality (which
individuals are best connected to others or have most
influence) and connectivity (whether and how individu-
als are connected to one another through the network).
Recent years there have been a new change with the re-
search focus shifting from the analysis of single small
system and the property of individual nodes or edges
within such systems to consideration of large-scaled
(maybe millions or eve more of nodes and edges) statis-
tics properties of systems. Recent work in this area is
inspired particularly by a groundbreaking paper by Watts
and Strogatz [2]. This new approach has been driven
largely by the availability of computers and communica-
tion networks that allow us to gather and analyze data on
a scale further larger than previously possible. This
change of scale forces us a corresponding change in our
analytic approach – strategic supply chain network is the
case in point. For example, traditional research works
about supply chain network of tens or hundreds nodes, it
is relatively straightforward matter to draw a picture of
the network with actual points and lines, and to give spe-
cific analysis (the human eye is also an analytic tool)
about it through examining this picture. But this ap-
proach is not useful with a complex network of thou-
sands or even more nodes – that is very common now for
some modern multi-national companies’ supply chain
networks.
Furthermore, the theoretical body of complex network
is established to do primary three aspects: 1) to find and
highlight statistical properties, such as path lengths and
degree distributions, which characterize the structure and
behavior of a network, and to suggest appropriate ways
to measure these properties; 2) to create models of net-
works that can help us to understand the meaning of
these properties such as how they came to be as they are
and how they interact with one another; 3) to predict
what the behavior of networks system will be on the ba-
sis of measured structural properties and the local rules
governing individual nodes. In fact, the scientific field
has made an excellent start on the first two of these aims
by drawing on ideas from a broad variety of disciplines.
But such achievements are not well introduced in the
research field of supply chain systems; especially the
item (2) is understated in the planning of strategic supply
chain network. Therefore, this paper attempts to apply
complex networks theory to establish a modeling
framework to better describe and interpret the systems of
strategic supply chain.
3. Literatures Review and Properties
Description of a Strategic Supply Chain
Research works on optimization of the supply chain
through efficient planning decisions have been processed
for many years such as Erlenkotter D. [3], Fong CO. and
Srinivasan V. [4,5], Jacobsen SK [6], Sweeney DJ and
Tatham RL [7] and in the strategic planning level, typical
decisions concern the location of manufacturing and/or
warehousing logistics nodes [8,9,10]. Moreover, recent
years many research works have addressed the dynamic
location problem such as: Daskin et al. [11] propose an
extensive review of location problems, Beamon [12]
distinguishes models with deterministic data from those
with stochastic data, Owen and Daskin [13] clearly
separate the static and dynamic models. Cordeau et al.
[14] propose a static model considering a multi-commo-
dity, multi-facility and single-country network. The de-
cision variables concern the number of locations, the
capacity and technology of manufacturing in plants and
warehouses, selection of suppliers, selection of distribu-
tion channels, transportation modes and material flows.
Hamer-Lavoie and Cordeau [15] simplify this model by
removing the suppliers and the bills of materials. They
suppose that the location has already been chosen for
plants and the model focuses on warehouse location. The
model is dynamic with stochastic demands, and takes
inventories into account, including the safety stock. Dias
et al. [16] work on the re-engineering of a two-echelon
network (facilities and customers). The authors suppose
that facilities can be opened, closed and reopened more
than once during the planning horizon. They study these
conditions within three scenarios: with maximum capac-
ity restrictions; with both maximum and minimum ca-
pacity restrictions; and with a maximum capacity that
decreases. With the same flexibility idea, Melo et al. [17]
aim at relocating the network with expansion/reduction
capacity scenarios. Despite of so many important re-
searching works, some important real world issues have
not received adequate attention. These include the exter-
nal supply of products, inventory opportunities for prod-
ucts, storage limitations, availability of capital for in-
vestments, and relocation, expansion or reduction of
nodes’ capacities. Even though some of these issues have
been researched individually in the literature, it is ig-
nored that the structure of a network is strongly affected
by the simultaneous consideration of these and other
practical needs. One observes a lack of reasonably sim-
ple, yet comprehensive, models which can illustrate the
effect of such factors on network configuration deci-
sions.
In this paper, a supply chain is defined as a network of
nodes (e.g. suppliers, manufacturing plants, distribution
centers, warehouses, etc.) and lines (including physical
lines, e.g. transportation lines, and virtual lines, e.g. in-
formation and communication channels) that perform a
set of operations ranging from the acquisition of raw
materials, the transformation of these materials into in-
termediate and finished products, to the distribution of
the finished products to the customers network (Figure 1).

JIANGBO ZHENG 131
Figure 1. A network of supply chain
This paper attempts to bridge the gap between the com-
plicated dynamic strategic supply chain in practice and
the sound describing models in theory. So the main con-
tribution is to provide a mathematical modeling frame-
work for assisting decision-makers in the design of their
supply chains. It is necessary to point out that the
mathematical modeling framework in this paper firstly
includes the relocation of existing logistics nodes, and
can reflect the expansion and reduction of the nodes – it
is very common in the practical supply chain operations.
Further more, the notion of production in this paper is a
wide conception which includes service and production.
Then, the setup or shutdown of a node, or the expansion
or reduction of a node, is usually a time-and-cost-consu-
ming process. Finally, in strategic supply chain circum-
stances, it is emphasized that resources should be made
full use and be integrated for better efficiency. So the
capacity should be transmit to new nodes when some
existing ones are shut down. Therefore, to implement
smooth transition to a new network configuration needs
better coordination of all operational aspects involved in
this process, and better management of the required in-
vestment capital. Hence, to abate the financial burden put
on such a comprehensive project, capital expenditures
and network design decisions should be planned over
some periods. Based on such contents, this paper tries to
put forward a modeling framework which can generally
reflect the factors taken into account in optimizing stra-
tegic supply chain.
4. Notation and Definition of Decision
Variables
In order to simply describe the principle of the problem
and precisely reflect the planning of logistics nodes in
the supply chain, there is a very important disposal in
this paper. That is, the planning horizon is partitioned
into a set of consecutive and integer time periods which
may not necessarily be equal. In total, there are n plan-
ning periods. Then, it is assumed that if capacity is to be
shifted then this will occur at the beginning of period t
(), and will have a relatively short duration
compared to the period length. Finally, it is assumed that
prior to the planning all relevant data (costs, capacities,
and other factors) were collected through appropriate
forecasting methods or company-specific business analy-
ses.

1, 2,,t
4.1 Sets
It is defined that:
N: set of logistics nodes.

: set of selectable logistics nodes, N

.
s

: set of selectable existing logistics nodes, s

.
n

: set of potential sites for establishing new logistics
nodes, n

.

: set of product types.
According to such definition, setcontains all types
of logistics nodes and these are categorized in so-called
selectable and non-selectable logistics nodes which can
be denoted as “
N
\N

”. Selectable logistics nodes form
the set

, a subset of , and include existing logistics
nodes
N
s

and potential sites for establishing new logis-
tics nodes n

. Note that
s

n

=

,
s

+n

=

. An-
other important assumption is: at the beginning of the
planning horizon, all the logistics nodes in the set
s

are operating. Afterwards, capacity can be shifted from
these logistics nodes to new nodes located at the sites.
4.2 Costs
It is defined that:
,
t
mp
PC : Variable cost of purchasing or producing one
unit of product p

 by node in period t. mN
,,
t
lmp
TC
p
: variable cost of shipping one unit of prod-
uct

 from node l to node m (1, ) in
period t.
,mNlm
,
t
mp
I
C: variable inventory carrying cost per unit on
hand of product p in node m at the end of period t.
,
t
ij
M
C: unit variable cost of moving capacity from the
existing node
s
i


to a new established node n j


at the beginning of period t.
t
m
OC : fixed cost of operating node m in period t.
t
i
SC : fixed cost charged in period t for having shut
down the existing node
s
i

 at the end of period
(1)t

.

nt
j
F
C: fixed setup cost charged in period t when a new
facility established at node n
j


1
starts its operation at
the beginning of period t

.

JIANGBO ZHENG 132
4.3 Important Parameters ,,
t
lmp
x
: amount of product p shipped from node l to
node m (1, ,mNlm

) in period t.
During the research of this paper, there are such impor-
tant parameters:
,
t
mp
y
: amount of product p held in stock in node
mN

at the end of period t.
t
m
K
: maximum allowed capacity at node m in period t
(similarly, t
m
K
is the minimum required capacity at
node m in period t). ,
t
ij
z: amount of capacity shifted from the existing
node
s
i

 to a newly established node n j

 at the
beginning of period t.
,mp

: unit capacity consumption factor of product p at
node m in period t.
,mp
I
:stock of product p of node m at the beginning of
the planning horizon, observe thatfor
,0 jp
In j

.
t

: capital not invested in period t.
t
m

: It’s a “0-1” variable, if the selectable node
mN

is operated during period t ,then t
m

=1; other-
wise, t
m

=0.
t
B: available budget in period t where interest rate is

, and assume that

is a constant.
It is necessary to emphasize on that since each existing
node
s
i

 may have its capacity transferred to one or
more new nodes, it is assumed that its maximum capac-
ity is non-increasing during the planning horizon, that is,
1tt
i
According to such definition, it’s obvious that 1
,0
ij
z

because the capacity is not transferred at the beginning
of planning horizon. What’s more, at that time all exist-
ing nodes are operating and new nodes aren’t established,
so 11 0, 1
ji


.
i
K
K ≥.Similarly, potential new nodes must have
non-decreasing capacities during the planning horizon,
that is, 10 j K for n j

，and 1tt
j
j
K
K ≥.
5. Mathematical Modeling Framework and
4.4 Decision Variables
the Interpretation
The decision variables of this paper are as follows:
5.1 Mathematical Modeling Framework
,
t
mp
A
: amount of product p produced or purchased
from an outside supplier by node in period
t. mNThe formulation of this paper’s model is as follows:

,,,, ,,,,
\
min ttt ttt
mpmplmp lmpmpmp
tmNptlNmNlptmNp
PC ATCxIC y 
 
 
 
\sn
ttt tt
mmm ij
tmtmNtt j
i
OCOC SCFC
 


 

 


(1)
The formulation shows that the goal of planning horizon
is to minimum the total costs. Where, the total costs are con-
sist of purchasing/producing cost, shipping cost, inventory
holding cost, operating cost, shutdown cost and establishing
cost. The constraints are as follows (constraints of variables
for non-negativity and integrality conditions are omitted):
S.t.
 
1
, ,,,,,,,
\\
,
tttttt
mplmp mpmpmlp mp
mN lmN l
A
xyDxyl




N
(2)
1
,
1,
s
n
ttt
i
iiji
j
KzKi






 
(3)
,
1,
s
ttt
j
ij j
i
zK j


n



 
 (4)
1
,
1,
s
n
t
i
ij
j
zKi





 (5)

JIANGBO ZHENG 133

1
1
,, ,,,,
\1
,
s
n
t
ttt
i
ipiplip ipij
plNi j
AxyKzi





 

 



  (6)

1
,, ,,,,
\1
,
s
t
ttt
jpjpljp jpij
plNi i
Axy zj


n



 

 



  (7)

1
,, ,,,
\
\
,
t
ttt
m
mpmplmpmp
plNm
AxyKmN



 

 



 (8)

1
,, ,,,
\,
t
ttt t
m mpmplmp mpm
plNm
AxyKm



 

 




 (9)
1
,
s
tt
iii
 

 (10)
1
,
tt
jjjn
 

 (11)
12 11
n
jj
j
F
C



B

(12)




11
,,
sn sn
tttttt ttttt
ij ijiiijjj
ji j
i
MC zSCFCB
 

1




 

  
  (13)


11
,,
sn s
nnn nnnnn
ij ijiii
ij i
MC zSCB
 

 


 
 
  (14)
.2 Interpretations of the Modeling Framework
ure that only feasible capacity
rel
5
Constraint (2) is the usual demand-supply flow conser-
vation conditions which must hold for each product, lo-
gistics node, and period.
Constraints (3–5) ens
ocations can take place during the planning horizon.
Where, constraint (3) guarantees that only operating ex-
isting logistics node
s
i

 can have their capacity
moved to new facilitiestraint (4) imposes that by
period t a new node has been constructed at site n j
; cons


in order for a potential capacity relocation; constr
states that if the capacity of an existing node has been
completely transferred to others then the node has to be
closed. The combination of (3) and (5) ensures that if an
existing logistics node doesn’t operate in a given period
then its entire capacity was removed in one of the previ-
ous periods. Moreover, by constraint (5) no more capac-
ity can be shifted out at the beginning of the planning
horizon.
Constraint
aint (5)
s (6–8) impose that the capacity of each
no
tate that it is only worth to operate a
se
of each selectable node to change at most once. Hence, if
can be
sp
de can't be exceeded in each period. Observe that con-
straint (6) also prevents any supply chain activities from
taking place in existing nodes whose capacity has been
totally relocated.
Constraint (9) s
lectable node if its output is above a given minimum
level. Constraints (10) and (11) allow the configuration
an existing node is closed, it can’t be re-opened. Simi-
larly, when a new node is established it will remain in
operation until the end of the planning horizon.
Conditions (12–14) are budget constraints. In each
period, there is a limited amount of capital that
ent on capacity transfers, shutting down existing nodes
and establishing new logistics nodes. So the amount is
given by the budget initially available in that period
(represented by Bt ) plus the remained capital not in-
vested in previous periods (represented by1t


). In the
first period, the allowed investments are as setting up
new facilities that will start operating at the nning of
the second period (see constraint (12)). Moreover, in
each one of the following period t, the available capital
may cover capacity transfers, the costs incurred by clos-
ing existing logistics at the end of period t − 1, and set-
ups of new nodes that start operating at the beginning of
period t +1 (see constraint (13)). In the last period n, the
allowed investments concern capacity transfers as well
as shutdowns of nodes that ceased operating at the end of
period n − 1 (see constraint (14)).
Thus, through reasonable assumptions and simplified
methods, this paper puts forward a
begi
practical mathemati-
ca
to give a computational experience.
l modeling framework that is very easy to be solved by
normal software. In fact, this model is a mixed-integer
planning problem, and after given relational data or pa-
rameters we can obtain the results. So it’s not necessary

JIANGBO ZHENG 134
6. Numerical Simulation by Computer
A simple numerical example simulated by computer
software is given in this part to prove the correctness and
d rela-
tive restrains described in the previous sections were
alternatives for the flow of products such as
in
nodes in
strategic supply chain as well as through reasonable as-
analysis, this paper makes research
on it systematically. Based on the references of existing
Figure 2. A tri-echelon network generated for computer
simulation
Table 1. The results of computer simulation
efficiency of my model. The objective function an
implemented using the modeling language ILOG OPL
Studio 3.6, and a variety of test problems were solved
with standard mathematical programming software,
namely with the branch-and-bound algorithm of ILOG
CPLEX 8.0, on a computer with the hardware of AMD
Athlon(tm) 64X2 Dual PC with 1.8 GHz processor and
1GB RAM.
In order to simulate the dynamic supply chain network
circumstances and indefinite original quantities of logis-
tics nodes, I randomly generated a tri-echelon network
with various
ter-facility transportation, direct deliveries from the
manufacturer to the customer level, and reverse arcs for
the return of goods (Figure 2). For such a problem, Table 1
indicates the number of facilities selected and non-se-
lected and displays the average, minimum, and maxi-
mum CPU times (in seconds) required to attain optimal-
ity of this problem for various variants of the original
model. Some important contents should be noted: the
second column of Table 1 gives the number of problems
considered in this kind of network (for details about the
problem characteristics we refer the reader to relative
literatures). Five instances were randomly generated for
this problem, thus yielding a total of 20 instances. The
generated problems cover small and medium-scale net-
works. In an attempt to generate problems related to re-
alistic cases, the amount of arcs available for the trans-
portation of goods in the networks is restricted to 60%.
Also, only a given number of product types can actually
flow through each generated arc. In this way, we can
constrain the volume of traffic in the networks. In all the
problems, the relocation decisions involve the distribu-
tion centers and retailers. Furthermore, all data (costs,
capacities, demands, etc.) were drawn at random from a
uniform distribution over given intervals. These intervals
were selected in such a way that a large variety of in-
stances was created that differ by the number of periods,
products and facilities, the availability of transportation
arcs, the range of fixed and variable costs, and the range
of capacities and capital for investments. For each sub-
sequent period, the previous parameter value was in-
creased or decreased by a certain percentage (for in-
stance, 8%) which was randomly selected over a given
interval. For example, customer demands for the first
period were drawn following a uniform distribution in
the interval [0, 25]. In the second period, the percentage
increase compared to the first period was randomly gen-
erated by 8%. This procedure was repeated until the last
period of the planning horizon was attained, thus creat-
ing an increasing demand sequence. As mentioned above,
all the details can be found in Melo et al. [18].
7. Conclusions
Aiming at the planning problem of logistics
sumption and deep
research woks and their insufficiencies, this paper estab-
lishes a mixed integer programming modeling frame-
work for strategic supply chain design from the view-
point of the planning of logistics nodes. The aspects con-
sidered include the relocation of existing nodes through
Problems 4
Periods 3,4,5
Products 5
Manufactures 5 Non-selectable
Customers
facilities 50,75
DCs 8 Existing
facilities Retailers 12 Selectable
DCs 4
Retailers 8
facilities New
facilities
Average 26268
Minimal 14568
Variables
Maximal 34204
Average 1968
Minimal 1363
Constraints
Maximal 2315
Average 234
Minimal 21
CPU time(s)
Maximal 1246
Manufacturers Distribution
Centers
Retailers Customers

JIANGBO ZHENG 135
capacity transfers to new locations, integration of inv
totation aly decisions, the avility
oudget foents in node loca and
relocation, and the gructure of the supp
r, such a modification
w
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network. This paper has shown that capacity expansion
and reduction scenarios as well as modular capacity
shifts can easily be incorporated into this model. To ver-
ify the efficiency and correctness of the model, a com-
putational simulation is generated by software. The
simulation results show that a number of randomly gen-
erated test problems can be solved to optimality within
no more than 2 hours at average. Therefore, my model is
worthy of being applied for the dynamic situation and
complex supply chain design.
In future research, an important extension for this
model is expected to change the assumption of determi-
nistic demand, costs, and other factors in the problem to
stochastic variables. Howeve
30, p
ould have an impact on the complexity of the problem.
So it is necessary to develop efficient solution methods
to this very realistic and strategically significant practical
problem.
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