# An Optimal Method for Developing Global Supply Chain Management System

Authors: Hao-Chun Lu; Yao-Huei Huang
Journal: Journal of Optimization
 (2013)

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## Abstract

Owing to the transparency in supply chains, enhancing competitiveness of industries becomes a vital factor. Therefore, many developing countries look for a possible method to save costs. In this point of view, this study deals with the complicated liberalization policies in the global supply chain management system and proposes a mathematical model via the flow-control constraints, which are utilized to cope with the bonded warehouses for obtaining maximal profits. Numerical experiments illustrate that the proposed model can be effectively solved to obtain the optimal profits in the global supply chain environment.


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## Body

## 1. Introduction

Traditionally, supply chain management (SCM) mainly offers different ways to reduce the production and transportation costs such that either the total expenditures in a supply chain can be minimized [1, 2] or the profits can be maximized [3, 4] to enhance the industrial competitiveness. These concepts above have been formed as SCM mathematical models in the last few decades such as supplier’s pricing policy in a just-in-time environment [5], pricing strategy for deteriorating items using quantity discount when customer demand is sensitive [6], and an optimization approach for supply chain management models with quantity discount policy [7].On the other hand, a part of studies is focused on demand forecasting [8–11] to decrease the impact of the bullwhip effect [12, 13].  Additionally, some studies utilize the neural network method and regression analysis to improve the accuracy for forecasting customer demand [14–16], and furthermore, these connection weights in neural networks are assigned weighting based on fuzzy analytic hierarchy process methods without any tunings [14, 17]. By the previous mentions, we cannot guarantee that the solution are optimal. Based on the reason, this study proposes a deterministic method, an approximate method for linearizing nonlinear time series analysis model, to forecast customer demand in Section 3.2.Many researchers have suggested that information sharing is a key influence on SCM environments [11, 18] and that it impacts the SCM performance in terms of both total costs and service levels [11, 19, 20]. However, the development of a global SCM model must share information as much as possible. We then suppose that the information in our experimental tests is shared to simplify the SCM situations [21–23].In order to enhance the competitiveness of industries, a liberalization policy discussed in recent years becomes an important factor. Many developing countries have implemented a liberalization policy with bonded warehouses in the global supply chain environments. The liberalization policy with bonded warehouses in the different countries around the world, makes the goods be stored in the bonded warehouse, the liability of exporter is temporally cancelled, and the importer and warehouse proprietor incur liability. A bonded warehouse is one building or another secured area, where dutiable goods may be stored or processed without payment of duty. It may be managed by the state or by a private enterprise.  The liberalization policy with bonded warehouses not only enhances the industries competitiveness but also saves inventory, production and transportation costs. Of course, the objective is to find more bonded warehouses, and more costs can be saved. In this study, the policy has proved the advantage for the exporter obtaining more profit in our numerical examples [24–28].A global SCM is seen as a network that includes upstream, midstream and downstream sectors linkage, where we consider vendors as upstream, facilities and warehouses as midstream, and retailers (or customers) as downstream. The liberalization policy focuses on bonded warehouses of midstream in different countries around the world is not considered in the current SCM model [7, 29]. In this study, we then propose a global SCM model to be suitable for the international liberalization policy. The objective is to maximize the profits associated with inventory, production, transpiration, and distribution in the period of times. The global SCM model is formed as a linear mixed-integer program and solved by commerce software (i.e., [30]). Then, a flow chart for the proposed procedure is depicted in Figure 1.Figure 1
A flow chart of the proposed procedure.This paper is organized as follows. Section2 defines the notations in global SCM and forms a basic model of global SCM. Section 3 describes a procedure of global SCM. Section 4 shows the system architecture of a global SCM. Finally, numerical examples demonstrate that the proposed global SCM method can enhance profit ratio in Section 5.


## 2. A Global SCM Model

There are four stages in the global SCM environment discussed: the vendor, facility, warehouse, and retailer. Each stage may be located in different nations around the world. The general structure of a global supply chain network has been displayed in Figure2. For simplifying presentation, both income and cost statements occur in the dashed rectangle as follows.(i)
Income statement
(a)
sales of goods in warehouse,(b)
transfer price of goods in facility.(ii)
Cost statement
(a)
procurement cost from vendor,(b)
transportation cost (i.e., vendor to facility, facility to warehouse, and warehouse, to retailer),(c)
inventory cost (i.e., warehouse).Figure 2
Schema of a global SCM.Notations are described in Section2.1, and a basic model of global SCM is formulated in Section 2.2.


### 2.1. Notations

There are seven entity setsN: The set of nations nV:  The set of vendors vF:  The set of facilities fW: The set of warehouses wR: The set of retailers rT:   The set of times tP:  The set of parts (or goods) pfor presenting each entity associated with notations as shown above.All parameters are composite style, which are composed of uppercase English strings and suffixes with one or more lowercase alphabet characters, and each suffix single lowercase alphabet character presents the element of relative entity sets. These parameters arePRICEwp:  The sales price of part p  in warehouse  w.TPRICEfp:  The transfer price of part p   in facility  f.PPRICEvp:  The procurement cost of part p   from vendor  v.MCOSTfp:  The production cost of part p  in facility  f.TCOSTvf:  The basis of transportation costs from vendor   vto facility  f.TCOSTff′:  The basis of transportation costs from facility f to facility  f′.TCOSTfw:  The basis of transportation costs from facility f   to warehouse w.TCOSTwr:  The basis of transportation costs from warehouse wto retailer  r.ICOSTf: The basis of inventory costs in facility  f.ICOSTw:  The basis of inventory costs in warehouse w.Tvf:  The transportation time from vendor v  to facility  f.Tff′:  The transportation time from facility f  to facility  f′.Tfw: The transportation time from facility f to warehouse  w.Twr: The transportation time from warehouse w  to retailer r.Tbomfp: The production time of part p  in facility f.BOMp′p:  The amount for part  p reproducing as part  p′.PTp:  The weighting of transportation costs for partp.PIp:  The weighting of inventory costs for partp.Dtrp: The required quantities of part  p for retailer r  at time t.TAXn:  The tax in nation  n.DUTYnp:  The import tax of part p  in nation n.LOCnv: The vendor v in nation  n.LOCnf:  The facility  f in nation n.LOCnw:  The warehouse  w in nation  n.LOCnr:  The retailer r  in nation  n.M_Ufp:  The supplied upper level of part  p in the facility  f.R_Uvfp:  The supplied upper level of part  p from vendor v   to facility  f.R_Uff′p:   The supplied upper level of part p  from facility f  to facility  f′.R_Ufwp:  The supplied upper level of part p  from facility f   to warehouse  w.R_Uwrp:  The supplied upper level of part p  from warehouse  w to retailer r.I_Ufp:  The inventoried upper level of part p  in facility  f.I_Uwp:  The inventoried upper level of part p  in warehouse  w.All decision variables in global SCM are also compositestyle with lowercase suffix alphabet characters. The details of decision variables (integer variables) are described below:Rtvfp:  The amount of part p  transported from vendor v  to facility  f at time  tMtfp:  The amount of part  p produced in facility fat time tRtff′p:  The amount of part p   transported from facility f to facility f′at time tRtfwp:  The amount of part  p transported from facility  f to warehouse w  at time tRtwrp:  The amount of part  p transported from warehouse w  to retailer r  at time  tItfp: The inventory of part p   in facility f  at time  tItwp:  The inventory of part p  in warehouse  w at time  tRBtvfp:  The amount of bonded part  p transported from vendor  v to facility f   at time  tMBtfp:  The amount of bonded part p  produced in facility fat time tRBtff′p:  The amount of bonded part  p transported from facility f  to facility f′  at time tRBtfwp: The amount of bonded part  p transported from facility f  to warehouse  w at time tIBtfp:  The inventory of bonded part  p in facility f  at time  t.


### 2.2. A Proposed Model

We separately useibttn+, ibttn-, and TAXn as the symbols of sales profits, losses, and taxes in each nation at different times. The objective of the proposed model is to maximize the sales profits associated with inventory, production, transpiration, and distribution in each nation at a period of times. The linear global SCM model is formulated as follows.A Global SCM Model
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where all decision variables (i.e., Rtvfp,Mtfp, etc.) belong to integers.The objective is to maximize the profits (i.e., expression (1)) in the global SCM model. The revenue of sales (or losses) are obtained from the following statements.Income Statement
(2): sales of part p in warehouse w minus transportation costs from warehouse w to retailer r,
(7): transfer price of part p from facility f to warehouses w (i.e., transfer price),
(8): transfer price of part p from facility f to facility f′ (i.e., transfer price),Cost Statement
(3): transportation and ordering costs from facility f to warehouse w,
(4): import duty of part p from facility f to warehouse w,
(5): inventory costs of part p in warehouse w,
(6): fixed cost in warehouse w,
(9): transportation and ordering costs from facility f to warehouse w,
(10): import duty of part p from facility f to facilityf′,
(11): transportation and ordering costs from vendor v to facility f,
(12): import duty of parts from vendorv to facility,
(13): production cost in facilityf,
(14): inventory cost in warehouse w,
(15): fixed costs in facilities.Continuously, there are two kinds of constraints in the proposed model. One is flow conservation and the other is upper-lower bound constraints, which are described below.Flow ConservationWe have(16)Itfp+∑v∈VR(t-Tvf)vfp+∑f′∈F,f′≠fR(t-Tf′f)f′fp+M(t-Tbomfp)fp-∑p′∈P,p≠p′BOMp′p*Mtfp′-∑f′∈F,f′≠fRtff′p-∑w∈WRtfwp=I(t+1)fp∀t∈T,f∈F,p∈P,(17)Itwp+∑f∈FR(t-Tfw)fwp-∑r∈RRtwrp=I(t+1)wp∀t∈T,w∈W,p∈P,(18)IBtfp+∑v∈VRB(t-Tvf)vfp+∑f′∈F,f′≠fRB(t-Tf′f)f′fp+MB(t-Tbomfp)fp-∑p′∈P,p′≠pBOMp′p*MBtfp′-∑f′RBtff′p-∑wRBtfwp=IB(t+1)fp∀t∈T,f∈F,p∈P,(19)IBtwp+∑f∈FRB(t-Tfw)fwp-∑r∈RRtwrp=IB(t+1)wp∀t∈T,w∈W,p∈P,(20)∑w∈WR(t-Twr)wrp=Dtrp∀t∈T,r∈R,p∈P.
These flow conservation constraints are described as follows:(16): the limitation of the flow conservation in each facility,(17): the limitation of the flow conservation in each warehouse,(18): the limited bonded parts of the flow conservation in each facility,(19): the limited bonded parts of the flow conservation in each warehouse,(20): all of the supplied goods satisfy with retailer demand.Upper-Lower BoundWe have(21)Mtfp≤M_Ufp,(22)Itfp≤I_Ufp,(23)Itwp≤I_Uwp,(24)Rtvfp≤R_Uvfp,(25)Rtff′p≤R_Uff′p,(26)Rtfwp≤R_Ufwp,(27)Rtwrp≤R_Uwrp,(28)RBtvfp≤Rtvfp,(29)RBtff′p≤Rtff′p,(30)RBtfwp≤Rtfwp,
for t∈T,v∈V,f,f′∈F and f≠f′,p∈P,w∈W, and r∈R.The upper-lower bound constraints are noted as follows:(21): capacities in which facilities produce goods,(22): inventory of parts in facilities,(23): inventory of parts in warehouses,(24): quantities of raw parts transported from vendors to facilities,(25): quantities of parts transported from facilities to facilities,(26): quantities of parts transported from facilities to warehouses,(27): quantities of parts transported from the warehouse to retailers,(28): quantities of bonded parts transported from vendors to facilities,(29): quantities of bonded parts transported from facilities to other facilities,(30): quantities of bonded parts transported from facilities to warehouses.


## 2.1. Notations

There are seven entity setsN: The set of nations nV:  The set of vendors vF:  The set of facilities fW: The set of warehouses wR: The set of retailers rT:   The set of times tP:  The set of parts (or goods) pfor presenting each entity associated with notations as shown above.All parameters are composite style, which are composed of uppercase English strings and suffixes with one or more lowercase alphabet characters, and each suffix single lowercase alphabet character presents the element of relative entity sets. These parameters arePRICEwp:  The sales price of part p  in warehouse  w.TPRICEfp:  The transfer price of part p   in facility  f.PPRICEvp:  The procurement cost of part p   from vendor  v.MCOSTfp:  The production cost of part p  in facility  f.TCOSTvf:  The basis of transportation costs from vendor   vto facility  f.TCOSTff′:  The basis of transportation costs from facility f to facility  f′.TCOSTfw:  The basis of transportation costs from facility f   to warehouse w.TCOSTwr:  The basis of transportation costs from warehouse wto retailer  r.ICOSTf: The basis of inventory costs in facility  f.ICOSTw:  The basis of inventory costs in warehouse w.Tvf:  The transportation time from vendor v  to facility  f.Tff′:  The transportation time from facility f  to facility  f′.Tfw: The transportation time from facility f to warehouse  w.Twr: The transportation time from warehouse w  to retailer r.Tbomfp: The production time of part p  in facility f.BOMp′p:  The amount for part  p reproducing as part  p′.PTp:  The weighting of transportation costs for partp.PIp:  The weighting of inventory costs for partp.Dtrp: The required quantities of part  p for retailer r  at time t.TAXn:  The tax in nation  n.DUTYnp:  The import tax of part p  in nation n.LOCnv: The vendor v in nation  n.LOCnf:  The facility  f in nation n.LOCnw:  The warehouse  w in nation  n.LOCnr:  The retailer r  in nation  n.M_Ufp:  The supplied upper level of part  p in the facility  f.R_Uvfp:  The supplied upper level of part  p from vendor v   to facility  f.R_Uff′p:   The supplied upper level of part p  from facility f  to facility  f′.R_Ufwp:  The supplied upper level of part p  from facility f   to warehouse  w.R_Uwrp:  The supplied upper level of part p  from warehouse  w to retailer r.I_Ufp:  The inventoried upper level of part p  in facility  f.I_Uwp:  The inventoried upper level of part p  in warehouse  w.All decision variables in global SCM are also compositestyle with lowercase suffix alphabet characters. The details of decision variables (integer variables) are described below:Rtvfp:  The amount of part p  transported from vendor v  to facility  f at time  tMtfp:  The amount of part  p produced in facility fat time tRtff′p:  The amount of part p   transported from facility f to facility f′at time tRtfwp:  The amount of part  p transported from facility  f to warehouse w  at time tRtwrp:  The amount of part  p transported from warehouse w  to retailer r  at time  tItfp: The inventory of part p   in facility f  at time  tItwp:  The inventory of part p  in warehouse  w at time  tRBtvfp:  The amount of bonded part  p transported from vendor  v to facility f   at time  tMBtfp:  The amount of bonded part p  produced in facility fat time tRBtff′p:  The amount of bonded part  p transported from facility f  to facility f′  at time tRBtfwp: The amount of bonded part  p transported from facility f  to warehouse  w at time tIBtfp:  The inventory of bonded part  p in facility f  at time  t.


## 2.2. A Proposed Model

We separately useibttn+, ibttn-, and TAXn as the symbols of sales profits, losses, and taxes in each nation at different times. The objective of the proposed model is to maximize the sales profits associated with inventory, production, transpiration, and distribution in each nation at a period of times. The linear global SCM model is formulated as follows.A Global SCM Model
(1)
Maximize
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t
∈
T
,
n
∈
N
(
(
1
-
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S
T
f
)
(15)
-
∑
f
∈
F
,
p
∈
P
(
F
C
O
S
T
f
)
)
for
t
∈
T
,
n
∈
N
,
where all decision variables (i.e., Rtvfp,Mtfp, etc.) belong to integers.The objective is to maximize the profits (i.e., expression (1)) in the global SCM model. The revenue of sales (or losses) are obtained from the following statements.Income Statement
(2): sales of part p in warehouse w minus transportation costs from warehouse w to retailer r,
(7): transfer price of part p from facility f to warehouses w (i.e., transfer price),
(8): transfer price of part p from facility f to facility f′ (i.e., transfer price),Cost Statement
(3): transportation and ordering costs from facility f to warehouse w,
(4): import duty of part p from facility f to warehouse w,
(5): inventory costs of part p in warehouse w,
(6): fixed cost in warehouse w,
(9): transportation and ordering costs from facility f to warehouse w,
(10): import duty of part p from facility f to facilityf′,
(11): transportation and ordering costs from vendor v to facility f,
(12): import duty of parts from vendorv to facility,
(13): production cost in facilityf,
(14): inventory cost in warehouse w,
(15): fixed costs in facilities.Continuously, there are two kinds of constraints in the proposed model. One is flow conservation and the other is upper-lower bound constraints, which are described below.Flow ConservationWe have(16)Itfp+∑v∈VR(t-Tvf)vfp+∑f′∈F,f′≠fR(t-Tf′f)f′fp+M(t-Tbomfp)fp-∑p′∈P,p≠p′BOMp′p*Mtfp′-∑f′∈F,f′≠fRtff′p-∑w∈WRtfwp=I(t+1)fp∀t∈T,f∈F,p∈P,(17)Itwp+∑f∈FR(t-Tfw)fwp-∑r∈RRtwrp=I(t+1)wp∀t∈T,w∈W,p∈P,(18)IBtfp+∑v∈VRB(t-Tvf)vfp+∑f′∈F,f′≠fRB(t-Tf′f)f′fp+MB(t-Tbomfp)fp-∑p′∈P,p′≠pBOMp′p*MBtfp′-∑f′RBtff′p-∑wRBtfwp=IB(t+1)fp∀t∈T,f∈F,p∈P,(19)IBtwp+∑f∈FRB(t-Tfw)fwp-∑r∈RRtwrp=IB(t+1)wp∀t∈T,w∈W,p∈P,(20)∑w∈WR(t-Twr)wrp=Dtrp∀t∈T,r∈R,p∈P.
These flow conservation constraints are described as follows:(16): the limitation of the flow conservation in each facility,(17): the limitation of the flow conservation in each warehouse,(18): the limited bonded parts of the flow conservation in each facility,(19): the limited bonded parts of the flow conservation in each warehouse,(20): all of the supplied goods satisfy with retailer demand.Upper-Lower BoundWe have(21)Mtfp≤M_Ufp,(22)Itfp≤I_Ufp,(23)Itwp≤I_Uwp,(24)Rtvfp≤R_Uvfp,(25)Rtff′p≤R_Uff′p,(26)Rtfwp≤R_Ufwp,(27)Rtwrp≤R_Uwrp,(28)RBtvfp≤Rtvfp,(29)RBtff′p≤Rtff′p,(30)RBtfwp≤Rtfwp,
for t∈T,v∈V,f,f′∈F and f≠f′,p∈P,w∈W, and r∈R.The upper-lower bound constraints are noted as follows:(21): capacities in which facilities produce goods,(22): inventory of parts in facilities,(23): inventory of parts in warehouses,(24): quantities of raw parts transported from vendors to facilities,(25): quantities of parts transported from facilities to facilities,(26): quantities of parts transported from facilities to warehouses,(27): quantities of parts transported from the warehouse to retailers,(28): quantities of bonded parts transported from vendors to facilities,(29): quantities of bonded parts transported from facilities to other facilities,(30): quantities of bonded parts transported from facilities to warehouses.


## 3. A Procedure of Global SCM

There are different procedures in a global supply chain environment such as optimal transportation in logistic management, demand forecasting in preprocessing, bill of materials’ (BOM) table, and considering the liberalization policies with bonded warehouses. These procedures are discussed below.


### 3.1. Logistic Management

In this study, we assume that a global SCM goes through four stages such as procurement, production, warehousing, and distribution (i.e.,Tvf+Tf_Bom+[Tff′+Tf_Bom]+Tfw+Twr), where the semifinished goods will be transferred to another facility for reproduction (i.e., [Tff′+Tf′_Bom]) to enhance the transfer price of goods. The course of the logistic management needs to go through a phase or a cycle (i.e., t=1,2,…,n). The processing flow of global SCM is presented in Figure 3.Figure 3
Processing flow of the global SCM.In order to avoid delaying the demand of retailers in the future, in the beginning, we let the quantities of inventories equal zero in each stage in the first phase. Then, we will addmtimes for utilizing demand forecast method. The period of n+m times will be calculated in this global. Occurring in the period from (n+1) to (n+m) times, all of the goods in transportation and processing will be restored to the inventories of the adjacent warehouses.


### 3.2. Demand Forecast Method—Time Series Analysis

As mentioned above, we need to forecast the quantity of retailers’ (i.e., customer) demand. Time series forecasting is a well-known method [31, 32] to forecast future demands based on known past events.By referring to Li’s method [33], we then have the following nonlinear time series analysis’ model.A Nonlinear Demand Forecasting Model (NDF Model)
(31)
Min
∑
t
=
1
T
|
S
t
-
(
a
+
b
Q
t
)
y
t
|
(32)
s
.
t
.
y
t
=
y
t
′
(
∀
t
,
t
′
and
t
≠
t
′
,
which
mean
t
and
t
′
belong
to
the
same
quarter
)
,
(33)
∑
t
=
1
k
y
t
=
k
,
(34)
y
t
≥
0
,
S
t
,
a
,
and
b
are
free
sign
variables
,
where k is sum of seasons (usually k=4) and St, Qt, and yt denotes the sales, quarter numbers, and seasonal indexes, respectively. For example, if T=8, then t=(1,5) represent the first quarter, t=(2,6) represent the second quarter, t=(3,7) represent the third quarter, and t=(4,8) represent the fourth quarter.A NDF model is nonlinear because of existing absolute functions and nonlinear terms. Following linear systems can linearize them. The linear approximation of the functionF1,t(a,yt)=ayt is a continuous function f1,t(a,yt), which is equal to F1,t(a,yt) (i.e., f1,t(al1,at,l2)=F1,t(a,yt) at each grid point (l1,l2)) and a linear function of its variables (a,yt) on the interior or edges of each of the indicated triangles. To describe the linear approximation of the function F1,t(a,yt), we then have the following linear system (referring to the models in Babayev [34]).Let(35)f1,t(a,yt)=ayt≅αt=∑l1=1m+1∑l2=1m+1F1,i(d1,l1,d2,t,l2)ωl1,l2,(36)a=∑l1=1m+1∑l2=1m+1d1,l1ωl1,l2,(37)yt=∑l1=1m+1∑l2=1m+1d2,t,l2ωl1,l2,(38)∑l1=1m+1∑l2=1m+1ωl1,l2=1,(39)∑l1=1m∑l2=1m(ul1,l2+vl1,l2)=1,(40)ωl1,l2+ωl1,l2+1+ωl1+1,l2+1≥ul1,l2forl1=1,…,m,l2=1,…,m,(41)ωl1,l2+ωl1+1,l2+ωl1+1,l2+1≥vl1,l2forl1=1,…,m,l2=1,…,m,
whereωl1,l2≥0 and ul1,l2,vl1,l2∈{0,1}.Expressions (36)~(38) define the point (a,yt) as the convex linear combination of the vertices of the chosen triangle. Expressions (39)~(41) imply that if ul1,l2=1, then ωl1,l2+ωl1,l2+1+ωl1+1,l2+1=1 and f1,t(a,yt)=F1,t(d1,l1,d2,t,l2)ωl1,l2+F1,t(d1,l1,d2,t,l2+1)ωl1,l2+1+F1,t(d1,l1+1,d2,t,l2+1)ωl1+1,l2+1; or if vl1,l2=1, then ωl1,l2+ωl1+1,l2+ωl1+1,l2+1=1 and f1,t(a,yt)=F1,t(d1,l1,d2,t,l2)ωl1,l2+F1,t(d1,l1+1,d2,t,l2)ωl1+1,l2+F1,t(d1,l1+1,d2,t,l2+1)ωl1+1,l2+1.The mentions above give a basic formulation satisfying the piecewise linear approximation ofF1,t(a,yt)=ayt≅αt. Similarly, F2,t(b,yt)=byt≅βt can be also linearized by the same way (for the proof, refer to Babayev [34]).On the other hand, we use additional binary variables to treat the absolute function. A piecewisely linear demand forecasting model can be reformulated as follows.A Piecewisely Linear Demand Forecasting Model (PLDF Model)
(42)
Min
∑
t
=
1
T
Φ
t
(43)
s
.
t
.
(
32
)
and
(
33
)
,
(44)
(
u
t
-
1
)
M
+
S
t
-
(
α
t
+
β
t
Q
t
)
≤
Φ
t
≤
S
t
-
(
α
t
+
β
t
Q
t
)
+
(
1
-
u
t
)
M
,
(45)
-
u
t
M
+
(
α
t
+
β
t
Q
t
)
-
S
t
≤
Φ
t
≤
(
α
t
+
β
t
Q
t
)
-
S
t
+
u
t
M
,
where M is a big enough constant, ut∈{0,1}, Φt≥0, αt, and βt are piecewisely linear variables of ayt and byt, respectively, referred to(35)–(41).Considering the following situations  we know that the nonlinear objective function can be linearized by linear system, that is, (44) and (45).(i)
ifut=1, then Φt=St-(αt+βtQt), which is forced by (44) because of Φt≥0,(ii)
ifut=0, then Φt=(αt+βtQt)-St, which is forced by (45) because of Φt≥0.


### 3.3. Bill of Materials (BOM)

A bill of materials’ (BOM) table is expressed as the “parts list” of components. In order to understand the BOM for this global SCM model, the symbols ofpandp′could be expressed as a material or goods (i.e., parameter BOMp′p). Hence, we can utilize a two-dimensional matrix to express the relationship between partialand goods. For example, a p4 with a p5 can produce a p3, and a p3 with two p2 can produce a p1. The BOM table of the sparse matrix is expressed in Figure 4. The aim is to design a friendly interface for our system design.Figure 4
BOM figure.


### 3.4. Liberalization Policy with Bonded Warehouses

This study proposes a global SCM model which is capable of treating liberalization policy for bonded warehouses in the different countries around the world [24–28]. A bonded warehouse is one building or any other secured area, where dutiable goods may be stored or processed without payment of duty. It may be managed by the state or by private enterprise.While the goods are stored in the bonded warehouse, the liability of exporter is temporally cancelled, and the importer and warehouse proprietor incur liability. These goods are in the bonded warehouse, and they may be processed by assembling, sorting, repacking, or others. After processing and within the warehousing period, the goods may be exported without the payment of duty, or they may be withdrawn for consumption upon payment of duty at the rate applicable to the goods in their manipulated condition at the time of withdrawal. Bonded warehouses provide specialized storage services such as deep freeze, bulk liquid storage, commodity processing, and coordination with transportation and are an integral part of the global supply chain.The liberalization policy with bonded warehouses not only enhances the industries competitiveness but also saves inventory, production, and transportation costs. Of course, the objective aims to find more bonded warehouses, and more costs could be saved.


## 3.1. Logistic Management

In this study, we assume that a global SCM goes through four stages such as procurement, production, warehousing, and distribution (i.e.,Tvf+Tf_Bom+[Tff′+Tf_Bom]+Tfw+Twr), where the semifinished goods will be transferred to another facility for reproduction (i.e., [Tff′+Tf′_Bom]) to enhance the transfer price of goods. The course of the logistic management needs to go through a phase or a cycle (i.e., t=1,2,…,n). The processing flow of global SCM is presented in Figure 3.Figure 3
Processing flow of the global SCM.In order to avoid delaying the demand of retailers in the future, in the beginning, we let the quantities of inventories equal zero in each stage in the first phase. Then, we will addmtimes for utilizing demand forecast method. The period of n+m times will be calculated in this global. Occurring in the period from (n+1) to (n+m) times, all of the goods in transportation and processing will be restored to the inventories of the adjacent warehouses.


## 3.2. Demand Forecast Method—Time Series Analysis

As mentioned above, we need to forecast the quantity of retailers’ (i.e., customer) demand. Time series forecasting is a well-known method [31, 32] to forecast future demands based on known past events.By referring to Li’s method [33], we then have the following nonlinear time series analysis’ model.A Nonlinear Demand Forecasting Model (NDF Model)
(31)
Min
∑
t
=
1
T
|
S
t
-
(
a
+
b
Q
t
)
y
t
|
(32)
s
.
t
.
y
t
=
y
t
′
(
∀
t
,
t
′
and
t
≠
t
′
,
which
mean
t
and
t
′
belong
to
the
same
quarter
)
,
(33)
∑
t
=
1
k
y
t
=
k
,
(34)
y
t
≥
0
,
S
t
,
a
,
and
b
are
free
sign
variables
,
where k is sum of seasons (usually k=4) and St, Qt, and yt denotes the sales, quarter numbers, and seasonal indexes, respectively. For example, if T=8, then t=(1,5) represent the first quarter, t=(2,6) represent the second quarter, t=(3,7) represent the third quarter, and t=(4,8) represent the fourth quarter.A NDF model is nonlinear because of existing absolute functions and nonlinear terms. Following linear systems can linearize them. The linear approximation of the functionF1,t(a,yt)=ayt is a continuous function f1,t(a,yt), which is equal to F1,t(a,yt) (i.e., f1,t(al1,at,l2)=F1,t(a,yt) at each grid point (l1,l2)) and a linear function of its variables (a,yt) on the interior or edges of each of the indicated triangles. To describe the linear approximation of the function F1,t(a,yt), we then have the following linear system (referring to the models in Babayev [34]).Let(35)f1,t(a,yt)=ayt≅αt=∑l1=1m+1∑l2=1m+1F1,i(d1,l1,d2,t,l2)ωl1,l2,(36)a=∑l1=1m+1∑l2=1m+1d1,l1ωl1,l2,(37)yt=∑l1=1m+1∑l2=1m+1d2,t,l2ωl1,l2,(38)∑l1=1m+1∑l2=1m+1ωl1,l2=1,(39)∑l1=1m∑l2=1m(ul1,l2+vl1,l2)=1,(40)ωl1,l2+ωl1,l2+1+ωl1+1,l2+1≥ul1,l2forl1=1,…,m,l2=1,…,m,(41)ωl1,l2+ωl1+1,l2+ωl1+1,l2+1≥vl1,l2forl1=1,…,m,l2=1,…,m,
whereωl1,l2≥0 and ul1,l2,vl1,l2∈{0,1}.Expressions (36)~(38) define the point (a,yt) as the convex linear combination of the vertices of the chosen triangle. Expressions (39)~(41) imply that if ul1,l2=1, then ωl1,l2+ωl1,l2+1+ωl1+1,l2+1=1 and f1,t(a,yt)=F1,t(d1,l1,d2,t,l2)ωl1,l2+F1,t(d1,l1,d2,t,l2+1)ωl1,l2+1+F1,t(d1,l1+1,d2,t,l2+1)ωl1+1,l2+1; or if vl1,l2=1, then ωl1,l2+ωl1+1,l2+ωl1+1,l2+1=1 and f1,t(a,yt)=F1,t(d1,l1,d2,t,l2)ωl1,l2+F1,t(d1,l1+1,d2,t,l2)ωl1+1,l2+F1,t(d1,l1+1,d2,t,l2+1)ωl1+1,l2+1.The mentions above give a basic formulation satisfying the piecewise linear approximation ofF1,t(a,yt)=ayt≅αt. Similarly, F2,t(b,yt)=byt≅βt can be also linearized by the same way (for the proof, refer to Babayev [34]).On the other hand, we use additional binary variables to treat the absolute function. A piecewisely linear demand forecasting model can be reformulated as follows.A Piecewisely Linear Demand Forecasting Model (PLDF Model)
(42)
Min
∑
t
=
1
T
Φ
t
(43)
s
.
t
.
(
32
)
and
(
33
)
,
(44)
(
u
t
-
1
)
M
+
S
t
-
(
α
t
+
β
t
Q
t
)
≤
Φ
t
≤
S
t
-
(
α
t
+
β
t
Q
t
)
+
(
1
-
u
t
)
M
,
(45)
-
u
t
M
+
(
α
t
+
β
t
Q
t
)
-
S
t
≤
Φ
t
≤
(
α
t
+
β
t
Q
t
)
-
S
t
+
u
t
M
,
where M is a big enough constant, ut∈{0,1}, Φt≥0, αt, and βt are piecewisely linear variables of ayt and byt, respectively, referred to(35)–(41).Considering the following situations  we know that the nonlinear objective function can be linearized by linear system, that is, (44) and (45).(i)
ifut=1, then Φt=St-(αt+βtQt), which is forced by (44) because of Φt≥0,(ii)
ifut=0, then Φt=(αt+βtQt)-St, which is forced by (45) because of Φt≥0.


## 3.3. Bill of Materials (BOM)

A bill of materials’ (BOM) table is expressed as the “parts list” of components. In order to understand the BOM for this global SCM model, the symbols ofpandp′could be expressed as a material or goods (i.e., parameter BOMp′p). Hence, we can utilize a two-dimensional matrix to express the relationship between partialand goods. For example, a p4 with a p5 can produce a p3, and a p3 with two p2 can produce a p1. The BOM table of the sparse matrix is expressed in Figure 4. The aim is to design a friendly interface for our system design.Figure 4
BOM figure.


## 3.4. Liberalization Policy with Bonded Warehouses

This study proposes a global SCM model which is capable of treating liberalization policy for bonded warehouses in the different countries around the world [24–28]. A bonded warehouse is one building or any other secured area, where dutiable goods may be stored or processed without payment of duty. It may be managed by the state or by private enterprise.While the goods are stored in the bonded warehouse, the liability of exporter is temporally cancelled, and the importer and warehouse proprietor incur liability. These goods are in the bonded warehouse, and they may be processed by assembling, sorting, repacking, or others. After processing and within the warehousing period, the goods may be exported without the payment of duty, or they may be withdrawn for consumption upon payment of duty at the rate applicable to the goods in their manipulated condition at the time of withdrawal. Bonded warehouses provide specialized storage services such as deep freeze, bulk liquid storage, commodity processing, and coordination with transportation and are an integral part of the global supply chain.The liberalization policy with bonded warehouses not only enhances the industries competitiveness but also saves inventory, production, and transportation costs. Of course, the objective aims to find more bonded warehouses, and more costs could be saved.


## 4. System Development

Currently, global supply chain management (global SCM) system always needs experts offering the qualities of goods in bonded warehouses to calculate the production capacity since there is a lack of kernel technique (i.e., deterministic mathematical model) for developing global SCM system. At the same time, considering the policy of trade liberalization with bonded warehouses by manual is a difficult job. Therefore, this study develops a global SCM system with optimization technique to cope with the bonded warehouses for obtaining the maximal profits, automatically.


### 4.1. System Design

This study designs a system to apply for a global SCM system based on a proposed mathematical model. The architecture of the global SCM system includes an application server in the middle tier to distribute all of the processing jobs. Establishing a Broker Server can not only distribute the jobs into different application servers, but also the jobs work much more efficient. The basic architecture of the global SCM system is shown in Figure5.Figure 5
Architecture of the multitier web server.Furthermore, the system architecture includes three tiers which are composed of various modules. In the first tier, GUI layer, an intuitive and friendly interface for users is built. In the second tier, the application (AP) server layer, is a kernel in the global SCM system whose base is based on the Java programming language and an optimal software component (i.e., LINGO’s Solver). In the last tier, database layer stores all of the data such as the username, password, environment setting, and logistics information into database system. Moreover, the data must be backed up to the other database to protect it from hacking or crashing. Then, the system architecture is shown in Figure6.Figure 6
Architecture of the global SCM system.


## 4.1. System Design

This study designs a system to apply for a global SCM system based on a proposed mathematical model. The architecture of the global SCM system includes an application server in the middle tier to distribute all of the processing jobs. Establishing a Broker Server can not only distribute the jobs into different application servers, but also the jobs work much more efficient. The basic architecture of the global SCM system is shown in Figure5.Figure 5
Architecture of the multitier web server.Furthermore, the system architecture includes three tiers which are composed of various modules. In the first tier, GUI layer, an intuitive and friendly interface for users is built. In the second tier, the application (AP) server layer, is a kernel in the global SCM system whose base is based on the Java programming language and an optimal software component (i.e., LINGO’s Solver). In the last tier, database layer stores all of the data such as the username, password, environment setting, and logistics information into database system. Moreover, the data must be backed up to the other database to protect it from hacking or crashing. Then, the system architecture is shown in Figure6.Figure 6
Architecture of the global SCM system.


## 5. Numerical Examples

In our numerical examples, we assume that the situation occurred in three different overseas locations. There are three vendors (v1,v2,v3), four facilities (f1,f2,f3,f4), four warehouses (w1,w2,w3,w4), three retailers (r1,r2,r3). Under the liberalization policies, these limited quantities of bonded warehouses are listed in the Appendix. There are three parts (p2,p4,p5) supplied from the vendor to the facility, and the parts be produced another two parts (p1,p3) in different facilities. The period of time includes two demands: one is actual customer demand (i.e., tn=15), and the other is forecasting demand (i.e., tm=2), so that the total period of time is 17 (i.e., t=1 to 17). The other parameters are expressed in Tables 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, and 26 of the Appendix. The numerical example was solved via a global SCM system; these logistic results at different times t are depicted in Figures 7, 8, 9, 10 and 11.Figure 7
The logistic flow at time = 1.Figure 8
The logistic flow at time = 2.Figure 9
The logistics flow at time  = 6.Figure 10
The logistic flow at time = 7.Figure 11
The logistic flow at time = 8.Solving the example, the objective value is $603,010 with consideration of the bonded warehouses. We then calculate them without bonded warehouses again, and the objective value is 514,680. Comparing both of them, the profit ratio increases to 14.6% as shown in Table1.Table 1
Profit ratio.
Items
Objective
Profit ratio
Having bonded warehouse (Hb)
$603,010
14.6%↑((Hb-Wb)/Hb)
Without bonded warehouse (Wb)
$514,680Table 2
Vendor location.
L
O
C
v
v
1
v
2
v
3
Location
1 (Taiwan)
2 (China)
3 (Japan)Table 3
Facility location.
L
O
C
f
f
1
f
2
f
3
f
4
Location
1 (Taiwan)
2 (China)
2 (China)
3 (Japan)Table 4
Warehouse location.
L
O
C
w
w
1
w
2
w
3
w
4
Location
1 (Taiwan)
2 (China)
2 (China)
3 (Japan)Table 5
Retailer location.
L
O
C
r
r
1
r
2
r
3
Location
1 (Taiwan)
2 (China)
3 (Japan)Table 6
The weighting of transportation costs of parts.
P
T
p
p
1
p
2
p
3
p
4
p
5
Weighting
1
0.2
0.8
0.1
0.5Table 7
The weighting of inventory costs of parts.
P
I
p
p
1
p
2
p
3
p
4
p
5
Weighting
0.5
0.1
0.5
0.1
0.4Table 8
The duty of parts in different nations.
D
U
T
Y
n
p
p
1
p
2
p
3
p
4
p
5
n
1
0.2
0.3
0.2
0.01
0.05
n
2
0.3
0.02
0.3
0.01
0.1
n
3
0.1
0.01
0.1
0.05
0.03Table 9
The tax in different nations.
T
a
x
n
n
1
n
2
n
3
0.07
0.03
0.08Table 10
Sales price of each part for each vendor.
P
P
R
I
C
E
v
p
p
1
p
2
p
3
p
4
p
5
v
1
28
v
2
40
v
3
40
30
All blank cells are disabled.Table 11
Maximum supplied limitation in each vendor.
R
_
U
v
f
p
f
1
f
2
f
3
f
4
v
1
0
p
4
=
1000
0
0
v
2
0
0
p
5
=
500
p
5
=
500
v
3
p
2
=
750
,
p
4
=
1500
0
p
3
=
1500
p
2
=
700
All blank cells are disabled.Table 12
Production costs and limitations for each facility.
M
C
O
S
T
f
p/M_Ufp
p
1
p
2
p
3
p
4
p
5
f
1
20/400
f
2
30/350
f
3
28/300
f
4
30/450
All blank cells are disabled.Table 13
Transportation costs and lead time from each vendor to each facility.
T
C
O
S
T
v
f
/
T
v
f
f
1
f
2
f
3
f
4
v
1
3/1
v
2
1/1
1/1
v
3
4/2
3/1
2/1Table 14
Amount of partp needed for producing part p′.
B
O
M
p
1
′
p
2
′
p
3
′
p
4
′
p
5
′
p
1
0
2
1
0
0
p
2
0
0
0
0
0
p
3
0
0
0
1
1
p
4
0
0
0
0
0
p
5
0
0
0
0
0Table 15
The lead time of the facility for producing partp′ and sales price in the facility.
T
b
o
m
f
p
/
T
P
R
I
C
E
f
p
p
1
p
2
p
3
p
4
p
5
f
1
1/250
f
2
1/150
f
3
1/150
f
4
1/260
All blank cells are disabled.Table 16
The base of inventory costs.
I
C
O
S
T
f
f
1
f
2
f
3
f
4
6
2
1
12Table 17
Maximum stock level in each facility.
I
_
U
f
p
p
1
p
2
p
3
p
4
p
5
f
1
200
400
200
0
0
f
2
0
0
300
300
300
f
3
0
0
400
400
400
f
4
100
200
100
0
0Table 18
Transportation costs and lead time from one facility to another facility.
T
C
O
S
T
f
f
′
/
T
f
f
′
f
1
f
2
f
3
f
4
f
1
f
2
2/2
f
3
3/2
f
4
All blank cells are disabled.Table 19
Maximum transferable quantity from one facility to another facility.
R
_
U
f
f
′

p
f
1
f
2
f
3
f
4
f
1
0
0
0
0
f
2
p
3
=
1000
0
0
0
f
3
0
0
0
p
3
=
1000
f
4
0
0
0
0Table 20
The base of inventory costs and fixed costs.
I
C
O
S
T
w
(
F
C
O
S
T
w
)
w
1
w
2
w
3
w
4
5 (50)
1 (10)
1 (10)
10 (100)Table 21
Transportation costs and lead time from the facility to the warehouse.
T
C
O
S
T
f
w
/
T
f
w
w
1
w
2
w
3
w
4
f
1
1/1
f
2
2/1
1
f
3
1/1
f
4
1/1
All blank cells are disabled.Table 22
Maximum transferable quantity from the facility to the warehouse.
R
_
U
f
w
p
w
1
w
2
w
3
w
4
f
1
p
1
=
800
0
0
0
f
2
p
3
=
800
p
3
=
600
0
0
f
3
0
0
p
3
=
1000
0
f
4
p
1
=
700
0
0
0Table 23
Transportation costs and lead time from the warehouse to the retailer.
T
C
O
S
T
w
r
(
T
w
r
)
r
1
r
2
r
3
w
1
1 (1)
3 (1)
w
2
2 (2)
1 (1)
w
3
1 (1)
w
4
1 (1)
All blank cells are disabled.Table 24
Maximum transferable quantity from the warehouse to the retailer.
R
_
U
w
r
p
r
1
r
2
r
3
w
1
p
1
=
700
,
p
3
=
800
0
p
1
=
300
w
2
p
3
=
800
p
3
=
8000
0
w
3
0
p
3
=
800
0
w
4
0
0
p
1
=
1000Table 25
Sales price of each part and limitation in each warehouse.
P
R
I
C
E
w
p
/
I
_
U
w
p
p
1
p
2
p
3
p
4
p
5
w
1
380/300
0
280/300
0
0
w
2
0
0
200/500
0
0
w
3
0
0
200/600
0
0
w
4
450/150
0
0
0
0Table 26
Retailer demand and forecasting at each time.
RetailerR1
RetailerR2
RetailerR3
D
t
r
p
p
1
p
2
p
3
p
4
p
5
p
1
p
2
p
3
p
4
p
5
p
1
p
2
p
3
p
4
p
5
t
=
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
t
=
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
t
=
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
t
=
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
t
=
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
t
=
6
0
0
180
0
0
0
0
120
0
0
0
0
0
0
0
t
=
7
0
0
190
0
0
0
0
110
0
0
0
0
0
0
0
t
=
8
52
0
170
0
0
0
0
100
0
0
83
0
0
0
0
t
=
9
38
0
160
0
0
0
0
130
0
0
90
0
0
0
0
t
=
10
60
0
210
0
0
0
0
120
0
0
50
0
0
0
0
t
=
11
43
0
180
0
0
0
0
110
0
0
60
0
0
0
0
t
=
12
52
0
190
0
0
0
0
100
0
0
76
0
0
0
0
t
=
13
56
0
170
0
0
0
0
110
0
0
56
0
0
0
0
t
=
14
48
0
180
0
0
0
0
130
0
0
76
0
0
0
0
t
=
15
58
0
200
0
0
0
0
120
0
0
99
0
0
0
0
t
=
16
31
0
190
0
0
0
0
90
0
0
80
0
0
0
0
t
=
17
52
0
180
0
0
0
0
120
0
0
50
0
0
0
0In order to observe the advantages of the proposed method, this study experiments different numerical examples by generating parameters below.(i)
The total locations are randomly generated from a uniform distribution according to 2 ≤ vendors ≤ 20, 3 ≤ facilities ≤ 20, 4 ≤ warehouses ≤ 20, and 2 ≤ retailers ≤ 40.(ii)
The period of time is randomly generated from the uniform distribution over the range of [2, 16].(iii)
The capacities of bonded warehouses are according to the capacities of original warehouses based on uniform distribution from 50% to 90%.(iv)
In order to balance between the supply and demand, all of the coefficients follows feasible sets for the global SCM models.According to the computational results followed rules (i) to (iv), we observe that the liberalization policy with bonded warehouses directly affects the activities of the global SCMs. When we fixed the number of bonded warehouses to 5, the profit ratio approaches 15%. When we take the number of bonded warehouses being 40 as an example, the profit ratio enhances to 20%. Finally, the profit ratio is close to 25% at 50 bonded warehouses. That is, considering that more nodes have bounded constraints, there is a greater cost saving. The tendency of the other 10 tests is depicted in Figure 12.Figure 12
The tendency of the profit ratios for different numbers of warehouses.The proposed model considers the liberalization policy with bonded warehouses as flow-control constraints to obtain optimal profits. Additionally, numerical experiments also illustrate that the proposed model can enhance the profit ratio when the number of bonded warehouses is large.


## 6. Conclusions

This study proposes a global SCM model which is capable of treating liberalization policy with bonded warehouses. All of the constraints about bonded warehouses can be added to the proposed global SCM model. Additionally, the proposed model is embedded into a global SCM system we developed. The system can automatically calculate the profit ratio to further enhance the competitiveness. Numerical experiments’ reports illustrate that the proposed model can be effectively solved to obtain the optimal profit.Future research can consider different quantity discount policies, artificial neural network method for solving the uncertainty demand forecast, heuristic methods for accelerating solving speed, and linearization technique for resolving the proposed demand forecasting model.



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*Source: 197370-2013-10-20.xml*