Title: An optimal model for developing global supply chain

management system

Authors:

Hao-Chun, Lu, Assistant Professor, Department of Information Management, College

of Management, Fu Jen Catholic University, Taiwan

Yao-Huei, Huang, Ph. D., Institute of Information Management, National Chiao Tung

University, Taiwan

Correspond Author: Yao-Huei, Huang

E-mail: yaohuei.huang@gmail.com

Tel: +886-3-5712121~57416

Fax: +886-3-5723792

Postal: Institute of Information Management, National Chiao Tung University,

Management Building 2, 1001 Ta-Hsueh Road, Hsinchu, 300, Taiwan.

1

An optimal method for developing global

supply chain management system

Abstract

Owing to the transparency in supply chains, enhancing competitiveness of industries

becomes a vital factor. Therefore, many developing countries look for possible methods to

save costs. In the point of views, this study deals with the complicated liberalization policies

in the global supply chain management system, and proposes a mathematic model via the

flow-control constraints, which are utilized to cope with the bonded warehouses for obtaining

maximal benefits. Numerical experiments illustrate that the proposed model can be

effectively solved to obtain the optimal benefits in the global supply chain environment.

Keywords: Transparency; Liberalization policy; bonded warehouse; supply chain

management; mathematical model;

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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 (Thomas & Griffin, 1996; Graves & Willems, 2005) or the benefits

can be maximized (Lee & Rosenblatt, 1986; Monahan, 1984) 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

(Hoffmann, 2000), pricing strategy for deteriorating items using quantity discount when

customer demand is sensitive (Yang, 2004), and an optimization approach for supply chain

management models with quantity discount policy (Tsai, 2007).

On the other hand, a part of studies is focused on demand forecasting (Foote, 1995;

Zhao & Leung, 2002; Ghobbar & Friend, 2003; Chu, 2004) to decrease the impact of the

bullwhip effect (Lee et al., 1997; Chen et al., 2000). Additionally, some studies utilize the

neural network method and regression analysis to improve the accuracy for forecasting

customer demand (Kuo, 2001; Gorucu et al., 2004, Chen et al., 2009), and furthermore these

connection weights in neural networks are assigned weighting based on fuzzy analytic

hierarchy process methods without any tunings (Kuo, 2007; Bilgen, 2010). By mentions

above, we cannot guarantee the solution is 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 (Moberg et al., 2002; Zhao & Leung, 2002) and it impacts the SCM

performance in terms of both total costs and service levels (Li & Lin, 2006; Lin et al., 2002;

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Zhao et al., 2002). The development of a global SCM model must share information as much

as possible. We then suppose that all information in our experimental tests is shared to

simplify the SCM situations. (Cachon & Fisher, 2000; Huang & Lin, 2010, Yu et al., 2010).

Moreover, to enhance the competitiveness of industries, a liberalization policy discussed

in recent years becomes an important factor. Many developing countries have implemented

liberalization policy with bonded warehouses in the global supply chain environments. The

liberalization policy with bonded warehouses in the different countries around the world,

where make 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 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 of advantage for the exporter to get more benefit in our numerical

examples (Trefler, 1993; Iman & Nagata, 2005; Romagnoli et al., 2007; Israel, 2010; Yang,

2011).

A global SCM is 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. Then the liberalization policy focuses on bonded

warehouses of midstream in different countries around the world. The policy is not

considered in the current SCM model (Yu, & Li, 2000; Tsai, 2007). In this study, we propose

a global SCM model to be suitable for the international liberalization policy. The objective is

to maximize the benefits associated with inventory, production, transpiration and distribution

in the period of times. The global SCM model is formed as a mixed integer linear program

4

and solved by commerce software (i.e., LINGO, 2002). Then a flow chart for the proposed

procedure is depicted in Fig. 1.

Figure 1: A flow chart of the proposed procedure

This paper is organized as follows: Section 2 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 global SCM. Finally, numerical examples demonstrate that

the proposed global SCM method can enhance benefit ratio in Section 5.

2. A global SCM model

There are four stages in the global SCM environment discussed that includes 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 Fig 2.

For simplifying presentation, both income and cost statements are occurred in the dashed

rectangle as following descriptions.

(i) Income statement

Start

Solve a Global SCM Model

BOM Table Demand Forecasting

Visualize Results

(Global SCM System)

End

Decide Nodes

(Upstream, Midstream, Downstream)

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sales of goods in warehouse,

transfer price of goods in facility.

(ii) Cost statement

procurement cost from vendor,

transportation cost (i.e., vendor to facility, facility to warehouse and warehouse to

retailer),

inventory cost (i.e., warehouse).

Figure 2. Schema of a global SCM

Notations are described in Section 2.1, and a basic model of global SCM is formulated

in the Section 2.2.

2.1 Notations

There are seven sets for presenting each entity associated with notations as follows:

Table 1. Entity sets

N The set of nations n

V The set of vendors v

F The set of facilities f

V1

V2

V3

F1

F2

lity 2

W1

W2

R1

R2

R3

Vendor Facility Warehouse Retailer

6

W The set of warehouses w

R The set of retailers r

T The set of times t

P The set of parts (or goods) p

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 are

described below:

Table 2. Parameters

PRICEwp 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 v to 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 w to 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

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BOMp’p The amount of part p to produce part p

PTp The weighting of transportation costs for part p

PIp The weighting of inventory costs for part p

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 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 composite-style with lowercase suffix

alphabet characters. The details are described below:

Table 3. Decision variables (Integer variables)

Rtvfp The amount of part p transported from vendor v to facility f at time t

Mtfp The amount of part p produced in facility f at time t

Rtff’p The amount of part p transported from facility f to facility f at time t

Rtfwp The amount of part p transported from facility f to warehouse w at time t

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Rtwrp The amount of part p transported from warehouse w to retailer r at time t

Itfp The inventory of part p in facility f at time t

Itwp The inventory of part p in warehouse w at time t

RBtvfp The amount of bonded part p transported from vendor v to facility f at time t

MBtfp The amount of bonded part p produced in facility f at time t

RBtff’p The amount of bonded part p transported from facility f to facility f at time t

RBtfwpz The amount of bonded part p transported from facility f to warehouse w at time

t

IBtfp The inventory of bonded part p in facility f at time t

2.2 A Proposed Model

We separately use

tnibt , tnibt and nTAX as the symbols of sales benefits, losses and

taxes in each nation at different times. The objective of the proposed model is to maximize

the sales benefits 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

Maximize ,

1 n tn tn

t T n N

TAX ibt ibt

(1)

subject to

p

tntn ibtibt

, ,

* *twrp wp p wr

w W r R p P

R PRICE PT TCOST

(2)

, ,

* *tfwp fp p fw

f F w W p P

R TPRICE PT TCOST

(3)

, ,

* *tfwp tfwp fp np

f F w W p P

R RB TPRICE DUTY

(4)

,

* *twp p w

w W p P

I PI ICOST

(5)

9

w

w W

FCOST

(6)

, ,

*tfwp fp

f F w W p P

R TPRICE

(7)

, , ,

*tff p fp

f f F f f p P

R TPRICE

(8)

, , ,

* *tf fp f p p f f

f f F f f p P

R TPRICE PT TCOST

(9)

, , ,

* *tf fp tf fp f p np

f f F f f p P

R RB TPRICE DUTY

(10)

, ,

* *tvfp vp p vf

v V f F p P

R PPRICE PT TCOST

(11)

, ,

* *tvfp tvfp vp np

v V f F p P

R RB PPRICE DUTY

(12)

,

*tfp fp

f F p P

M MCOST

(13)

,

* *tfp p f

f F p P

I PI ICOST

(14)

,

f

f F p P

FCOST

for t T and n N . (15)

where all decision variables (i.e., Rtvfp, Mtfp, etc.) belong to integers.

The objective is to maximize the benefits (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 ,

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(5): inventory costs of part p in warehouse w ,

(6): fixed cost in warehouse w ,

(9): transportation and ordering costs from facility f to warehouses w ,

(10): import duty of part p from facility f to facility f ,

(11): transportation and ordering costs from vendor v to facility f ,

(12): import duty of parts from vendor v to facility,

(13): production cost in facility f ,

(14): inventory cost in warehouse w ,

(15): fixed costs in facilities.

Continuously, there are two kinds of constraints which are considered for the proposed

model. One is flow conservation and the other is upper-lower bound constraints, which are

described below.

Flow conservation

( ) ( ) ( )

, ,

*vf f f bomfptfp t T vfp t T f fp t T fp p p tfp

v V f F f f p P p p

I R R M BOM M

( 1)

,

tff p tfwp t fp

f F f f w W

R R I

, ,t T f F p P ,(16)

( ) ( 1)fwtwp t T fwp twrp t wp

f F r R

I R R I

, ,t T w W p P , (17)

( ) ( ) ( )

, ,

*vf f f bomfptfp t T vfp t T f fp t T fp p p tfp

v V f F f f p P p p

IB RB RB MB BOM MB

( 1)tff p tfwp t fp

f w

RB RB IB

, ,t T f F p P , (18)

( ) ( 1)fwtwp t T fwp twrp t wp

f F r R

IB RB R IB

, ,t T w W p P , (19)

( )wrt T wrp trp

w W

R D

, ,t T r R p P , (20)

These flow conservation constraints are described as follows:

(16): the limit of the flow conservation in each facility.

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(17): the limit 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 will be satisfied with retailer demand.

Upper-lower bound

fptfp UMM _ , (21)

fptfp UII _ , (22)

wptwp UII _ , (23)

vfptvfp URR _ , (24)

pffpftf URR _ , (25)

fwptfwp URR _ , (26)

wrptwrp URR _ , (27)

tvfptvfp RRB , (28)

pftfpftf RRB , (29)

tfwptfwp RRB , (30)

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,

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(28): quantities of bonded parts transported from vendors to facilities,

(29): quantities of bonded parts transported from facilities to another 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 to reduce

the expenditure taxes. These procedures are discussed below.

3.1 Logistic management

In this study, we assume that a global SCM will go through four stages such as

procurement, production, warehousing and distribution (i.e., _ ' '_[ ]vf f Bom ff f Bom fwT T T T T

wrT ) and the semi-finished goods will be transferred to another facility for reproduction (i.e.,

]'[ _' Bomfff TT ) to enhance the transfer price of goods. The course of the logistic management

needs to go through a phase or a cycle (i.e., nt ,...,2,1 ) in the supply chain. The processing

flow of global SCM is presented in Fig. 3 below.

Figure 3. Processing flow of the global SCM

Additionally, in order to avoid delaying the demand of retailers in the future, in the

Vendor Tvf

Facility

Facility’

Warehouse Retailers

T ff’

T fw T rw

Reproduce

Parts

(Materials)

Semi-finished

goods

Finished goods

BOMp’p

Stage 1 Stage 2 Stage 3 Stage 4

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beginning we let the quantities of inventories equal zeros in each stage in the first phase.

Then, it will be plus m times by utilizing demand forecast method. The period of n+m times

will be calculated in this global SCM model if the calculated times is set during the n times.

Occurring in the period from ( 1)n to ( )n m times, all of the 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 (Kantz et al. 1997; Schreiber 1998) to

forecast future demands based on known past events to predict the future demand.

By referring to Li’s method (2004), we then have following nonlinear time series analysis’

model.

A nonlinear demand forecasting model (NDF model)

Min 1

T

t t t

t

S a bQ y

(31)

s.t. t ty y ( ,t t and t t , which mean t and t belong to the same quarter), (32)

1

t

k

t

ky

, (33)

0ty , tS , a and b are free sign variables. (34)

where k is sum of seasons (usually 4k ), and denotes tS , tQ and ty as the sales,

quarter numbers and seasonal indexes, respectively. For example, if 8T then 1,5t

represent the first quarter, 2,6t represent the second quarter, 3,7t represent the third

quarter, and 4,8t represent the fourth quarter.

A NDF model is nonlinear because of existing absolute functions and nonlinear terms.

14

Following linear systems can linearize them. The linear approximation of the function

1, ( , )t t tF a y ay is a continuous function 1, ( , )ttf a y , which is equal to 1, ( , )ttF a y (i.e.,

211, ,, 1( , ) ( , )t l t tt lf a a F a y at each grid point 1 2( , )l l ) and a linear function of its variables

( , )ta y on the interior or edges of each of the indicated triangles. To describe the linear

approximation of the function 1, ( , )ttF a y , we then have following linear system (referring to

the models in Babayev (1997)).

1 2 1 2

1 2

1 1

1, 1, 1, 2, , ,

1 1

( , ) ( , )m m

t t t i l tt l l l

l l

f a y ay F d d

(35)

1 1 2

1 2

1 1

1, ,

1 1

m m

l l l

l l

a d

, (36)

2 1 2

1 2

1 1

2, , ,

1 1

m m

t l l l

l l

ty d

, (37)

1 2

1 2

1 1

,

1 1

1m m

l l

l l

, (38)

1 2 1 2

1 2

, ,

1 1

( ) 1l l l l

l

m m

l

u v

, (39)

1 2 1 1 22 2 ,1, , 1 1, 1

l ll l ll ll u for 1 1, ,l m and 2 1, ,l m , (40)

1 2 1 2 1 2 1 2, 1, 1, 1 , l l l l l l l lv for 1 1, ,l m and 2 1, ,l m ,, (41)

where 1 2, 0l l and

1 2 1 2, ,, {0,1}l l l lu v .

Expressions (36)~(38) define the point ( , ta y ) as the convex linear combination of the

vertices of the chosen triangle. Expressions (39)~(41) imply that if 1 2, 1l lu then

1 2 1 2 1 2, , 1 1, 1 1l l l l l l and 1 1 2 1 21 22 ,1, 1, 1, 2, , 1, 1, 2, , 1 , 1( , ) ( , ) ( , )t t l t l t l t l l lt l lf a y F d d F d d

1 2 1 21, 1, 1 2, , 1 1, 1( , )t l t l l lF d d ; or if 1 2, 1l lv then

1 2 1 2 1 2, 1, 1, 1 1l l l l l l and

1 2 1 2 1 2 1 2 1 2 1 21, 1, 1, 2, , , 1, 1, 1 2, , 1, 1, 1, 1 2, , 1 1, 1( , ) ( , ) ( , ) ( , )t t l t l l l t l t l l l t l lt t l lf a y F d d F d d F d d .

Mentions above give a basic formulation satisfying the piecewise linear approximation of

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1, ( , )t t t tF a y ay . Similarly, 2, ( , )t t t tF b y by can be also linearized by the same way

(for the proof, refer to Babayev (1997))

On the other hand, we use additional binary variables to treat the absolute function. Then a

piecewisely linear demand forecasting model can be reformulated as follows:

A Piecewisely Linear Demand Forecasting model (PLDF model)

Min1

T

t

t

(42)

s.t. (32) and (33),

( 1) (1 )t t t t t t t t t t tu M S Q S Q u M , (43)

t t t t t t t t t t tu M Q S Q S u M , (44)

where {0,1}tu , 0t , t and t are piecewisely linear variables of tay and tby ,

respectively, referred to (35)-(41).

Consider the following situations we know that the objective of the sum of absolute function

can be linearized by linear system, that is, (43) and (44).

(i) if 1tu then t t t t tS Q , which is forced by (43) because of 0t ,

(ii) if 0tu then t t t t tQ S , which is forced by (44) because of 0t ,

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 of p and p could be

expressed as a material or goods (i.e., parameter BOMp’p). So we can utilize a two-dimension

matrix to express the relationship between partial and 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

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expressed in Table 4 below. The aim is to design a friendly interface for our system design.

Table 4. BOM table

Parts p 1 p 2 p 3 p 4 p5 p 1 - 2 1 - -

p 2 - - - - - p 3 - - - 1 1 p 4 - - - - 0 p 5 - - - - -

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 (Treflerm, 1993;

Iman & Nagata, 2005; Romagnoli et al., 2007; Israel, 2010; Yang, 2011). A bonded

warehouse is one building or the 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, they may be processed by assembling, sorting, repacking, or

others, in which changing their condition that do not amount to manufacturing. 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

17

objective is to find more bonded warehouses, and more costs can be saved. In this study, the

policy has proved of advantage for the exporter to get great benefit in our numerical

examples.

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 lack of a kernel technique (i.e., deterministic mathematical model) for

developing global SCM system. At the same time, consider 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 benefits, 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. There lacks for optimum

efficiency and capability in the application server causing the heavy burden of CPU. For this

reason, by establishing a Broker Server can not only distribute the jobs into different

application servers but can also work in more efficiently processing and also maintaining the

load balance in networking. The basic architecture of the global SCM system is shown in the

following Fig. 4.

18

End User 1

Middle-Tier

Broker Server

Middle-Tier

Application

Server 2

Database

Backup DB

.

.

.

End User 2

End User 3

End Users

Middle-Tier

Application

Server 1

Middle-Tier

Application

Servers

Figure 4. Architecture of the multi-tier 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 data such as the username,

password, environment setting, logistics, etc., into database system. Moreover, the data must

back up to the other database to protect it from hacking or crashing. Then, the system

architecture is shown in the following Fig 5.

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Figure 5. Architecture of the Global SCM system

5. Numerical Examples

In our numerical examples assumed that the situation occurred in three different

overseas locations. There are three vendors ( 1v , 2v , 3v ), four facilities ( 1f , 2f , 3f , 4f ), four

warehouses ( 1w , 2w , 3w , 4w ), three retailers ( 1r , 2r , 3r ).Under the liberalization policies these

limited quantities of bonded warehouses are listed in Appendix. There are three parts

( 2p , 4p , 5p ) supplied from the vendor to the facility, and then these parts will be produced

another two kinds of parts ( 1p , 3p ) in different facilities. The period of time includes, one is

actual customer demand (i.e., 15nt ) and the other is forecasting demand (i.e., 2mt ) so

that the total period of time is 17 (i.e., 1t to 17). The other parameters are expressed in

Tables 6 to 30 of Appendix A. Moreover, the objective of the proposed model will make the

possible profits as a maximum of all nations in this supply chain environment. The numerical

example was solved via a global SCM system; these logistic results at different times t are

Browser Input Output

Client-Tier

(GUI Layer)

Security Module

Optimal Software Module

Demand Forecast Module

AP Controller

Module

Middle-Tier

(AP Server

Layer)

Backup DB

Server-Side

(Database

Layer)

Controller of Web and Map

Communication Module

(Serv let, EJB)

Google map

Map API

Database (DB)

DB access Module

Vector map

20

depicted in Figures 6 to 10.

Figure 6. The logistic flow at Time=1

Figure 7. The logistic flow at Time=2

Figure 8. The logistics flow at Time =6

P4=76

P4=342

P5=342

P5=76

V1

V2

V3

F2

F3

F1

F4

W1

W2

W3

W4

R1

R2

R3 P4=56

P4=386

P5=386

P5=56

P2=100

P2=86

P2=180 P1=83

P3=60 P3=90

P2=76

P3=110

P3=190

P3=190

P3=110

P3=180

P3=120

P1=52 P3=38

P3=43

P3=170

P3=110

P4=83

P4=111

P5=111

P5=83

V1

V2

V3

F2

F3

F1

F4

W1

W2

W3

W4

R1

R2

R3 P4=90

P4=279

P5=279

P5=90

P4=83

P4=111

P5=111

P5=83

V1

V2

V3

F2

F3

F1

F4

W1

W2

W3

W4

R1

R2

R3

21

Figure 9. The logistic flow at Time =7

Figure 10. The logistic flow at Time =8

By utilizing the proposed method, the objective value of the example is $603,010 with

consideration of the bonded warehouses. We then calculate them without bonded warehouses

again, the objective value is 514,680. Comparing both of them, the benefit ratio is increased

to 14.6% as shown in Table 5.

Table 5. Benefit ratio

Items Objective benefit ratio

Having bonded warehouse (Hb) $603,010 14.6%↑( -Hb Wb

Hb)

Without bonded warehouse (Wb) $514,680

P4=76

P4=338

P5=338

P5=76

V1

V2

V3

F2

F3

F1

F4

W1

W2

W3

W4

R1

R2

R3 P4=99

P4=348

P5=348

P5=99

P2=152

P2=112

P2=120 P1=50

P3=56

P3=60

P2=86

P3=130

P3=160

P3=160, P1=38

P3=130

P3=100

P1=60 P3=43

P3=56

P3=210

P3=120

P1=38

P1=90 P1=90

P3=170, P1=52

P1=83

P4=56

P4=386

P5=386

P5=56

V1

V2

V3

F2

F3

F1

F4

W1

W2

W3

W4

R1

R2

R3 P4=76

P4=338

P5=338

P5=76

P2=120

P2=104

P2=100 P1=90

P3=60 P3=50

P2=120

P3=100

P3=170

P3=170, P1=52

P3=100

P3=190

P3=110

P1=38 P3=60

P3=52

P3=160

P3=130

P1=52

P1=83 P1=83

22

In 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

[5, 10].

(iii)The capacities of bonded warehouses are according to the capacities of original

warehouses based on uniform distribution from 50%~90%.

(iv) In order to balance between the supply and demand, all of the coefficients are feasible

sets for the global SCM models.

According to the computational results which follow rules (i) to (iv), we observe that the

liberalization policy with bonded warehouses directly affect the activities of the global SCM.

We fixed the number of bonded warehouses is 5, the benefit ratio approaches 15%. When we

take the number of bonded warehouses to be 40 as an example, the benefit ratio enhances to

20%. Finally, the benefit ratio is close to 25% at 50 bonded warehouses. That is, considering

that more nodes have bounded constraints, there is a greater cost savings. Then the tendency

of the other 10 tests is depicted in Fig. 11.

The proposed model considers the liberalization policy with bonded warehouses as

flow-control constraints to obtain optimal benefits. Additionally, numerical experiments also

illustrate that the proposed model can enhance the benefit ratio when the number of bonded

warehouses is large.

23

14.6%

15.3%

16.3%

17.7%

18.1%

18.7%

19.1%

19.6%

20.4%

23.7%

25.1%

0%

5%

10%

15%

20%

25%

30%

3 5 10 15 20 25 30 35 40 45 50

# of warehouses

ratio

(%)

benefit ratio

Figure 11. The tendency of the benefit ratios for different numbers of warehouses

6. Conclusions

This study proposes a global SCM model which has 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 benefit ratio to

furthermore enhance the competitiveness. Numerical experiments’ reports are provided to

illustrate that the proposed model can be effectively solved to obtain the optimal benefit.

In the 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 to resolve the proposed demand

forecasting model.

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28

Appendix A

Table 6. Vendor Location

vLoc 1v

2v 3v

Location 1 (Taiwan) 2 (China) 3 (Japan)

Table 7. Facility Location

fLoc 1f

2f 3f 4f

Location 1(Taiwan) 2(China) 2(China) 3(Japan)

Table 8. Warehouse Location

wLoc 1w 2w 3w

4w

Location 1(Taiwan) 2(China) 2(China) 3(Japan)

Table 9. Retailer Location

rLoc 1r 2r 3r

Location 1 (Taiwan) 2 (China) 3 (Japan)

Table 10. The Weighting of Transportation Costs of Parts

pPT 1p 2p 3p

4p 5p

Weighting 1 0.2 0.8 0.1 0.5

Table 11. The Weighting of Inventory Costs of Parts

pPI 1p 2p 3p

4p 5p

Weighting 0.5 0.1 0.5 0.1 0.4

29

Table 12. The Duty of Parts in Different Nations

npDuty 1p

2p 3p 4p 5p

1n 0.2 0.3 0.2 0.01 0.05

2n 0.3 0.02 0.3 0.01 0.1

3n 0.1 0.01 0.1 0.05 0.03

Table 13. The Tax in Different Nations

nTax 1n

2n 3n

0.07 0.03 0.08

Table 14. Sales Price of Each Part for Each Vendor

vpPPRICE 1p 2p 3p

4p 5p

1v 28

2v 40

3v 40 30

*all blank cells are disabled

Table15. Maximum Supplied Limitation in Each Vendor

vfpUR _ 1f 2f 3f

4f

1v 0 10004 p 0 0

2v 0 0 5005 p 5005 p

3v 15004,7502 pp 0 15003 p 7002 p

※all blank cells are disabled

Table 16. Production Costs and Limitations for Each Facility

30

fpMCOST /fpUM _ 1p

2p 3p 4p 5p

1f 20/400

2f 30/350

3f 28/300

4f 30/450

※all blank cells are disabled

Table 17. Transportation Costs and Lead Time from Each Vendor to Each Facility

vfvf TTCOST / 1f

2f 3f 4f

1v 3/1

2v 1/1 1/1

3v 4/2 3/1 2/1

Table 18. Amount of Part p Needed for Producing Part p’

BOM 1p 2p 3p 4p 5p

1p 0 2 1 0 0

2p 0 0 0 0 0

3p 0 0 0 1 1

4p 0 0 0 0 0

5p 0 0 0 0 0

Table 19. The Lead-Time of Facility for Producing Part p’ and Sales Price in Facility

fpfp TPRICETbom / 1p 2p 3p

4p 5p

1f 1/250

2f 1/150

31

3f 1/150

4f 1/260

※all blank cells are disabled

Table 20. The Base of Inventory Costs

fICOST 1f

2f 3f 4f

6 2 1 12

Table 21. Maximum Stock Level in Each Facility

fpUI _ 1p 2p 3p

4p 5p

1f 200 400 200 0 0

2f 0 0 300 300 300

3f 0 0 400 400 400

4f 100 200 100 0 0

Table 22. Transportation Costs and Lead Time from One Facility to Another Facility

ffff TTCOST / 1f 2f 3f

4f

1f

2f 2/2

3f 3/2

4f

※all blank cells are disabled

Table 23. Maximum Transferable Quantity from One Facility to Another Facility

pffUR _ 1f 2f 3f

4f

32

Table 24. The Base of Inventory Costs and Fixed Costs

)( ww FCOSTICOST 1w

2w 3w 4w

5(50) 1(10) 1(10) 10(100)

Table 25. Transportation Costs and Lead-Time from the Facility to the Warehouse

fwfw TTCOST / 1w 2w 3w

4w

1f 1/1

2f 2/1 1

3f 1/1

4f 1/1

※all blank cells are disabled

Table 26. Maximum Transferable Quantity from the Facility to the Warehouse

Table 27.Transportation Costs and Lead Time from the Warehouse to the Retailer

1f ０ ０ ０ ０

2f 10003 p ０ ０ ０

3f ０ ０ ０ 10003 p

4f ０ ０ ０ ０

fwpUR _ 1w 2w 3w

4w

1f 8001 p 0 0 0

2f 8003 p 6003 p 0 0

3f 0 0 10003 p 0

4f 7001 p 0 0 0

33

wrwr TTCOST 1r

2r 3r

1w 1(1) 3(1)

2w 2(2) 1(1)

3w 1(1)

4w 1(1)

※all blank cells are disabled

Table 28. Maximum Transferable Quantity from the Warehouse to the Retailer

Table 29. Sales Price of Each Part and Limitation in Each Warehouse

wpwp UIPRICE _/ 1p 2p 3p

4p 5p

1w 380/300 0 280/300 0 0

2w 0 0 200/500 0 0

3w 0 0 200/600 0 0

4w 450/150 0 0 0 0

Table 30. Retailer Demand and Forecasting at Each Time

Retailer 1R Retailer 2R Retailer 3R

Dtrp 1p 2p 3p 4p 5p

1p 2p 3p 4p 5p

1p 2p 3p 4p 5p

1t 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

wrpUR _ 1r 2r 3r

1w 800,700 31 pp 0 3001p

2w 8003p 8003p 0 0

3w 0 8003p 0

4w 0 0 10001p

34

2t 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

3t 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

4t 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

5t 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

6t 0 0 180 0 0 0 0 120 0 0 0 0 0 0 0

7t 0 0 190 0 0 0 0 110 0 0 0 0 0 0 0

8t 52 0 170 0 0 0 0 100 0 0 83 0 0 0 0

9t 38 0 160 0 0 0 0 130 0 0 90 0 0 0 0

10t 60 0 210 0 0 0 0 120 0 0 50 0 0 0 0

11t 43 0 180 0 0 0 0 110 0 0 60 0 0 0 0

12t 52 0 190 0 0 0 0 100 0 0 76 0 0 0 0

13t 56 0 170 0 0 0 0 110 0 0 56 0 0 0 0

14t 48 0 180 0 0 0 0 130 0 0 76 0 0 0 0

15t 58 0 200 0 0 0 0 120 0 0 99 0 0 0 0

16t 31 0 190 0 0 0 0 90 0 0 80 0 0 0 0

17t 52 0 180 0 0 0 0 120 0 0 50 0 0 0 0