全球產銷供應鏈管理之節稅模式

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國

立

交

通

大

學

交通運輸研究所

博士論文

No.060

全球產銷供應鏈管理之節稅模式

A tax savings model for managing a global

production-distribution supply chain

指導教授

指導教授：

：

：馮正民

：

馮正民

研

研究

究

究生

生

生：

生

：

：吳沛儒

：

吳沛儒

中

中華

華民

華

民

民國

國

國九

國

九

九十

十八

十

八

八年

年

年六

六

六月

六

月

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全球產銷供應鏈管理之節稅模式

A tax savings model for managing a global

production-distribution supply chain

研究生：吳沛儒 Student：Pei-Ju Wu

指導教授：馮正民博士 Advisor：Dr. Cheng-Min Feng

國立交通大學交通運輸研究所

博士論文

A Dissertation

Submitted to Institute of Traffic and Transportation College of Management

National Chiao Tung University in Partial Fulfillment of the Requirements

for the Degree of Doctor of Philosophy in

Management

June 2009

Taipei, Taiwan, Republic of China

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全球產銷供應鏈管理之節稅模式

學生: 吳沛儒指導教授: 馮正民博士國立交通大學交通運輸研究所

摘要

複雜的全球產銷供應鏈網路包括課稅區、國際運籌區、深層與淺層加工製造程序之區位點特性，以及運輸之節線特性。妥善地選擇節稅區位與製造程序，用以增加稅後利潤，對於全球性製造業者相當地重要。基此，本研究旨在提出幾個節稅方法，進而發展出該複雜網路下之稅後利潤最大化的節稅模式。數值實驗說明本研究提出的模式係為一有效的方法，可以讓全球性製造業者達到稅率節省之目的，而本模式也指出重要關鍵的節稅運籌行為。關鍵字關鍵字關鍵字關鍵字：全球產銷網路、國際運籌區、稅後利潤、節稅模式、運籌行為

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A tax savings model for managing a global

production-distribution supply chain

Student: Pei-Ju Wu Advisor: Dr. Cheng-Min Feng Institute of Traffic and Transportation

National Chiao Tung University

ABSTRACT

The complex global production-distribution network involves nodal location features of tax areas and international logistics zones, manufacturing procedures of simple process and deep process, as well as transportation arcs. Since choosing tax savings locations and manufacturing procedures that increase after-tax profit is important to global manufacturers, this study aims to present several tax savings approaches and to develop a tax savings model for maximizing after-tax profit in the complex network. Numerical illustration demonstrates that the proposed model is an effective approach for global manufacturers to achieve tax savings. The proposed model elucidates the crucial logistics behavior associated with tax savings.

Keywords: Global production-distribution network, International logistics zone, After-tax profit, Tax savings model, Logistics behavior

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ACKNOWLEDGMENTS

I owe a debt of graduate to many people whose help has been crucial to my success in completing this dissertation. First of all, I have been privileged to have the direction and guidance of my excellent mentor, Prof. Cheng-Min Feng. From the inception of this dissertation, he has been generous with his time and has provided eminently helpful advice on everything from the methodological design to the writing process. His faith in me and his ability to bring me back on track at difficult times have been a godsend. He has likewise made invaluable contributions to the development of my ideas and organization of the analysis. He has always motivated me to do my best work, offering timely feedback on each chapter and keen insight into the significance of my research. My other committee members, Prof. Pao-Long Chang, Gwo-Hshiung Tzeng, Ren-Jieh Kuo, Mu-Chen Chen and Jiuh-Biing Sheu, have contributed insightful and critical comments and suggestions. Special thanks to Prof. Mu-Chen Chen for stimulating conversation that reassured me of the significance of my research, helped me to focus some of the theoretical ideas, and provided me encouragement at a crucial time. I also received valuable suggestions from professors at each Ph.D. student seminar, comprising Prof. Lawrence Lan, Jinn-Tsai Wong, Tai-Sheng Huang, Cherng-Chwan Hwang and Yu-Chiun Chiou.

My heartfelt appreciation goes out to Dr. Tsai-Chu Wang who has helped me over the years. He was extremely generous with his time and provided invaluable assistance and enthusiasm. I have enjoyed the camaraderie of Chien-Yun, Shue-Mei, Yu-Kai, Yi-San, Hui-Chan, Yen-Heng, Shih-Chang, Chih-Cheng, Chao-Hung, Yan-Fei, Cheng-Hsien, Chun-Ming, Yu-Szu, Yung-Hsiang, Yi-Shih, Shih-Hsuan, Jau-Rong, Sheng-Chung, Su-Ru, Li-Chin, Chia-Yang, Wei Yu, Chi-Lun, Zih-Huei, Kao-Chou, Ri-Xin

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various times and places. My esteemed colleague and dear friend Chun-Ying Chen provided just the right amount of everything I needed from a friend to get through this process and not lose perspective-most memorably, countless parties. Many other people have helped me weather the emotional storms and stress of graduate school, some of whom deserve special mention. To my classmates of my elementary school, junior high school, senior high school, university, and graduate school, I am grateful for the companionship, diversions, and nourishment of body and soul.

Finally, I owe much to my parents, Chia-Hao Wu and Shih-Chiao Huang, for always believing in me and encouraging me to achieve my goals. They, to whom this dissertation is dedicated, provided me with rare opportunities as a child to learn foreign languages and to expand my horizon. They, more than anyone, nurtured my intellectual curiosity and fostered my creation of a spirit of community. They have always been there for me, and have never failed to do what they could to further my progress. Their compassion, generosity, and steadfast emotional support have been invaluable in helping me to focus on my academic pursuits. They forever inspire me with their infinite capacity for love, joy, and faith. Furthermore, thanks to my wonderful aunt, Kuei-Chih Cheng, far and near for her constant support of my efforts. Additionally, my brother and sister, Hsu-Kang and Ting-Chin, have always offered me their support, sympathy, and admiration.

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A tax savings model for managing a global

production-distribution supply chain

LIST OF TABLES

PAGES

TABLE 6.1MAIN CHARACTERISTICS OF THE BASIC SCENARIO...51

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LIST OF FIGURES

PAGES

FIGURE 1-1RESEARCH PROCEDURE...7

FIGURE 3-1TYPES OF GOODS...16

FIGURE 3-2DEEP PROCESS AND SIMPLE PROCESS FUNCTIONS...20

FIGURE 3-3FLOW OF GOODS...21

FIGURE 4-1CHARGE CONDITION OF IMPORT DUTY...23

FIGURE 4-2IMPORT FROM LOW DUTY COUNTRY...23

FIGURE 4-3IMPORT DUTY AND PRODUCT FORMS...24

FIGURE 4-4CHARGE CONDITION OF VAT ...26

FIGURE 4-5ROUTES FOR MINIMIZING CORPORATE TAX...27

FIGURE 6.1GLOBAL NETWORK USED FOR THE NUMERICAL STUDY...50

FIGURE 6.2NUMERICAL RESULTS FOR LOGISTICS BEHAVIOR...52

FIGURE 6.3AN ILLUSTRATIVE EXAMPLE OF THE DEEP PROCESS AND THE SIMPLE PROCESS...55

FIGURE 6.4SENSITIVITY OF AFTER-TAX PROFIT WITH RESPECT TO VARIANT TAX PARAMETERS...56

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CHAPTER 1 INTRODUCTION

This chapter is divided into four sections: (1) background and motivation; (2) purpose and scope; (3) research procedures; and (4) chapter organization.

1.1 Background and Motivation

Global logistics can be conceptualized as the geographic expansion of domestic logistics into markets abroad (Bowersox and Closs, 1996; Sheu, 2004). Fierce competition in a rapidly changing global market has imposed tremendous pressure on manufacturing enterprises, forcing them transform and adjust their supply chain operations abroad (Chia et al., 2002). Enterprises need to incorporate fragmented logistics activities into an international business operation (Birkinshaw and Morrison, 1995; Greis and Kasarda, 1997; Porter, 1998). Albino et al. (2002) indicated that a necessary policy for managing resources is to negotiate the supply chain both at a global and a local level. Prater and Ghosh (2006) also noted that globalization permits enterprises with expanded supply chains to access and coordinate global resources. Manufacturers are increasingly capable of dealing with full system production, and currently seek to add value to existing production systems (Zhai et al., 2007). Accordingly, global

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manufacturers are currently integrating their operations in different countries to achieve manufacturing efficiency across markets and in units that operate worldwide (Cavusgi et al., 2004). Furthermore, facilities with both manufacturing and distribution functions can better cope with rapid changes in global logistics (Simchi-Levi et al.,2003; Sheu, 2004; DHL, 2006).

However, once goods are transferred from one place to another, complicated tax factors arise, such as import duties, corporate taxes, value added taxes, sales taxes, etc. (Goetschalckx et al., 2002; Sheu, 2003; Meixell and Gargeya, 2005; Power, 2005). Therefore, both the practitioners (such as Foxconn, Weblink International, DHL, etc.) and academics (Arntzen et al., 1995; Vidal and Goetschalckx, 2001; Fandel and Stammen, 2004; Avittathur et al. 2005; Vila et al., 2006; Balaji and Viswanadham, 2008) are actively seeking appropriate ways to save tax costs. Moreover, most enterprises using transfer prices to avoid taxation are illegal. Thus, it is worthwhile to look for legitimate tax savings approaches.

Governments recognize that most global enterprises pay a great deal of attention to the impact of tax factors on their global profit. Therefore, a common governmental strategy is to develop “international logistics zones” (Lu and Yang, 2007) offering tax-exemption strategies (e.g., exemptions

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from corporate tax or import duties) to attract investment and ideally to spark economic growth. Taking advantage of preferential taxation is extremely important for global manufacturers to achieve tax savings.

Nevertheless, few studies have investigated the optimal tax savings route and manufacturing procedures to increase after-tax profit for managing a production-distribution supply chain in the global network with international logistics zones.

1.2 Purpose and Scope

With the background and motivations mentioned above, the main purposes of this study are as follows:

1. To represent the concept of various tax savings approaches.

2. To develop a tax savings model for the purpose of managing a global production-distribution supply chain in the complex global production-distribution network with international logistics zones.

(1) To maximize after-tax profits while simultaneously considering tax factors (import duties, corporate taxes, VAT) and other basic cost factors (e.g., transportation cost, inventory cost, etc.). (2) To determine the legal optimal tax savings route and

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manufacturing procedures.

To facilitate model formulation, the study scope is postulated as follows: 1. Goods are classified in this study as modular components,

semi-products and finished products.

2. Supply chain members include both internal and external members responsible for different global logistics functions. Internal supply chain members include manufacturing centers and processing DCs, while external supply chain members are vendors and brand name companies. Moreover, the number and location of all supply chain members are given. A hybrid fuzzy integral decision-making model for selecting locations can be found in Feng et al. (2009).

There are still some factors that affect the determination of the optimal tax savings route and manufacturing procedures in the global production-distribution network with international logistics zones, such as quotas, certificates of origin and local content that will not be discussed in this study.

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1.3 Research Procedures

The research procedures are briefly explained as follows and shown in Figure 1-1.

1. Problem identification

The first step is to identify the background, motivation, purposes and scope of this study. Herein, the research problems were derived from the first step.

2. Literature review

The second step is to achieve an adequate understanding of the relevant literature on global production-distribution supply chains, international logistics zones and tax savings models. This step assists in understanding the development and management of a global production-distribution supply chain in the global production-distribution network with international logistics zones. 3. Problem statement

The third step is to state the problem and clarify the scope of the study. This step also facilitates model formulation.

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4. Tax savings approaches

The fourth step is to investigate key tax factors contributing towards operating income under the characteristics of international logistics zones.

5. Modeling

The fifth step is to formulate a tax savings model for the purpose of deriving after-tax solutions that are able to maximize profit in the global production-distribution network with international logistics zones.

6. Numerical illustration

The sixth step is to test the applicability and the solvability of the proposed model. Here, a simplified numerical study is out through an interview. Sensitivity analysis is used for varying tax parameters such as corporate tax rates, duty, VAT rates and VAT drawback rates. To further examine logistics behavior, three extended scenarios and their numerical results are presented.

7. Conclusions and suggestions

The seventh step is to summarize crucial findings based on the numerical results of the logistics behavior. Furthermore, the

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distinction between this study and previous studies are discussed as well. Finally, related issues not addressed in this study are identified for further research.

Tax Savings Model

Problem identification

Literature review

International Logistics Zone Global Production-distribution

Supply Chain

Extended Scenarios

Conclusions and suggestions

The Basic Scenario

Sensitivity Analysis

Tax savings approaches

Modeling

Numerical illustration Problem statement

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1.4 Chapter Organization

The rest of the study is organized as follows. Chapter two conducts a thorough review of the global production-distribution supply chain and the international logistics zone and tax savings model. Chapter three outlines the main problem studied. Chapter four describes the concept of tax savings approaches. Chapter five provides a model with tax savings, with incorporation of an emerging global production-distribution network, to find after-tax profit-maximizing solutions. Chapter six tests the effectiveness of the proposed model and discusses the findings and numerical results. Finally, Chapter seven summarizes the conclusions.

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CHAPTER 2 LITERATURE REVIEW

The literature review includes the following: (1) global production-distribution supply chains; (2) international logistics zones; (3) tax savings models.

2.1 Global Production-distribution Supply Chain

In order to satisfy worldwide customer requirements, many manufacturers desire to transform their domestic logistics into global logistics. To become a global manufacturer in the present day, a manager needs to devise not only production but also distribution strategies.

Each manufacturing base only produces special ancestor goods (e.g. components) for the total demand in participating countries, and ships these ancestor goods to other manufacturing bases for further transformation of ancestor goods into descendant goods (e.g. finished products) (Arntzen et al., 1995; Hiraki, 1996). Consequently, a distributed product often has its manufacturing activities dispersed throughout many locations (Lakhal et al., 2005).

Mattsson (2003) pointed out that the globalization of manufacturers requires global coordination between distribution and manufacturing activities. Swafford et al. (2006) observed that enterprises can adopt

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manufacturing and distribution processes that reduce the influence of demand uncertainty. Boissière et al. (2008) argued that global supply chain management needs to consider limited production capacity and distribution costs.

Manufacturers are increasingly capable of dealing with full system production, and currently seek to add value to existing production systems (Zhai et al., 2007). Minimizing manufacturing cost and production time combined with the increasing quality and shipment reliability are important challenges to all production systems (Mezgár et al., 2000).

Specifically, manufacturers must devise effective global logistics strategies that maximize profit and fulfill customer orders within the manufacturing networks (Hammami et al., 2003). Hameri and Paatela (2005) also observed that contract manufacturers focus on integrating value added operations in networks to maintain and recreate profitable business in markets with narrow margins.

Enterprises can extend spatiotemporal coordination to move towards supply chain collaboration. Supply chain integration significantly affects the performance improvement of the supply chain (Frohlich and Westbrook, 2001; Petersen et al., 2005; Elmuti et al., 2008). Supply chain

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collaboration is especially effective in realizing an enhanced speed-to-market (Samaranayake, 2005, Soosay et al., 2008), as demonstrated by looking at Hyundai (Hahn et al., 2000) and BMW (Miles and Snow, 2007).

Model formulations and solution algorithms for the production-distribution problem have been proposed in the past (Lee and Kim, 2002; Yan et al., 2003; Chan et al., 2005; Chen and Vairaktarakis, 2005; Nonino and Panizzolo, 2007).

Vidal and Goetschalckx (1997) conducted an extensive review of strategic production-distribution models. Barbarosoglu and Özgür (1999) built the hierarchical design of an integrated production and distribution system. Björk and Carlsson (2007) pointed out that seeking the optimal manufacturing plan and the coordination of shipments with said optimal manufacturing plan is very critical and difficult.

Aliev et al. (2007) put forth a fuzzy-genetic approach to aggregate the production-distribution planning in supply chain management. Selim et al. (2008) developed a fuzzy goal programming approach to deal with the collaborative production–distribution planning in a supply chain.

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focused on computational efficiency or special cases, which has limited the applicability of their results to reality.

2.2 Tax Savings and International Logistics Zone

Governments recognize that most global enterprises pay a good deal of attention to the impact of tax factors on their global profit. Therefore, a common governmental strategy is to develop “international logistics zones” (Lu and Yang, 2007) offering tax-exemption strategies (e.g., exemptions from corporate tax or import duties) to attract investment and ideally to spark economic growth. Examples of these logistics zones are free trade zones, export processing zones, free port zones, bonded zones, global logistics hubs and customs-free zones (Prasad and Sounderpandian, 2003; Lee and Yang, 2003; Oum and Park, 2004; Lu and Yang, 2007; Lee, 2007).

International logistics zones provide opportunities to implement functional activities involving transportation, distribution, assembly, storage, clearance, consolidation, labeling, packing, inspecting, and marketing (Lu, 2003; Sheu, 2004; Teng et al., 2007).

Lin et al. (2006) pointed out that many countries have instituted export processing zones, foreign trade zones, and logistics centers, and further

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market their finished products around the world. Lee (2007) mentioned that multinational corporations have focused logistics functions such as warehousing, distribution, and reprocessing in a global logistics hub.

For the purposes of this study, “international logistics zones” are defined as zones offering tax-exemptions, while “tax areas” are defined as areas which do not offer tax preferences. Taking advantage of preferential taxation is extremely important for global manufacturers in order to achieve tax savings. Herein, tax savings means the amount enterprises save on taxes.

Additionally, global enterprises have typically used the transfer price (Van Mieghem, 1999; Gjerdrum et al., 2002; Eden and Rodriguez, 2004) to manipulate profit distribution among their subsidiaries. However, this makes them easy prey for costly audits and litigation (Lakhal et al., 2005). Many countries now have international logistics zones that reduce taxes for global enterprises. Thus, discussing legitimate tax savings approaches associated with international logistics zones is worthwhile.

2.3 Tax Savings Model

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studies. Arntzen et al. (1995) proposed a global supply chain model for minimizing the total cost at the Digital Equipment Corporation with consideration to duty drawbacks and duty relief.

Simchi-Levi et al. (2003) further noted that implementing a strategy in which the manufacturing process is completed in a local DC can reduce costs associated with duties as duties are lower for semi-products than for finished products. Accordingly, manufacturers must decide whether to: (1) import semi-products and then convert these products into finished products in tax areas to reduce duties; or (2) manufacture finished products in international logistics zones and then import the finished products to tax areas to reduce corporate tax.

Since a differential tax structure contributes to distribution network decisions that can cause logistic inefficiency, Avittathur et al. (2005) developed a model for determining the locations of distribution centers (DCs) which considered the impact of differential sales taxes which was applicable in inter-state trade.

Nonetheless, corporate taxes are not easily incorporated into a profit-maximizing model, mainly because some of the subsidiaries of a global manufacturer may operate at a loss. Restated, unprofitable

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subsidiaries are not required to pay corporate taxes, but others are subject to corporate tax. Vidal and Goetschalckx (2001) constructed a global supply chain model to cope with the above problem. Their model maximized the after-tax profit of a multinational enterprise by considering transfer pricing and transportation cost allocation.

Fandel and Stammen (2004) and Vila et al. (2006) extended previous research to construct an after-tax profit-maximizing model that would reflect similar tax factors such as duties and corporate taxes, with an emphasis on product life cycles and divergent process industries. Balaji and Viswanadham (2008) proposed a tax model to choose between outsourcing versus foreign direct investment (FDI) alternatives at the various stages of a global supply chain.

However, there has been little done to develop a model which simultaneously considers import duties, value added taxes and corporate taxes in a global production-distribution network with international logistics zones.

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CHAPTER 3 PROBLEM STATEMENT

To clarify the study scope and facilitate model formulation, the problem statement is postulated as follows: (1) types of goods; (2) supply chain members and the flow of goods; (3) transactions.

3.1 Types of goods

Goods, ancestral to descendent, are classified in this study as modular components, semi-products and finished products. The modular strategy has been discussed in detail elsewhere (Lamothe et al., 2006). Figure 3-1 shows three methods of goods transformation, including transforming modular components into semi-products, transforming modular components into finished products or transforming semi-products into finished products.

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3.2 Supply chain members and the flow of goods

Supply chain members include internal and external members responsible for different global logistics functions. Internal supply chain members include manufacturing centers and processing DCs, while external supply chain members include vendors and brand companies. Moreover, the number and location of all supply chain members are given. Kerbache and MacGregor Smith (2004) indicated that after manufacturers link their internal processes to external supply chain members, the resulting supply chain often comprises a very large network of activities and resources. The modeling and optimization of such a complex system is very difficult.

Facilities functioning only as manufacturing centers or only as distribution centers are less responsive to rapid changes in global commerce than facilities capable of both. Simchi-Levi et al. (2003) pointed out that intense competitive pressure has forced manufacturers to add manufacturing capability at DCs. Sheu (2004) also noted that manufacturers with combined production and distribution facilities have significant advantages in global logistical management. Furthermore, DCs in international logistics zones can be classified as “deep process” and “simple process” facilities (DHL, 2006). Deep processing DCs have manufacturing

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functions proceeding with serious manufacture producing added value, while simple processing DCs cannot manufacture and merely own the functions of simple and convenient processes (e.g. assembling). For clarity, DCs serving the functions of either simple or deep processing, or both are defined as “processing DCs” in our study. In practice, DCs can be divided into three types: deep processing DCs, simple processing DCs and non-bonded DCs, depending on their locations and manufacturing procedures. Deep processing DCs located in international logistics zones have both deep process and simple process functions. Although located in international logistics zones, simple processing DCs only have the simple process function. Non-bonded DCs perform the same functions as deep processing DCs, but they are located in tax areas. Accordingly, the emerging global production-distribution network comprises nodal location characteristics of tax areas and international logistics zones, manufacturing procedures of simple process and deep process in these nodes, as well as transportation arcs.

Manufacturing centers receive modular components from vendors which are then transformed into semi-products or finished products. Then, manufacturing centers send semi-products or finished products to DCs.

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The basic functions of DCs are consolidating and distributing finished products from manufacturing centers to brand companies. Nevertheless, processing DCs may also have simple, deep (or both) processing functions, depending on their location in international logistics zones or tax areas. Accordingly, DCs can be divided into three types: deep processing DCs, simple processing DCs and non-bonded DCs. As Figure 3-2 illustrates, deep processing DCs located in international logistics zones have both deep process and simple process functions. Here, deep process involves transforming modular components into semi-products, transforming modular components into finished products and transforming semi-products into finished products, while simple process involves simple processes of semi-products and finished products (e.g. transfer, assembling, and packaging). Although located in international logistics zones, simple processing DCs only have the functions of a simple process for semi-products and finished products. Non-bonded DCs perform the same functions as deep processing DCs, but they are located in tax areas. Based on the function of DCs mentioned above, deep processing DCs and non-bonded DCs receive modular components from vendors. DCs may also receive semi-products or finished products from manufacturing centers.

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Furthermore, semi-products or finished products can be transferred between all kinds of DCs.

Figure 3-2 Deep process and simple process functions

This analysis assumes venders in a typical supply chain to be located below the top upstream suppliers. They receive and then process raw materials from upstream suppliers in order to manufacture modular components, which are then sent to manufacturing centers, deep processing DCs or non-bonded DCs.

Brand companies will request global manufacturers to distribute finished products to assigned locations around the world. Assigned locations could be DCs or warehouses owned by these brand companies. Figure 3-3 shows the flow of goods.

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Figure 3-3 Flow of goods

Once both processing DCs and international logistics zones are incorporated in the emerging global production-distribution network, global manufacturers have difficulty in determining the optimal tax savings route and manufacturing procedures for each order. Moreover, to identify the best tax savings route and manufacturing procedures, an after-tax model should allow for goods free transfer among processing DCs. Restated, a finished product may be processed via simple or deep processing, or both, in various DCs.

3.3 Transactions

Since many brand companies often contract with global manufacturers for delivered duty paid (DDP) transactions, transactions in our model are based on the DDP value of the shipment. Herein, DDP means that the seller bears the risks and costs, including taxes, duties and other charges of transporting the goods until they have been delivered.

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CHAPTER 4 TAX SAVINGS APPROACHES

According to in-depth interviews with global manufacturers, the three key tax factors contributing to operating income are: import duties, value added tax and corporate tax. Furthermore, considering the characteristics of international logistics zones, the conditions for evaluation of import duties, value added tax and corporate tax are more complex in the emerging network than in a typical network. The tax savings approaches for these three taxes are outlined below.

4.1 Import Duty

Import duties are tariffs paid to the relative government as goods pass into tax areas. Issues of import duties can be divided into the following three dimensions.

1. Charge condition

As situation depicted in Figure 4-1, the charge condition of import duty is that for the same country original flows are in international logistics zones and destination flows are in tax areas, while for different countries destination flows are in tax areas.

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Country A international logistics zone tax area FA FA Country B international logistics zone tax area FA FA

Figure 4-1 Charge condition of import duty 2. Import from low duty rate country

Since duty rates may differ between countries for the same goods, enterprises can reduce costs by importing goods from countries with lower duties. As Figure 4-2 shows, import duties from country B

($80=$800*10%) are lower than from country A_{($400=$800*50%) for}

the same goods ($800). Consequently, assuming all other conditions are equal, the enterprise can save import duties by importing via the low duty country.

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3. Import duty and product forms

Duty rates change with respect to product form, and manufacturers must then determine the most advantageous trade-off between import duty and processing cost. For instance, assuming country B_{requires the finished}

products in Figure 4-3, manufacturers must decide whether to (1) convert raw materials into finished products in country A_{and then import the}

finished products to country B_{or (2) import raw materials from country} A_{and then convert the raw materials into finished products in country} B_.

Figure 4-3 Import duty and product forms

4.2 Value Added Tax

Assessment of value added tax (VAT) is based on the incremental increase in the value of goods from raw materials to finished products. For each transaction, VAT is levied on the increased value of a product after input from previous chain members. Value added tax is generally formulated as follows:

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where VATcost implies the cost of VAT; ps, pi, po represent the prices associated with sale, input and export, respectively; qs, qi, qo denote the quantities associated with sale, input and export, respectively; VAT indicates VAT rate (%) on the value of goods; DRT _{signifies VAT}

drawback rate (%) on the value of goods.

The first term in Eq. (1) represents sales VAT, and the second term denotes input VAT. Sales VAT can be offset by input VAT. Further, the third term is regarded as export VAT which refers to the VAT imposed on certain exported goods in some countries, e.g. China. Thus, governments adopt strategies for regulating the VAT drawback rate for exports. For example, a country may increase the VAT drawback rate to promote the exporting of certain goods (e.g. mechanical and electrical products) whereas a country may decrease the VAT drawback rate for goods that were restricted to exporting (e.g. natural resources).

As Figure 4-4 illustrates, according to a DC in tax areas or in international logistics zones, the charge condition of sales VAT is that destination flows are in tax areas for the same country, while the charge condition of input VAT is that neither original nor destination flows are in international logistics zones. Further, the charge condition of export VAT

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is that, in the same country, original flows are in tax areas, and destination flows are in international logistics zones; for different countries, both original and destination flows are not in international logistics zones. Consequently, international logistic zones enable enterprises to avoid government regulation strategies of export VAT.

Figure 4-4 Charge condition of VAT

4.3 Corporate Tax

Corporate tax is the tax paid by enterprises on the profit they earn. For tax savings, goods completely manufactured in international logistics zones

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are exempt from corporate tax. Nevertheless, manufacturers must identify the most advantageous trade-off between corporate tax and other costs (e.g., import duties).

Products can be manufactured primarily in international logistics zones in order to save corporate tax. As Figure 4-5 illustrates, an example of the tax-saving approach concerning corporate tax for the requirement of finished products in country C . Goods are transformed from raw materials into semi-products in country A, then the semi-products are shipped from country A to country B for further transformation from semi-products into finished products. Finally, the finished products are shipped from country B to country C. Accordingly, the tax-saving route (A_{BC) saves $750 over that of direct shipment (AC).}

Income of enterprise A =$10,000-$6000=$4,000 Corporate tax rate=25%

Total cost =$6,000

Manufacturer Customer

Subsidiary

Corporate tax =$4,000*25%=$1,000 Sales price of finished products=$10,000

Sales price of semi-products =$7,000

Income of enterprise A =$7,000-$6,000=$1,000 Corporate tax =$1000*25%=$250

Income of subsidiary =$10,000-$7,000=$3,000 Corporate tax =$3,000*0%=$0

Net income before tax =$1000+$3000=$4,000 Total corporate tax =$250+$0=$250

Net income after tax =$3,750 Corporate tax rate=0%

Country B

Country C Country A

international logistics zone tax area

tax area

Tax savings

A→B→C

{

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Furthermore, two possibilities exist with regard to paying corporate tax: (1) paying corporate tax to multiple governments in the various jurisdictions where the enterprise operates; (2) paying corporate tax to one government based on headquarter location. To facilitate model formulation, this study focuses on situation (1).

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CHAPTER 5 MODELING

Given the problem statement, a tax savings model is formulated to derive after-tax solutions that maximize profit in the emerging global production-distribution network. The proposed model is based on models developed by Vidal and Goetschalckx (1998), Vidal and Goetschalckx (2000), Vidal and Goetschalckx (2001), Fandel and Stammen (2004) and Vila et al. (2006). Nevertheless, once the after-tax model considers the emerging global production-distribution network, determining the optimal tax savings route and manufacturing procedure for each order is difficult. Furthermore, three principal tax factors—import duty, value added tax and corporate tax—are considered simultaneously in the proposed model. Before formulating the proposed model, basic notations and definitions are presented. This chapter is divided into three sections: (1) notations and definitions, (2) objective function and (3) constraints.

5.1 Notations and Definitions

All the notations and definitions for sets, decision variables and parameters are summarized as follows.

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FA Set of internal and external supply chain members. Herein, V

FA : set of vendors (abbreviated as V ); M

FA : set of manufacturing centers (abbreviated as M ); Ds

FA : set of simple processing DCs (abbreviated as Ds; Dd

FA : set of deep processing DCs (abbreviated as Dd); Dn

FA : set of non-bonded DC (abbreviated as Dn); B

FA : set of brand companies (abbreviated as B); I

FA : set of all internal supply chain members (abbreviated as I); DC

FA : set of all DCs, including deep processing DCs, simple processing DCs and non-bonded DCs (abbreviated as DC); FAC: set

of chain members in international logistics zones (abbreviated as C); FAT: set of chain members in tax areas

(abbreviated as T).

G Set of types of goods. Herein, r

G : set of modular components (abbreviated as r); s

G : set of semi-products (abbreviated as s ); p

G : set of finished products (abbreviated as p).

N _{Set of countries.}

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rs

SN : set of product lines involving transformation of modular components r into semi-products s

(abbreviated as rs); rp

SN : set of product lines involving transformation of modular components r into finished products p (abbreviated as rp ); sp

SN : set of product lines involving transformation of semi-products s into finished products p (abbreviated as sp); ss

SN : set of product lines involving simple processing of semi-products

s (abbreviated as ss ); pp

SN : set of product lines involving simple processing of finished products p

(abbreviated as pp); SNI : set of product lines of inbound

flow (abbreviated as I ); SNO: set of product lines of

outbound flow (abbreviated as O); R

SN : set of product lines of sum of corresponding modular components (abbreviated as R); S

SN : set of product lines of sum of corresponding semi-products (abbreviated as S); P

SN : set of product lines of sum of corresponding finished products (abbreviated as P).

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available transportation modes between a given chain member θ in the country x∈N and another given chain member λ in the country y∈N.

2. Decision variables

x

gotr_{θ αβ} _{Binary decision variable indicates whether goods}

transformation occurs at a given chain member θ in country x∈N when transferring ancestor goods α into descendant goods β.

x _f

gt_{θ α} _{Binary decision variable indicates whether goods} _α _{is in}

progress in a product line f at a given chain member θ in country x∈N.

x

oi_θ _{Operating income of a given chain member} _θ_{in country} x∈N for the period of analysis (dollar/unit of time).

x

ord_{θ α} _{Number of nodes visited on the transfer path from the}

origin up to node _θx

for goods α (i.e., the visit number of the _θx

th node).

x y_m

qu_{θ λ} _α _{Binary decision variable representing whether goods} _α_∈_G

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to another given chain member λ in country y∈N, using transportation mode ( x, y)

m∈Ωθ λ .

3. Parameters

y

BR_λ _{Required finished products for a given chain member} _λ_in

country y∈N (units of p/unit of time).

BOM_αβ _{Units of ancestor goods} _α_∈_G_{required to make one unit}

of descendant goods B∈G (α-units/ β-unit).

BN _{A big number.}

CSF _{Cycle stock factor (%).}

x

COT_θ _{Corporate tax rate (%) of country} _x_∈_N_{of a supply chain}

member θ.

CPRICE_α_{International contract price of goods} _α_∈_G_{(dollar/unit of}

goods α )

x

DRT_{θ α} _{Value added tax drawback rate (%) on the value of goods} G

α∈ of country x∈N of supply chain member θ.

x y

DUTY_{θ λ α}_{Import duty rate (%) on the value of goods} _α_∈_G_shipped

from a given chain member θ in country x∈N to another given chain member λ in country y∈N.

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x

E_θ _{Exchange rate of country} _x_∈_N_{of supply chain member} θ (monetary units of the respective country/dollar).

x

FIX_θ _{Fixed cost associated with a given chain member} _θ_in

country x∈N (monetary units of country of member θ per unit of time).

x y_m

FS_{θ λ} _{Frequency of goods shipments from a given chain member} θ in country x∈N to another given chain member λ in country y∈N , using transportation mode ( x, y)

m∈Ωθ λ

(units of time ).

H Holding cost ($/($. unit of time)).

x

IV_{θ α} _{Inventory value of goods} _α_∈_G_{, given in monetary units of}

a given chain member θ in country x∈N per unit of goods α .

NODE _{Number of DC nodes.}

y x

PROC_{λ θ α}_{Procurement cost (including total cost and taxes) of goods}

G

α∈ shipped from a given chain member λ in country

y∈N to another given chain member θ in country x∈N

(monetary units of country of member λ/unit of goods

(45)

x

PPA_θ _{Simple processing capacity of finished products in a given}

chain member θ in country x∈N (finished product units/unit of time).

x

PPC_θ _{Simple processing cost of finished products in a given chain}

member θ in country x∈N (monetary units of country of member θ/unit of finished product).

x

RSA_θ _{Capacity to transform goods associated with a given chain}

member θ in country x∈N for transferring modular components into semi-products (semi-product units/unit of time).

x

RSC_θ _{Cost of transforming goods associated with a given chain}

member θ in country x∈N for transferring modular components into semi-products (monetary units of country of member θ/ unit of semi-products).

x

RPA_θ _{Capacity to transform goods associated with a given chain}

member θ in country x∈N for transferring modular components into finished products (finished product units/unit of time).

x

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member θ in country x∈N for transferring modular components into finished products in country x∈N

(monetary units of country of member θ/ unit of finished products).

x

SPA_θ _{Capacity to transform goods associated with a given chain}

member θ in country x∈N for transferring semi-products into finished products (finished product units/unit of time).

x

SPC_θ _{Cost of transforming goods associated with a given chain}

member θ in country x∈N for transferring semi-products into finished products (monetary units of country of member θ/ unit of finished products).

x

SSA_θ _{Simple processing capacity of semi-product in a given}

chain member θ in country x∈N (semi-product units/unit of time).

x

SSC_θ _{Simple processing cost of semi-product in a given chain}

member θ in country x∈N (monetary units of country of member θ/unit of s).

(47)

x

SSF_{θ α} _{Safety stock factor of goods} _α_∈_G _{at a given chain}

member θ in country x∈N.

x

TP_{θ α} _{Transfer price of goods} _α_∈_G_{shipped from a given chain}

member θ in country x∈N (monetary units of country of member θ/unit of goods α ).

x y_m

TRC_{θ λ} _{Transportation cost per weight unit of goods shipped from a}

given chain member θ in country x∈N to another given chain member λ in country y∈N , using transportation mode ( x, y)

m∈Ωθ λ (monetary units of country of member θ/weight unit).

x y_m

TT_{θ λ} _{Average transportation time from a given chain member} _θ

in country x∈N to another given chain member λ in country y∈N , using transportation mode ( x, y)

m∈Ωθ λ

(units of time).

x

VC_θ _{Capacity of a given chain member} _θ_{in country} _x_∈_N_for

supplying modular components (modular component units/unit of time).

x

VAT_{θ α} _{Value added tax rate (%) on the value of goods} _α_∈_G_of

(48)

W_α _{Weight of a unit of goods} _α_∈_G_{(weight units/unit of}

goods).

5.2 The Objective Function

The objective function maximizes global after-tax profit in dollars for the period of analysis. The after-tax profit of internal supply chain members involved in the objective function are expressed in Eq. (2). The operating income variables oi_θx are free variables since operating income may be

positive, zero or negative. Accordingly, each variable is treated as the difference between a plus non-negative variable (operating profit) oi_θx oi_θx

+ ₌

and a minus non-negative variable (operating loss) oi_θx oi_θx

− _{= −} _{(Vidal and}

Goetschalckx, 1998; Vidal and Goetschalckx, 2001; Fandel and Stammen, 2004; Vila et al., 2006). (1 x) x x x _FAI Maximize COT_θ oi_θ oi_θ θ + − ∈  − −   

∑

(2)

Each operating income variable is measured by subtracting the corresponding aggregate costs cost_θx (=

24 1 x k k z_θ =

∑

) from the respective aggregate revenues revenue_θx (= 1 x θ π + 2 x θ π ), as Eq. (3) demonstrates. , x x x x x I oi_θ+ −oi_θ− =revenue_θ −cost_θ ∀θ ∈FA (3)

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produces the corresponding aggregate revenue, as expressed in Eqs. (4) and (5), respectively. Here, transfer price TP_{θ λ α}x y is given to avoid costly

auditing and litigation. An effective method for obtaining market-driven transfer prices was proposed in Lakhal et al. (2005).

1 ( ) ( , ) 1 , x x x y y x y I x y sp _x x I m FA m G TP qu FA E θ θ α θ λ α λ θ λ θ λ α _θ π θ ≠ ∈ ∈Ω ∈ =

∑

∑ ∑

× × ∀ ∈ (4) 2 ( , ) , x x y y B x y p x DC m FA m G CPRICE_α qu FA θ θ λ α λ θ λ α π θ ∈ ∈Ω ∈ =

∑

∑ ∑

× ∀ ∈ (5) The aggregate cost is composed of 24 items. They are the corresponding aggregate costs in terms of transforming modular components into semi-products (Eq. (6)), transforming modular components into finished products (Eq. (7)), transforming semi-products into finished products (Eq. (8)), simple process of semi-products (Eq. (9)), simple process of finished products (Eq. (10)), transportation cost of trading with internal supply chain members (Eq. (11)), transportation cost of trading with brand companies (Eq. (12)), inventory cost of trading with internal supply chain members (Eq. (13)), inventory cost of trading with brand companies (Eq. (14)), procurement cost of raw materials (Eq. (15)), procurement cost of semi-products or finished products (Eq. (16)), fixed cost (Eq. (17)), sales VAT trading with internal members (Eq. (18)), sales VAT trading with brand companies (Eq. (19)), input VAT trading with vendors (Eq. (20)), input VAT

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trading with internal members (Eq. (21)), export VAT trading with internal members in the same country (Eq. (22)), export VAT trading with brand companies in the same country (Eq. (23)), export VAT trading with internal members in different countries (Eq. (24)), export VAT trading with brand companies in different countries (Eq. (25)), import duty trading with internal members in the same country (Eq. (26)), import duty trading with brand companies in the same country (Eq. (27)), import duty trading with internal members in different countries (Eq. (28)), import duty trading with brand companies in different countries (Eq. (29)). Note that Eqs. (20) and (21) are minus items as mentioned in Chapter four. Furthermore, the term

x y_m x y_m x x y_m

TT_{θ λ} CSF FS_{θ λ} SSF_{θ α} TT_{θ λ}

 ₊ _× ₊ 

  in Eqs. (13) and (14) is the total

time required to calculate inventory costs (Vidal and Goetschalckx, 2000). Herein, the first term is the time required to measure the pipeline inventory; the second term is the time required to measure the cycle inventory; the third term is the time required to measure the safety stock (Vidal and Goetschalckx, 2000). The gamma distribution was adopted in the safety stock for modeling stochastic lead times and inventory problems (Vidal and Goetschalckx, 2000).

(51)

{

}

1 1 , , , x x x s rs _x O x M Dd Dn f G f SN z RSC gt FA FA FA E θ θ θ α α _θ θ ∈ ∈ =

∑ ∑

× × ∀ ∈ (6)

{

}

2 1 _, _, _, x x x p rp _x O x M Dd Dn f G f SN z RPC gt FA FA FA E θ θ θ α α _θ θ ∈ ∈ =

∑ ∑

× × ∀ ∈ (7)

{

}

3 1 _, _, x x x p sp _x O x Dd Dn f G f SN z SPC gt FA FA E θ θ θ α α _θ θ ∈ ∈ =

∑ ∑

× × ∀ ∈ (8) 4 1 _, x x x s ss _x O x DC f G f SN z SSC gt FA E θ θ θ α α _θ θ ∈ ∈ =

∑ ∑

× × ∀ ∈ (9) 5 1 _, x x x p pp _x O x DC f G f SN z PPC gt FA E θ θ θ α α _θ θ ∈ ∈ =

∑ ∑

× × ∀ ∈ (10) 6 ( ) ( , ) 1 , x x y x y y x y I x y SP _x x I m m FA m G z TRC W qu FA E α θ θ λ θ λ α λ θ λ θ λ α _θ θ ≠ ∈ ∈Ω ∈ =

∑

∑ ∑

× × × ∀ ∈ (11) 7 ( , ) 1 , x x y x y y B x y P _x x DC m m FA m G z TRC W qu FA E α θ θ λ θ λ α λ θ λ α _θ θ ∈ ∈Ω ∈ =

∑

∑ ∑

× × × ∀ ∈ (12) 8 ( ) ( , ) , x x x y x y x x y x y y x y I x y SP _x x I m m m m FA m G IV H z TT CSF FS SSF TT qu FA E θ α θ θ λ θ λ θ α θ λ θ λ α λ θ λ θ λ α θ θ ≠ ∈ ∈Ω ∈ × _ _ = ∑ ∑ ∑ _ + × + _ ∀ ∈ (13) 9 ( , ) , x x x y x y x x y x y y B x y P x x DC m m m m FA m G IV H z TT CSF FS SSF TT qu FA E θ α θ θ λ θ λ θ α θ λ θ λ α λ θ λ α _θ θ ∈ ∈Ω ∈ × _ _ = ∑ ∑ ∑ _ + × + _ ∀ ∈ (14)

{

}

10 ( , ) 1 , , , x y x y x y V y x r _y x M Dd Dn m FA m G z PROC qu FA FA FA E θ λ θ α λ θ α λ λ θ α _λ θ ∈ ∈Ω ∈ =

∑

∑ ∑

× × ∀ ∈ (15) 11 ( ) ( , ) 1 , x y y x y x y I y x sp _y x I m FA m G z TP qu FA E θ λ α λ θ α λ θ λ λ θ α _λ θ ≠ ∈ ∈Ω ∈ =

∑

∑ ∑

× × ∀ ∈ (16) 12 1 _, x x x x I z FIX FA E θ θ θ θ = × ∀ ∈ (17) 13 ( & ) ( , ) 1 , x x x y x y x y I x y sp _x T x I m x y FA m G z TP qu VAT FA E θ θ α θ λ α θ α λ θ λ θ λ α _θ θ ≠ = ∈ ∈Ω ∈ =

∑

∑ ∑

× × × ∀ ∈ (18) 14 ( ) ( , ) , x x y x y B x y P T x DC m x y FA m G z_θ CPRICE_α qu_{θ λ} _α VAT_{θ α} FA λ θ λ α θ = ∈ ∈Ω ∈ =

∑

∑ ∑

× × ∀ ∈ (19)

{

}

15 , & ( , ) 1 , , , x y x y x y y V x y y x r _y C x M Dd Dn m FA FA m G z PROC qu VAT FA FA FA E θ λ θ α λ θ α λ α λ θ λ λ θ α λ θ ∈ ∉ ∈Ω ∈ =

∑

∑ ∑

× × × ∀ ∈ (20) 16 ( ) , & ( , ) 1 , x y y x y y x y I x y y x sp _y C x I m FA FA m G z TP qu VAT FA E θ λ α λ θ α λ α λ θ λ θ λ λ θ α _λ θ ≠ ∈ ∉ ∈Ω ∈ =

∑

∑ ∑

× × × ∀ ∈ (21) 17 ( & ) ( , ) 1 ( ), x x x y x x y x y I x y sp x C x I T m x y FA m G z TP qu VAT DRT FA E θ θ α θ λ α θ α θ α λ θ λ θ λ α _θ θ ≠ = ∈ ∈Ω ∈ =

∑

∑ ∑

× × × − ∀ ∈ (22) 18 ( & ) ( , ) ( ), x x y x x y x y B x y p C x DC T m x y FA m G z_θ CPRICE_α qu_{θ λ} _α VAT_{θ α} DRT_{θ α} FA λ θ λ θ λ α θ ≠ = ∈ ∈Ω ∈ =

∑

∑ ∑

× × − ∀ ∈ (23) 19 ( & ) , & ( , ) 1 ( ), x x x y x x y x y I x y x y sp x I m x y FA FA m G z TP qu VAT DRT FA E θ θ α θ λ α θ α θ α λ θ λ θ λ θ λ α θ θ ≠ ≠ ∈ ∉ ∈Ω ∈ =

∑

∑ ∑

× × × − ∀ ∈ (24)

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20 ( & ) , & ( , ) ( ), x x y x x y x y B x y x y p C x DC m x y FA FA m G zθ CPRICEα quθ λ α VATθ α DRTθ α FA λ θ λ θ λ θ λ α θ ≠ ≠ ∈ ∉ ∈Ω ∈ = ∑ ∑ ∑ × × − ∀ ∈ (25) 21 ( & ) ( , ) 1 ( ) , x x x y x y x y y x y I x y sp x T x I C m m x y FA m G z TP TRC W qu DUTY FA E α θ θ α θ λ θ λ α θ λ α λ θ λ θ λ α θ θ ≠ = ∈ ∈Ω ∈ = ∑ ∑ ∑ × + × × × ∀ ∈ (26) 22 ( & ) ( , ) 1 ( ) , x xy x y x y y x y B x y p x T x DC C m m x y FA m G z CPRICE TRC W qu DUTY FA E α α θ θ λ θ λ α θ λ α λ θ λ θ λ α θ θ ≠ = ∈ ∈Ω ∈ = ∑ ∑ ∑ + × × × × ∀ ∈ (27) 23 ( & ) ( , ) 1 ( ) , x x x y x y x y y x y I x y SP x T x I m m x y FA m G z TP TRC W qu DUTY FA E α θ θ α θ λ θ λ α θ λ α λ θ λ θ λ α θ θ ≠ ≠ ∈ ∈Ω ∈ = ∑ ∑ ∑ × + × × × ∀ ∈ (28) 24 ( & ) ( , ) 1 ( ) , x x y x y x y y x y _TB x y P x x DC m m x y FA m G z CPRICE TRC W qu DUTY FA E α α θ θ λ θ λ α θ λ α λ θ λ θ λ α _θ θ ≠ ≠ ∈ ∈Ω ∈ = ∑ ∑ ∑ + × × × × ∀ ∈ (29) 5.3 Constraints

Given that corresponding logistics conditions are limited by operating requirements, eleven groups of constraints are the following: flow conservation of deep and simple process, inbound flow conservation, outbound flow conservation, identifying goods transformations, maximum goods transformation, assignment of goods, brand company requirements, capacity of chain members, subtour breaking constraints, binary constraints, and non-negative constraints. These constraints are further elaborated below.

1. Flow conservation of deep and simple process

As Figure 3-2 shows, deep process, including transforming modular components into semi-products, transforming modular components into finished products and transforming semi-products into finished products, are

(53)

expressed as Eqs. (30), (31) and (32), respectively.

{

}

, , , x x r rs s rs I O x M Dd Dn f f G f SN G f SN gt_{θ α} gt_{θ β} BOM_αβ FA FA FA α β θ ∈ ∈ ∈ ∈ = × ∀ ∈

∑ ∑

(30)

{

}

, , , x x r rp p rp I O x M Dd Dn f f G f SN G f SN gt_{θ α} gt_{θ β} BOM_αβ FA FA FA α β θ ∈ ∈ ∈ ∈ = × ∀ ∈

∑ ∑

(31)

{

}

, , x x s sp p sp I O x Dd Dn f f G f SN G f SN gt_{θ α} gt_{θ β} BOM_αβ FA FA α β θ ∈ ∈ ∈ ∈ = × ∀ ∈

∑ ∑

(32)

Simple process involving simple processing of semi-products and finished products are expressed as Eqs. (33) and (34), respectively.

{

}

, , , , x x ss ss I O x Dd Ds Dn s f f f SN f SN gt_{θ α} gt_{θ α} θ FA FA FA α G ∈ ∈ = ∀ ∈ ∀ ∈

∑

(33)

{

}

, , , , x x pp pp I O x Dd Ds Dn p f f f SN f SN gt_{θ α} gt_{θ α} θ FA FA FA α G ∈ ∈ = ∀ ∈ ∀ ∈

∑

(34)

2. Inbound flow conservation

Figure 3-2 shows three inbound flows: modular components, semi-products, and finished products. Consequently, the corresponding inbound flow constraints are expressed as Eqs. (35), (36) and (37), respectively.

{

}

( , ) , , , , x y y x V x y R I y M Dd Dn r m f FA m f SN qu_{θ λ} _α gt_{λ α} FA FA FA G θ θ λ λ α ∈ ∈Ω ∈ = ∀ ∈ ∈

∑

(35)

{

}

( ) ( , ) , , x y y x x y I x y S I y DC s m f FA m f SN qu_{θ λ} _α gt_{λ α} FA G θ θ λ θ λ λ α ≠ ∈ ∈Ω ∈ = ∀ ∈ ∈

∑

(36)

{

}

( ) ( , ) , , x y y x x y I x y P I y DC p m f FA m f SN qu_{θ λ} _α gt_{λ α} FA G θ θ λ θ λ λ α ≠ ∈ ∈Ω ∈ = ∀ ∈ ∈

∑

(37) 3. Outbound flow conservation

As Figure 3-2 shows, two outbound flows are semi-products and finished products. Regarding finished products, manufacturing centers only can

(54)

convey finished products to DCs, while DCs convey finished products to brand companies or other DCs. Consequently, the corresponding outbound flow constraints are expressed as Eqs. (38), (39) and (40), respectively.

( ) ( , ) , , x x y S y x y DC x y O x I s f m f SN FA m gt_{θ α} qu_{θ λ} _α FA G λ θ λ θ λ θ α ∈ ≠ ∈ ∈Ω = ∀ ∈ ∈

∑

(38) ( , ) , , x x y P y DC x y O x M p f m f SN FA m gt_{θ α} qu_{θ λ} _α FA G λ θ λ θ α ∈ ∈ ∈Ω = ∀ ∈ ∈

∑

(39) { } ( , ) ( ) , , , x x y P y x y DC B x y O x DC p f m f SN FA FA m gt_{θ α} qu_{θ λ} _α FA G θ λ λ θ λ θ α ∈ ≠ ∈ ∈Ω = ∀ ∈ ∈

∑

(40)

4. Identifying goods transformations

For the sake of rational goods transformations and assignments, the expression gotr_{θ αβ}x represents good transformations, including

transformations from modular components into semi-products, from modular components into finished products and from semi-products into finished products. Accordingly, the corresponding constraints on goods transformations are expressed in Eqs. (41), (42) and (43), respectively.

{

}

, , , , x x r rs O x x rs r O f G f SN x M Dd Dn s f f SN G gotr gt BN FA FA FA G gt gotr BN θ αβ θ β α θ β θ αβ α θ β ∈ ∈ ∈ ∈  ≤ ∗  ∀ ∈ ∈  ≤ ∗  

∑

(41)

{

}

, , , , x x r rp O x x rp r O f G f SN _x _M _Dd _Dn _p f G f SN gotr gt BN FA FA FA G gt gotr BN θ αβ θ β α θ β θ αβ α θ β ∈ ∈ ∈ ∈  ≤ ∗  ∀ ∈ ∈  ≤ ∗  

∑

(42)

{

}

, , , x x s sp O x x sp s O f G f SN _x _Dd _Dn _p f G f SN gotr gt BN FA FA G gt gotr BN θ αβ θ β α θ β θ αβ α θ β ∈ ∈ ∈ ∈  ≤ ∗  ∀ ∈ ∈  ≤ ∗  

∑

(43)

(55)

5. Maximum goods transformation

Equations (41), (42) and (43) ensure only that if goods transformation occurs, the sum of gotr_{θ αβ}x equals or exceeds one. Consequently, it is

necessary to limit the maximum number of goods transformations, including those from modular components into semi-products, from modular components into finished products, and from semi-products into finished products. Thus, these constraints are expressed as Eqs. (44), (45) and (46), respectively. { , , } , x r r x M Dd Dn s G G FA FA FA gotr_{θ αβ} BOM_αβ G α α θ β ∈ ∈ ∈ ≤ ∀ ∈

∑

(44) { , , } , x r r x M Dd Dn p G G FA FA FA gotr_{θ αβ} BOM_αβ G α α θ β ∈ ∈ ∈ ≤ ∀ ∈

∑

(45) { , } , x s s x Dd Dn p G G FA FA gotr_{θ αβ} BOM_αβ G α α θ β ∈ ∈ ∈ ≤ ∀ ∈

∑

(46) 6. Assignment of goods

Each modular component can only be used once. Only one of two manufacturing procedures, including from modular components into either semi-products or finished products, can be used. Therefore, the corresponding constraint is given by Eq. (47).

{ , , } { , , } 1, x x s p x M Dd Dn x M Dd Dn r G G FA FA FA FA FA FA gotr_{θ αβ} gotr_{θ αω} G β ω θ θ α ∈ ∈ ∈ ∈ + ≤ ∀ ∈

∑

(47)

Since each semi-product can only be used once, the corresponding constraint is given by Eq. (48).

(56)

{ , } 1, x p x Dd Dn s G FA FA gotr_{θ αβ} G β θ α ∈ ∈ ≤ ∀ ∈

∑

(48)

Finished products can be transferred among DCs, but one finished product only can be assigned once to a brand company. Restated, one company can only receive one unique finished product during the assignment process. Accordingly, the corresponding constraint is given by Eq. (49). ( , ) 1, x y x DC y B x y p m FA FA m qu_{θ λ} _α G θ λ θ λ α ∈ ∈ ∈Ω = ∀ ∈

∑ ∑

∑

(49)

7. Brand company requirements

To meet brand company requirements, the corresponding constraint is given by Eq. (50). ( , ) , x y y x DC x y p y B m FA m G qu_{θ λ} _α BR_λ FA θ θ λ α λ ∈ ∈ ∈ = ∀ ∈

∑ ∑ ∑

(50)

8. Capacity of chain members

In addition to vender capacity to supply modular components (Eq. (51)), there are five capacities of internal supply chain members for goods transformation, including from modular components into semi-products, from modular components into finished products, from semi-products into finished products, simple process of semi-products and simple process of finished products. Accordingly, the corresponding constraints on five capacities of internal supply chain members are expressed as Eqs. (52), (53),

全球產銷供應鏈管理之節稅模式

國

國

國

國

立

立

立

立

交

交

交

交

通

通

通

通

大

大

大

大

學

學

學

學

交通運輸研究所

交通運輸研究所

交通運輸研究所

交通運輸研究所

博士論文

博士論文

博士論文

博士論文

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