DOI 10.1007/s00170-003-1891-8 O R I G I N A L A R T I C L E
D.Y. Sha · Z.H. Che
Virtual integration with a multi-criteria partner selection model
for the multi-echelon manufacturing system
Received: 7 March 2003 / Accepted: 7 July 2003 / Published online: 27 October 2004 Springer-Verlag London Limited 2004
Abstract Virtual integration (VI) offers a way to make
manu-facturing systems more agile and competitive. VI integrates the production resources of many manufacturing systems (partners) efficiently, and that leads to a rapid response to market changes. Based on the VI concept these partners throughout the world will form a virtual enterprise (VE). Thus to select partners is the essential and the most important issue. The main objective of this paper is to develop a partner selection and production-distribution planning with the novel partner selection model, based on the analytic hierarchy process (AHP) methodology, multi-attribute utility theory (MAUT) and integer programming (IP), for the VI with multiple criteria. The AHP and MAUT methods are use to assess and set weights for each partner candidate and the IP model applies these weights to find the optimal partners from the potential ones and provide the suit-able production-distribution plan to the elective partners. Finally, a case study has been provided to substantiate a feasible quality solution of the proposed model.
Keywords Partner selection· Production-distribution
planning· Virtual enterprise · Virtual integration
1 Introduction
Virtual integration (VI) is a collaborative production-distribution network that unifies many independent business partners to plan, perform, and control operational interchanges effectively and ef-ficiently, from acquisition of raw materials to delivery of the finished product to the end user/customer. Every collaborative partner (enterprise) collectively interacts by sharing their product information, to transport the right quality and quantity of product at the right time. Under this concept these enterprises constitute a larger organization, that is, a virtual enterprise (VE).
D.Y. Sha · Z.H. Che (u)
Department of Industrial Engineering & Management, National Chiao Tung University,
1001 Ta Hsueh Road, Hsinchu, Taiwan 30050, R.O.C. E-mail: [email protected]
VE is a joint venture, which consists of suppliers, manufac-turers, distributors, and customers to develop and produce prod-ucts for fulfilling consumer requirements in the rapidly changing environment of the global manufacturing area. Davulcu et al. [1] stated that a VE is a temporary consortium of autonomous, di-verse, and possibly geographically dispersed organizations that pool their resources to meet short-term objectives, and exploit fast changing market trends. The VE is a dynamic alliance of member companies, which join to take advantage of a market op-portunity. Each member company will provide its own core com-petencies in areas such as marketing, engineering, and manufac-turing to the VE [2]. In addition, Walton and Whicker [3] and Song and Nagi [4] separately explain “The VE consists of a se-ries of co-operating ‘nodes’ of core competencies which form into a supply chain in order to address a specific opportunity in the market place” and “A VE, different from a traditional enterprise, is constructed by partners from different companies, who collaborate with each other to design and manufacture high quality and customized products. It is product-oriented, team-collaboration styled, and featured as being fast and flexible.” From these definitions, it is without doubt that the supply chain management (SCM) will be a good quality approach to enhance the competitiveness of the VE.
Christopher [5] stated that an adequate definition of supply chain from a logistical perspective is “a network of organiza-tions that are involved, through upstream and downstream link-ages, in different processes and activities that produce value in the form of products and services in the hands of the ultimate consumer.” The SCM increases the competitiveness of the indus-trial environment, and involves planning and managing the flow of information, material, and product through a multi-echelon of design, production/manufacturing, transportation, and distri-bution until it reaches the customer. While satisfying customer demand, the problem of distributing products/goods involves de-termining the optimal cost, size, and time of those participants so as to minimize the total cost associated with the supply chain transactions such as order, setup, production, delivery, inventory, quality, and reliability cost. The distribution decision is a long- or short-term strategy. If the distribution volume is very large, and
the relationship of the participants is not easily converted, the de-cision would be treated as a long-term strategy. Conversely, the short-term decision strategy usually involves a small volume of distribution and easily changed relationships among collabora-tors (suppliers or manufacturers/distribucollabora-tors).
SCM can help to simultaneously achieve the goals of the supplier and customer satisfaction in the manufacturing industry. The essence of the supply chain management is considered to be the integration of business activities to serve end customers, by establishing a strategic partner alliance. Figure 1 illustrates the relationship between the dependent natures of supplier-customer relations. For the supply chain, the relationship between supplier and customer tends to create a problem requiring a decision in-volving multiple selections. That is to say, the relationship is strategically collaborative, as shown in Fig. 1d. Achieving com-petitiveness in this industry thus requires efficient collaboration between suppliers and customers. Therefore, to select appro-priate partners in the processes of strategic collaboration is the major subject for promoting a smooth integration among inde-pendent enterprises in the supply chain.
To integrate enterprises completely, the product structure is the foundation, while computer aided implementation is indis-pensable for being successful in selecting partners. This pa-per proposes an interactive approach, based on analytic hierar-chy process (AHP) methodology, multi-attribute utility theory (MAUT), and the integer programming (IP) model, to solve the partner selection and production-distribution problem of a multi-echelon manufacturing system assuming a particular optimal sat-isfaction. This approach is preceded by an analysis to define the best potential production partner members to release a quantity of products for companies upstream, to determine a feasible dis-tribution of downstream collaborators and volume of products, and to gather extensive information on these possible
collab-Fig. 1. Supplier-customer relationship
orators. The proposed approach aims to help determine which companies among the feasible collaborators will be included in the production-distribution network, and the size of the release quantity obtained from upstream suppliers.
The application of this approach is demonstrated through a case study involving the complex semiconductor manufactur-ing system. To obtain an optimum solution, this study focused on presenting an efficient and systematic approach for modeling the distribution behavior of the semiconductor supply chain, so as to maximize overall satisfaction with the chain.
This paper is organized as follows: Sect. 2 presents a brief literature survey on related current approaches and models in partner selection. The proposed interactive methodology, com-bining the AHP, MAUT and IP approaches, can identify a partner selection decision for VI of manufacturing systems, and will be discussed in Sect. 3. Section 4 illustrates the effectiveness and efficiency of the proposed research approach in the actual semi-conductor industry environment. Finally, Sect. 5 summarizes the conclusions of this study.
2 Literature review
Capital investments are especially large for keeping the chain operating effectively. Successful partnerships create a synergis-tic supply chain in which the entire chain is more effective than the sum of the individual parts. Therefore, partner selection is a particularly important activity in establishing strategic al-liances to enhance the competitive advantage of the entire supply chain.
This section describes the literature survey related to part-ner selection of VE and SCM. Korhoren [8] and Davis [9] stated that the partner selection process is an important function for
the information management systems of extended virtual enter-prises. Talluri et al. [10], Papazoglou et al. [6], and Mikhailov [7] claimed that the key issue in forming a VE is to select agile, competent, and compatible partners.
In addition, many literatures presented that using multiple criteria decision for partner selection is necessary. Weber and Desai [12] illustrated multi-criteria evaluation and other effective methods for selecting vendors to secure a competitive advan-tage. Wang et al. [13] presented multiple factors (cost, due date, and the precedence of sub-project) to select appropriate partners. Muralidharan et al. [11] defined nine criteria to select good sup-pliers for achieving business efficiency. Cavusgil et al. [14] noted that distributor selection is a very important strategy for an in-ternational production-distribution system and showed that 35 criteria are grouped into five major dimensions (financial and company strengths, product factors, marketing skills, commit-ment, and facilitating factors).
According to the literature mentioned above, efficient vir-tual integration must be performed through partner selection with multi-criteria for the manufacturing systems. The interac-tive approach proposed in this study, and combined with the AHP approach, MAUT method, and IP model, is therefore a useful means of achieving these goals as defined above. AHP, a scoring method designed to visually structure complex decision prob-lems involving multiple criteria, is based on the principles of decomposition, comparative judgment, and the synthesis of pri-orities [15, 16]. Meanwhile, AHP is a measurement theory for dealing with quantifiable and intangible criteria, and has been applied to such diverse areas as decision theory and conflict reso-lution [17]. The MAUT, is comprised of the preference functions for individual attributes, and the weights that reflect the relative importance of these attributes, provides a logical and tractable means to make tradeoffs among conflicting objectives [18]. Fur-thermore, the IP is the mathematical technique that is concerned with optimization, which is finding the best possible answer to a problem under relevant restrictions.
Many researches have illustrated the wider fields of applica-tion research by associating with AHP, MAUT, or IP approaches. For example, the AHP have been used effectively earlier by Ko-rpela et al. [19–21] for formulating logistics network design. In addition the MAUT has previously been used for the capital allo-cation process of a petroleum exploration company by Walls and Dyer [22], for the transaction selection problem by Kumar and Sheble [24], and for technological innovation effect in a financial portfolio by Nepomuceno et al. [23].
VI is a team endeavor within manufacturing systems. The AHP is one available method for creating a systematic frame-work for group interaction and decision making [25]; the MAUT method should be able to display tradeoffs among different at-tributes in a useful manner; and the IP model is usually used to find an optimal solution for a decision problem. For handling this situation, the AHP should be incorporated into the construction procedure of the MAUT model, so as to construct the framework of educing multi-attribute utility functions and weighting param-eters. Then, the utility values, calculated by the MAUT model are included as decision variables in the IP model.
3 Proposed approach for partner selection
The VI requires a systematic and efficient mathematical method for making decisions regarding relationships and component and/or product distribution, among related co-operators. Mean-while, this method needs to cover all procedures involved in the multi-echelon manufacturing systems, from raw material supply to product distribution. Figure 2 depicts the decision making pro-cess for partner selection planning for VI.
A step-by-step explanation of the proposed methodology is presented in the following.
3.1 Attribute priorities assessment
To analyze VI behavior in the multi-echelon manufacturing sys-tems, an interaction oriented model based on the AHP, MAUT and IP approaches and designed to optimize distribution while explicitly satisfying all participants was used.
The AHP, a systematic decision approach first developed by Saaty [15], is a powerful tool for solving complex decision prob-lems that may have interactions and correlations among decision criteria. AHP is based on three principles: decomposition, com-parative judgments, and the synthesis of priorities. Figure 5a– b separately show two hierarchies used for customers of corpora-tion A and suppliers of corporacorpora-tion B in the illustrative example. Then, pair-wise comparisons among factors in each level of each hierarchy are made with respect to the factor in the level above, resulting in a set of pair-wise comparison matrices as shown in Table 3. The pair-wise matrix A, in which the element aij of the
matrix is the relative importance of the ith factor with respect to the jth factor, could be created as shown below:
A=aij = 1 a12 . . . a1n 1 a12 1 · · · a2n ... ... ··· ... 1 a1n 1 a2n . . . 1 (1)
For all i and j, it is necessary that aij= 1/ajiand aij= 1. In
order to calculate the individual and overall influence of factors in the goal, the eigenvector analysis [15], which is a unique tech-nique to determine the relative ranking of factors with respect to a certain objective, is used. The priority vector can be generated by normalizing the principal eigenvector W of the matrix A
A W= λmaxW (2)
whereλmaxis the principal or the largest eigenvalue of positive real values of judgment matrix.
Each pair-wise comparison contains many decision elements for the consistency index (CI) that measures the entire consis-tency judgment for each comparison matrix, and the hierarchy architecture. The consistency ratio (CR) is useful for this task, and the accepted upper limit value for CR is 0.1 for a good judg-ment. CR is calculated using
CR=CI
Attribute priorities assessment * Acquiring criteria data
* Using AHP methodology to figure out priorities of all criteria + Constructing hierarchy architectures
+ Executing pair-wise comparisons + Calculating systhesis priorities
Linear additive utility models construction * Using MAUT Approach to construct single utility functions * Aggregating all attribute scores by combining systhesis
priorities and single untility functions
Utility integration * Building overal objective functions * Normalizing utility values
Performance optimization
* Defining the objective function with normalized utility values * Establishing constratints with considering the average rate of
comforming product
* Identifying the optimal partnerships
VI implementation for the multi-echelon manufacturing system
Partner Selection Model for VI
New or potential companies participate in this network Redevelopment Criteria data is changed Reassessment Original partnership network development
Fig. 2. The proposed framework for VI
where
CI=λmax− n
n− 1 (4)
RI (Random Index) is obtained by n from a random index table,
as displayed in Table 1 below. If the consistency test is not eligi-ble (CR> 0.1), then the AHP may not yield meaningful results and must reconstruct the matrix A.
3.2 Linear additive utility models construction
The MAUT approach is based on the construction of individ-ual utility functions for each attribute, which is comprised of the preference functions for individual attributes and the weights that reflect the relative importance of these attributes. The first step of MAUT is to assign utility values for each attribute. The Ui(xi),
the single utility function or preference function associated with attribute i, represents the utility values the decision maker at-taches to each attribute. The utility value is usually defined as
Table 1. Random index table [26]
n 3 4 5 6 7 8 9
RI 0.58 0.90 1.12 1.24 1.32 1.41 1.45
a normalized scale that is bound between the lower and upper bounds of the attribute evaluate unit. The specific processes of single utility function setting and utility value calculating can be referred to in Keeney and Raiffa [18]. These utility values must be criticized carefully to ensure that the results of the evaluation are consistent with the preferences of the decision maker.
The next step is to aggregate the scores of each attribute in the MAUT process. The linear additive utility form is the fre-quently simplified assessment procedure as given by
Vx→y= n i=1 wx→y i U x→y i (xi) (5)
where x→ y is the viewpoint from corporation x to its candidate customer y; Vx→yis objective function, which is the overall util-ity for the perspective of x to its specific candidate y;wiis the
appropriate weight that represents the relative importance (prior-ity) of attribute i, for the n attributes, whereni=1wi= 1. In this
paper, thewivalue is obtained by using the AHP process, which
is described in the above Sect. 3.1. 3.3 Utility integration
The dependent nature of the supplier-customer relationship in the manufacturing system is strategically collaborative as shown in Fig. 1d. Therefore the integrate utility between corporation x
and y can be formulated by using the multiplication method as follows
Vx↔y= Vx→y× Vx←y (6)
where x↔ y denotes to integrate the viewpoints of corporation
x and y and x← y denotes the viewpoint from corporation y to
its supplier y. Vx←y is the utility for the perspective of y to its
specific supplier x, and Vx↔yis the overall objective function,
which is the overall utility between corporation x and y. To consider more then one corporation in the multi-echelon manufacturing system, for each corporation, the utility value be-tween it and any customer would be normalized to a total of 1 to represent the utility of each customer. The normalized process for each customer is shown below.
Normalized Vx↔yj= V x↔yj m j=1V x↔yj (7)
where j is the number of downstream co-operators for the spe-cific corporation x. Afterward, the multi-echelon manufacturing system could be established completely and efficaciously by nor-malized efficacious Vx↔yjas shown in Table 6 of the illustrative
example.
3.4 Optimization model
The delivery quantity between one corporation and its customer is a very important issue. Therefore, for the partner selection to achieve VI, to assign the right delivery quantities on all link-ages between two corporations of multi-echelon manufacturing system is the final task. The partner selection and distribution model is proposed to make a decision for the delivery quantities by using the IP approach. The objective function formulation ef-fectively integrates all evaluative criteria for designing a partner selection as follows: Max K −1 k=1 Ik i=1 Jk+1 j=1
Normalized Vpx(k,i)↔y(k+1, j)
Q(k,i)(k+1, j),p
(8) where Q(k,i)(k+1, j),prepresents the number of units shipped from supplier i of echelon k to customer j of echelon k+1 in period p.
k is the echelon index, k= 1, . . ., K. K is the number of echelons
in the multi-echelon manufacturing system. i, j are corporation indices, i= 1, . . ., Ik, j= 1, . . ., Jk. Ik, Jkare number of
corpo-rations in the echelon k. p is the period index, p= 1, . . ., P. P is the number of periods.
Four varieties of relevant restrictions must be involved in our proposed model. (1) Capacity constraints (Eqs. 9 and 10): the quantity of the product should be greater than the mini-mum quantity of the starting production and less than the pro-cessing capacity of each corporation. (2) Conservation-of-flow constraints (Eq. 11): to ensure that the commodity shipped into a corporation must also leave. (3) Demand constraints (Eq. 12):
to ensure that the customer demand is satisfied by using this production-distribution process. (4) Non-negative-integer con-straints (Eq. 13): the shipping quantity of the product should be a non-negative integer between two corporations:
LC(k+1, j),p≤ Ik i=1 k≤K−1 Q(k,i)(k+1, j),p≤ UC(k+1, j),p, ∀ j, k, p (9) LC(k,i),p≤ Jk+1 j=1
Q(k,i)(k+1, j),p≤ UC(k,i),p, ∀i, p, k = 1 (10) Ik i=1 k≤K−2 Q(k,i)(k+1, j),p= L k+2 l=1 k≤K−2 Q(k+1, j)(k+2,l),p, ∀ j, k, p (11) Ik−1 i=1 Jk j=1 Q(k−1,i)(k, j),p= Dp, ∀p, k = K (12) Q(k,i)(k+1, j),p≥ 0 and ∈ integer , ∀i, j, k, p (13) where LC(k,I),pand UC(k,I),pseparately represent the minimum quantity of starting production, and the processing capacity of corporation i of echelon k in period p. Dpis the total market
de-mand in period p. l is the corporation index, l= 1, . . ., Lk. Lkis
the number of corporations in the echelon k.
4 Illustrative example
This application study will demonstrate the effectiveness and ef-ficiency of our proposed approach in the actual environment of multi-echelon manufacturing systems within the semiconductor industry. Figure 3 demonstrates the multi-echelon semiconduc-tor manufacturing system. Specifically, this application involves several selectable partnerships for each enterprise for achiev-ing efficient VI, to enhance the competitiveness of the entire industry.
In this illustrative example, the multi-echelon semiconduc-tor manufacturing system with the architecture 2-3-3-2 is ap-plied. This architecture 2-3-3-2 expresses that there are 2, 3, 3, and 2 corporations in the first, second, third, and fourth ech-elon of this multi-echech-elon manufacturing system as is shown in Fig. 4. Following the above procedure, the foremost task of the proposed approach is to identify the related decision cri-teria for each corporation. These cricri-teria are used for ranking the proposed partnerships of the corporation A’s downstream customers and corporation B’s upstream suppliers that may in-fluence collaboration decisions. These factors, which were ini-tially presented by the outsourcing team from corporations A and B, were used to veritably assess the partnerships and were listed in Table 2. Herein, the details of the technique of the corporation A (node 2.1) and B (node 3.1) are described in detail. For the sake of expediency, the program of other cor-porations is the same with corporation A and B and will not
Silicon Material Materials Fabrication Wafer Fabrication Assembly Final Test Customer
Front End Back End
Distribution Route Demand Route Manufacturing/production Unit Demand Unit Fig. 3. Multi-echelon semiconductor
manufac-turing system Materials Fabrication Wafer Fabrication Assembly First Echelon Second Echelon Third Echelon Final Test Fourth Echelon N1.1 N1.2 N2.1 N2.2 N2.3 N3.1 N3.2 N3.3 N4.1 N4.2
Fig. 4. {2-3-3-2} original partnership network
topology
Table 2. The factors for ranking the proposed partnerships of corporation A
and B
For upstream supplier of corporation B Factor (criterion) Description
Price Unit product price
Matching Conjugation with products Delivery On-time delivery capability Quality Quality of incoming material For downstream customer of corporation A
Factor (criterion) Description
Quality Production quality
Yield The yield of O/S or assembly Delivery On-time delivery capability
Price Unit product price
Service Production capacity for fitting demand
to be explained again. The hierarchical structures used in this work of corporations A and B are shown in Fig. 5. After con-structing the complete hierarchies, the pair-wise comparisons of decision criteria are used rather than the absolute measure-ment scales, since absolute measuremeasure-ments tend to be very sub-jective. For the hierarchies of Fig. 5, the pair-wise matrices and priority vectors are calculated by Eqs. 1 and 2 and shown in
Table 3. It needs to be mentioned that, for the sake of business privacy considerations, in this paper, these analytic data have been modified. However, these data accord with the reality of production.
Table 3. The pair-wise comparison matrixes of corporation A and B
For upstream supplier of corporation B
Criterion Priority
Price Matching Delivery Quality
Price 1/2 1/2 3 0.179
Matching 1 8 0.384
Delivery 8 0.384
Quality 0.052
Criterion
For downstream customer of corporation A
Criterion Priority
Quality Yield Delivery Price Service
Quality 2 2 1/2 3 0.357 Yield 1 1/2 2 0.255 Delivery 1/2 2 0.153 Price 4 0.153 Service 0.081 Criterion
Fig. 5. The AHP-hierarchies for analyzing the
partnerships of corporation A and B
After obtaining the relative importance for each attribute by the AHP procedure, the preference functions for all attributes are assessed. To consider the single utility function for the at-tribute of delivery of corporation B for its upstream suppliers as an example, the value of this attribute delivery is in the range between 70 and 100%. The lower and upper bound of delivery represent the worst and best function performances respec-tively. Therefore, Udelivery(70%) = 0 and Udelivery(100%) = 1
can be set cleanly and definitely. According to the MAUT methodology, in order to obtain the Udelivery(xdelivery), three
equivalent utility values Udelivery(xdelivery0.25 ), Udelivery(x0delivery.5 ),
and Udelivery(xdelivery0.75 ) in this range of delivery measurements
must be assessed. With respect to Udelivery(x0delivery.5 ) = 0.5, there
are four candidates (80, 85, 90, and 95%) for the preference to be selected for x0delivery.5 . To pair-wise compare these preferences of these four candidates and use the eigenvector analysis for this pair-wise matrix, the judgment matrix and the priority vector is figured out by Eqs. 1 and 2 and given as
x0delivery.5 = 80 85 90 95 1 1/1.5 1/3.5 1/9 1.5 1 1/2 1/6 3.5 2 1 1/3.5 9 6 3.5 1 , priority vector= 0.06 0.11 0.20 0.63 .
With the result that the xdelivery0.5 would be calculated by its candi-dates and priority vector as
x0delivery.5 = [80 85 90 95](%) × 0.06 0.11 0.20 0.63 = 92(%) .
x0delivery.25 and x0delivery.75 also can be computed with the similar method for Udelivery(x0delivery.25 ) = 0.25 and Udelivery(x0delivery.75 ) =
0.75, and then those values are 83% and 97%. Having de-veloped to this point, in accordance with five points (xdeliveryk ,
Udelivery(xkdelivery)), k = 0, 0.25, 0.5, 0.75, and 1, the utility
func-tion of this delivery attribute could be formularized by a third-polynomial function. In a similar manner, the preference func-tions for other attributes of corporation B to assess its upstream suppliers and corporation A to assess its downstream customers can be formularized. Table 4 represents preference functions for all attributes that are used to assess utilities for suppliers (s) of corporation B and customers (c) of corporation A.
Table 4. Preference functions to assess utilities for suppliers (s) of
corpora-tion B and customers (c) of corporacorpora-tion A For suppliers (s) of corporation B Preference function
Uprices←B(xprice) = −0.8168xprice3 + 4.2775xprice2 − 7.6741xprice+ 5.2125
Us←B
matching(xmatching)= 0.0160x3matching− 0.1038x2matching+ 0.3762xmatching
−0.2889 Us←B
delivery(xdelivery) = 60.2196x3delivery− 144.2768xdelivery2 + 116.7063xdelivery
−31.6544 Us←B
quality(xquality) = 0.0022x2quality− 0.0774xquality+ 1.0057
For customers (c) of corporation A Preference function
UA→c
quality(xquality) = 87.3494x3quality− 55.8424xquality2 + 2.7840xquality
+1.0009 UA→c
yield (xyield) = 22.9973x3yield+ 15.0292x2yield+ 3.7672xyield+ 0.0002
UdeliveryA→c (xdelivery) = 27.1192x3delivery− 63.1545x
2
delivery+ 51.3218xdelivery
−14.2801 UA→c
price(xprice) = 0.1455x3price− 1.1677x2price+ 2.3027xprice− 0.3344
UA→c
service(xservice) = 1.3427x3service− 1.0313x2service+ 0.6846xservice
As mentioned previously, the linear additive utility function can be used for constructing the unidirectional objective func-tions for the suppliers and customers of the corporation B and A by combining the single preference functions, and priority pa-rameters can assume the following forms:
For suppliers of corporation B:
Vs←B= 0.179Uprices←B(xprice) + 0.384Umatchings←B (xmatching)
+ 0.384Us←B
delivery(xdelivery) + 0.052Uqualitys←B (xquality)
For customers of corporation A:
VA→c= 0.357UqualityA→c (xquality) + 0.255UyieldA→c(xyield)
+ 0.153UA→c
delivery(xdelivery) + 0.153UpriceA→c(xprice)
+ 0.081UA→c
service(xservice)
Table 5 shows corporation A’s candidate customers and B’s candidate suppliers, which are assessed by specific combina-tion of criterion values. The criterion values, which were
ini-Table 5. Criterion values of (1) corporation A’s candidate customers and (2)
corporation B’s candidate suppliers
(1) Price Matching Delivery Quality
N3.1 0.8 1.8 0.75 0.50
Candidate N3.2 2.0 4.8 0.73 0.10
N3.3 2.3 1.5 0.94 0.10
(2) Quality Yield Delivery Price Service
N2.1 0.080 0.40 0.97 2.0 0.95
Candidate N2.2 0.150 0.20 0.88 2.0 0.50
N2.3 0.150 0.45 0.88 2.5 0.85
Table 6. The results of normalized overall (integrated) objective utility
For upstream supplier For downstream customer Overall (integrated) Normalized Vx↔y Viewpoint Prior weight (Vx←y) Viewpoint Prior weight (Vx→y) objective utility (Vx↔y)
N1.1← N2.1 0.442 N1.1→ N2.1 0.367 0.217 0.420 N1.1← N2.2 0.352 N1.1→ N2.2 0.225 0.072 0.139 N1.1← N2.3 0.611 N1.1→ N2.3 0.408 0.228 0.441 N1.2← N2.1 0.558 N1.2→ N2.1 0.435 0.182 0.428 N1.2← N2.2 0.648 N1.2→ N2.2 0.102 0.088 0.207 N1.2← N2.3 0.389 N1.2→ N2.3 0.463 0.155 0.365 N2.1← N3.1 0.239 N2.1→ N3.1 0.376 0.100 0.378 N2.1← N3.2 0.610 N2.1→ N3.2 0.225 0.158 0.597 N2.1← N3.3 0.016 N2.1→ N3.3 0.389 0.007 0.025 N2.2← N3.1 0.392 N2.2→ N3.1 0.621 0.255 0.746 N2.2← N3.2 0.111 N2.2→ N3.2 0.357 0.080 0.233 N2.2← N3.3 0.240 N2.2→ N3.3 0.022 0.007 0.021 N2.3← N3.1 0.369 N2.3→ N3.1 0.136 0.063 0.142 N2.3← N3.2 0.279 N2.3→ N3.2 0.224 0.064 0.145 N2.3← N3.3 0.744 N2.3→ N3.3 0.640 0.317 0.713 N3.1← N4.1 0.440 N3.1→ N4.1 0.534 0.234 0.670 N3.1← N4.2 0.105 N3.1→ N4.2 0.466 0.116 0.330 N3.2← N4.1 0.102 N3.2→ N4.1 0.223 0.033 0.163 N3.2← N4.2 0.221 N3.2→ N4.2 0.777 0.172 0.837 N3.3← N4.1 0.458 N3.3→ N4.1 0.420 0.105 0.241 N3.3← N4.2 0.674 N3.3→ N4.2 0.580 0.330 0.759
tially presented by the outsourcing team from corporations A and B, are used to elicit the preference of each criterion with respect to all candidate participants. By these criterion values, the overall (integrated) objective utility Vx↔y and normalized
Vx↔y between two adjacent corporations for this illustrated multi-echelon system can be figured out correctly as depicted in Table 6 by Eqs. 6 and 7. The results for upstream suppliers and downstream customers of each corporation are displayed in Table 6.
For effective VI, quality corporations should organize the multi-echelon manufacturing system. As a result of the quality corporation participation, the competition of the manufacturing system will be increasing effectively and rapidly. Consequently, the optimal VI network could be constructed by using the IP-model (Eqs. 8–13), which involves the normalized overall ob-jective utility (normalized Vx↔y). In addition, this IP model can assign the optimal product volume to each appropriate company and it enhances the operational performance of the manufactur-ing system.
In this illustrative example, based on customer requirements, the total market demand is assumed at 1000 units (one hundred dies). The least and the most process units are associated with each node of the network, and depicted by enclosing their values in brackets attached to the node as shown in Fig. 6. The optimal VI structure, with the total supplier and customer preferences op-timized, is a multi-echelon network system that is constructed by some corporations (nodes) with the thicker arcs and appears in Fig. 6. Furthermore, the optimal number of transportation units to be shipped from a node to another is clearly identified and en-closed in a box attached to each arc. For example, in terms of the solution, N3.3must process 450 units from its upstream node N2.3and ship 0 and 450 to its downstream nodes N4.1and N4.2
Fig. 6. The optimal solution for
VI
Table 7. Illustration of the best VI patterns at different market demands
Transportation Demand (unit: hundred dies)
600 800 1000 1100 1200 N1.1→ N2.1 50 150 N1.1→ N2.2 N1.1→ N2.3 350 450 450 450 450 N1.2→ N2.1 100 100 100 150 150 N1.2→ N2.2 150 250 450 450 450 N1.2→ N2.3 N2.1→ N3.1 100 200 N2.1→ N3.2 100 100 100 100 100 N2.1→ N3.3 N2.2→ N3.1 150 250 450 450 450 N2.2→ N3.2 N2.2→ N3.3 N2.3→ N3.1 N2.3→ N3.2 N2.3→ N3.3 350 450 450 450 450 N3.1→ N4.1 150 250 450 550 650 N3.1→ N4.2 N3.2→ N4.1 N3.2→ N4.2 100 100 100 100 100 N3.3→ N4.1 N3.3→ N4.2 350 450 450 450 450 Optimal solution 1098.864 1452.350 1776.841 1923.979 2070.724
In the result of our demonstrative example, each corpo-ration finds optimal suppliers and customers for performing VI to satisfy the end customer demand with maximum pref-erences. For instance, under customer demand 1,000 units N1.2, N2.2, N3.1 and N4.1 are virtual integrated corporations. In Table 7, we show the best VI patterns at different mar-ket demands given by our proposed method. According to this analytical outcome that reveals that the best VI pattern and the quantities of each node for processing in its own plant and transporting to its downstream customers simultan-eously matches the supplier and customers’ multi satisfactory preferences.
5 Conclusions
Without a doubt, the VI is at the core of strategic planning for multi-echelon manufacturing systems. All virtually integrated companies possess core business functions, and virtually inte-grated firms are very tightly organized. As a result, the firms op-erate as a single organization with shared goals, processes, and, oftentimes, corporate cultures. The integration will be constantly shifting to take advantage of existing conditions and changed as the competitive environment is altered. Therefore, for keeping the competitive edge in an often and fast changing environment, the evaluation and selection of good corporations for integration is an absolute necessity.
This work proposed a systematic and flexible approach to efficiently and effectively solve the complex partner selection and product distribution decision problems by integrating vari-ous systems. Relationships are acquired by using AHP-, MAUT-and IP-based methodologies, which enables both quantitative and qualitative factors to be included in the decision process. It models the veritably behavior of a multi-echelon manufacturing process by employing the interactive technique, which simul-taneously integrates suppliers and customers’ multi-satisfactory preferences.
This novel approach is an interactive method to analytically select corporations and distribute entities from the viewpoints of the upstream and downstream corporations, and provides the expected optimal satisfaction for all the participants of the whole multi-echelon system, while the collaborative information is shared totally and effectively. The present companies can be analyzed periodically, e.g., thrice a year, or non-periodically, to keep relationships between corporations prospective. In the fu-ture, new or potential companies could be readily included in the existing multi-echelon manufacturing system. Accordingly, this approach can provide a feasible quality partner selection and production-distribution planning solutions that can easily and
expeditiously be applied to real world applications while the co-operative information of all participators is shared perfectly and effectively in the entire chain.
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