> mY bjbjWW fe==vF]80MPX$H%"%%&?B[]]]?$u)?%&X$*.%&[[[2[&""a(CVI Operations Research offers many useful decision models for supplier selection
From the review of the existing decision models for supplier selection, it has become clear that the majority of these models only aims at supporting the choice phase in supplier selection and employs compensatory decision rules for this. Considering the often much more complicated and diverse nature of supplier selection decisions, as became clear in the early chapters, it seems that other generic models from Operations Research will be more useful if these models to a larger extent cover the properties that the existing models lack. In this chapter we present the results of an extensive investigation of the literature regarding the possibly useful decision models in that respect. The position of this chapter in the overall stepwise planning is shown in figure 6.1.
Figure 6.1: Positioning of chapter VI
The results show that contemporary Operations Research offers various promising decision models for supplier selection as these models cover the issues and properties that the current models in the purchasing literature lack.
There are various decision models available for supporting problem definition in supplier selection
The survey of existing models in chapter V has made clear that support in the phase of problem definition is an underdeveloped area in purchasing. Only a few decision models found in the survey pay attention to this important phase (see table 6.25). In this section we discuss some approaches that explicitly deal with problem definition but thus far have not been used in purchasing. Any systematic approach, technique or model, aimed at supporting at least one of the following aspects of problem definition has been included in our overview:
 better understanding of the problem;
 arriving at possible courses of action;
formulating criteria for selecting one or more courses of action.
It is recognised that the list of models presented here is not exhaustive. Nevertheless, we believe the overview here gives a fair picture of the variety of approaches available to support the phase of problem definition.
Several decision models investigate the need for supplier selection and generate possible alternatives
In this subsection, we successively discuss the following contributions: Cognitive Mapping (Warren, 1995), Strategic Choice (Friend and Hickling, 1987), WWSanalysis (Basadur et al., 1994), Influence Diagrams (Howard, 1988), Strategy generation table (Howard, 1988), Framework for formulation of alternatives (Arbel & Tong, 1982) and ValueFocused Thinking (Keeney, 1992).
An intuitive explanation of Cognitive mapping
Warren describes the technique of cognitive mapping as a "...relatively simple technique to help teams build scenarios (i.e. alternatives, De Boer)...and that makes explicit the views of teams about factors influencing their industry and firm". In the most simple form, a cognitive map consists of a network of causeandeffect relationships between factors in the problem situation on hand. Usually, the individual team members are first interviewed in order to identify their opinions as to what might be relevant future factors and consequences. In a next step these individual views are combined into a composite map of the whole team. In this way, individual team members may raise unique issues and consequences not mentioned by others thereby providing a valuable diversity in the views of the team. In addition, the composite map may indicate opposing views concerning an outcome of any causal influence. Put together, the technique of cognitive mapping facilitates the (group)process of exploring and more precisely defining a problem as well as generating possible alternative courses of action.
An example of Cognitive Mapping applied to supplier selection
An example of a possible cognitive map is depicted in figure 6.2.
Figure 6.2: Cognitive map applied in a purchasing setting
The cognitive map in figure 6.2 may be the composite result of several maps, each representing an individuals view on a particular supply situation (i.e. for a particular item or group of items). Such cognitive maps could be constructed by asking the various individuals involved (e.g. purchasing, R&D, marketing, engineering) the following questions:
What will be the most important developments or changedrivers in this
particular supply situation?
 What consequences might they have?
 What actions regarding our suppliers could/should be taken?
For various items and services purchased, such a cognitive may be composed periodically in order to aid the process of reviewing the existing supply base. For example, the cognitive map identifies events and developments that seem to require the selection or replacement of suppliers. In that way, the cognitive map (CM) aids in anticipating on and preparing for (future) supplier selection decisions as well as investigating such decisions vis a vis other solution directions, e.g. changing the substance of the relationship with the current suppliers. In addition, CM could also be made for (resources) items and activities that are currently not purchased. A CM covering important future developments and change drivers may indicate under which conditions the purchasing of those resources or activities might come into play. For example, suppose we consider the (inhouse) development of certain software. A cognitive map could be constructed by asking the following questions regarding these development activities:
What will be the most important developments or changedrivers concerning this inhouse activity?
What consequences might they have?
Which actions could/should be taken/considered?
The answers to these questions could subsequently be analysed regarding their interrelationships, see figure 6.3.
Figure 6.3: Example of Cognitive Map
Summarised, CM can aid the purchaser in understanding and checking the need for selecting a supplier (or otherwise changing the supplier base) more thoroughly and earlier. In addition, the map may indicate (rough) criteria for the selection process. For example, in figure 6.2 the element ever increasing speed of technological developments constitutes an indicator of a criterion (i.e. the extent to which suppliers keep up with technological developments).
Cognitive maps are extremely flexible but may be most effective within the scope of a periodical purchasing plan
Obviously, a CM will not be made on daily basis. They might be most useful in the scope of writing a middle and long range purchasing plan for an organisation or a group of purchased items or services. CM are extremely flexible: they can be made as detailed and comprehensive as the purchaser wants them to be and virtually any factor or aspect can be included. This is also relevant in the light of the spreading of the purchasing function throughout the organisation and the increased multidisciplinary involvement of people in purchasing decisions. In order to handle bigger maps efficiently, specific software (e.g. COPE) or the use of a whiteboard is required. Although it is not likely that CM will be made on a daily basis (because of the efforts involved and the longterm scope of the issue under consideration), it may very well be that the completed map is consulted on such basis.
An intuitive explanation of Strategic Choice
Our discussion here of this approach is based on Rosenhead (1989). The central theme of the Strategic Choice approach concerns the question how to deal with interconnectedness of decision problems. Within the approach four complementary modes of decision making activity are distinguished. In the shaping mode the structure of the set of decision problems is addressed. The designing mode involves arriving at possible courses of action. Next, in the comparing mode, the decision makers address their concerns as to the ways in which the consequences and implications of the possible courses of action should be compared. Finally, in the choosing mode, among other things, the decision maker considers whether there are particular commitments to action (Rosenhead, 1989). For each of the decision modes, the Strategic Choice approach provides techniques that are supportive to the decision makers. The shaping mode is structured through the use of the concept of decision areas, which facilitate a more explicit representation of problem areas and their interrelationships. The comparing mode involves using socalled comparison areas. It consists of a structured process of arriving at broadly defined criteria. Using these comparison areas, possible courses of action are evaluated in terms of their comparative advantage. Finally, in the choosing mode, several techniques are available to the decision makers to systematically analyse various types and levels of uncertainty surrounding the possible options as well as to ultimately arrive at specific action schemes. In the designing mode, decision makers use a technique which is referred to as the Analysis of Interconnected Decision Areas (AIDA). AIDA involves (Rosenhead, 1989) "...representing the range of alternatives available within any decision area in terms of a limited set of mutually exclusive options, and then introducing a set of tentative yes/no assumptions about whether options in different decision areas can be combined".
An example of Strategic Choicetechnique AIDA
Suppose we define the following decision areas, i.e. fields of choice in which it is possible to conceive of two or more mutually exclusive alternatives:
decision area A: purchasing strategy for purchased items belonging to category X;
decision area B: purchasing strategy for purchased items belonging to category Y;
decision area C: purchasing strategy for purchased items belonging to category Z;
decision area D: allocation of resources available to the purchasing department.
The categories X, Y and Z may correspond to existing classifications, e.g. based on ABC and/or portfolio analysis. These analyses result in several possible courses of action, e.g. whether or not to find backup suppliers, starting up supplier reduction programmes, rationalising order procedures et cetera. By means of the AIDA technique it is possible to systematically analyse the interactions between these courses of action. In figure 6.3 the result of this analysis is shown in the socalled compatibilitymatrix. The alternatives belonging to the four decision areas A, B, C and D are respectively a1, a2, a3, b1, b2, c1, c2 , d1, d2 and d3.
Figure 6.3: Compatibility matrix in AIDA
In this compatibilitymatrix the following notation is used to characterise the interaction between two alternatives:
x = the two alternatives are incompatible;
? = the two alternatives are inconsistent;
o = the two alternatives are feasible, i.e. no positive or negative interaction;
ok = there is mutual enhancement.
Thus, in the example in figure 6.3, the replacement of all senior buyers is incompatible with many of the other decision areas except for a limited downsizing of the supplier base. Conversely, the possibility of selecting (additional) suppliers is not considered possible when replacing senior purchasing staff. We emphasise that this is only an example. Naturally, other decision areas (including other alternatives) are possible. In addition, decision areas covering nonpurchasing areas, e.g. marketing, corporate finance, may be included in the process.
Strategic choice is collection of tools rather than one model
In many aspects, the comments made regarding Cognitive Mapping also apply to Strategic Choice (SC). SC also seems most appropriate within the framework of formulating middle to long range purchasing plans. More than CM however, SC will require the support of a facilitator. In addition, as far as we know, no specific software is (yet) available. If we more specifically look at the AIDAtechnique, a revised comment is appropriate. AIDA may also be useful on a more frequent basis. For example, the decision areastructure can be used as a checklist (in which the contents of the decision areas may change but the structure as such can be maintained). In that way, the idea to initiate certain actions in one decision area (e.g. the idea to reduce the number of suppliers for a certain category of items) can immediately and systematically be assessed in relation to other (predefined) areas. In that way, AIDA facilitates the required investigation of supplier selection decisions in relation to other decisions (about purchasing matters as well as issues such as strategy, marketing and finance) something that was found to be lacking in the existing decision models for supplier selection.
An intuitive explanation of WWSanalysis
This approach consists basically of a threestep thinking process which, starting with the original problem statement, facilitates both the systematic construction of broader and narrower problem statements. In this way, possible `hidden`, or underlying bigger problems may be identified as well as a decomposition into one or more subproblems. The WWSanalysis therefore results in a hierarchy of problem definitions which aids the decision makers in developing a more meaningful and leveragable problem statement as well as a graphical representation of the `big picture`.
An example of WWSanalysis applied to supplier selection
WWS stands for WhyWhats Stopping us. Starting with an initial problem statement, e.g. How might we find a backup supplier for bottleneck item X?, the question Why would we want to find such a supplier? leads to broader problem statement whereas the question Whats stopping us from finding such a supplier leads to a more narrow version of the original statement. A possible series of questions for this example is given in table 6.1
How might we find a backup supplier for bottleneck item X?Why would we want to find such a supplier?
Answer: in order to reduce the risk of nondeliveryWhats stopping us from finding such a supplier? Answer: the unique specification that is tailored to our current sole supplierWhy would we want to reduce this risk?
Answer: because of the high costs of not having the part in time Whats stopping us from reducing this risk? Answer: a) the unwillingness of the supplier b) the suppliers unreliable delivery timesWhy would we want to make the specification more general? Answer: to make it possible for other suppliers to share some of the riskWhats stopping us from making the specification more general? Answer: the specific assembly process in which part X is usedTable 6.1: Examples of WWSquestions
In figure 6.4 the hierarchy of problem statements matching the questions of table 6.1 is depicted.
Figure 6.4: Hierarchy of broader and narrower problem definitions
Naturally, for each Why.. or Whats stopping us.. question, several answers may be possible. In the same way, additional Why else... or What else is ... questions may follow a previous result. All the answers to the Why.. and the Whats stopping us.. questions can be formulated in a How might we.. manner, e.g. the answer To reduce the risk of nondelivery would become: How might we reduce the risk of nondelivery?. In this way, a hierarchy of broader as well as narrower problem statements can be constructed. Next, a careful investigation of these problem statements might aid the purchaser in two ways.
First, it urges the purchaser to reconsider the (scope of the) problem statement that was chosen originally. Perhaps a broader or a narrower focus is more appropriate. Given the initial problem statement: How might we find an additional supplier for this bottleneck item?, a broader statement would be (according figure 6.4): How might we reduce the risk of nondelivery?. Obviously, the latter statement offers a wider range of possible answers. Conversely, a narrower statement could read: How might we arrive at a more general specification?. Clearly, this statement does not necessarily require another supplier. If the specification becomes more standard, it will be easier to switch to another supplier if necessary.
Secondly, once the right scope has been identified, possible answers to the questions posed in the ovals should be given. This may lead to alternative or complementary solutions for the problem that initially triggered the supplier selection.
WWSanalysis is a flexible tool for checking the need to select a supplier
Compared to CM and SC, WWS is a more structured and defined technique. Nevertheless, it is still very flexible and it may be used for short term (specific) as well as longer term (more illdefined) issues concerning suppliers. The WWSanalysis is especially suited for situations where a purchaser (or a purchasing department) is faced with explicit targets or problems (e.g. reduce the dependence on suppliers for a certain item). The way this target (or problem) is formulated, as well as the initial solution (e.g. selecting one new supplier) can be systematically questioned and possible alternatives can be derived. In the absence of supportive software, hierarchies containing many ovals might become to cumbersome to handle, especially in case of problem statements that involve suppliers and items that are not considered very important and consequently do not justify an extensive analysis.
An intuitive explanation of a Strategy Generation Table
The strategygeneration table is intended for situations where there seems to be an extensive list of possible strategies or alternatives for solving a problem. The strategygeneration table systematically leads to the identification of a limited number of socalled strategy themes. A strategy theme enables the decision makers to identify and consider a few, yet significantly different strategies rather than a combinatorial exhaustive and exhausting list. These strategy themes are subsequently submitted to further analysis.
An example of a Strategy Generation Table
An example of strategy generation table applied to a purchasing setting is given below in table 6.2. In this table possible strategychoices (alternatives) are given for three categories of purchased parts. These categories contain parts that require a similar purchasing strategy. The various choices that are listed here for the three categories may me derived from for example a purchasing portfolio analysis or a SWOTanalysis. In addition, possible alternative courses of action with respect to purchasing personnel and purchasing systems are listed. Naturally, other areas (both within purchasing management and outside purchasing) may be included. Finally, some of the targets that the purchasing department has set to achieve, are placed in the last column of the table.
Strategy themePurchased parts  category APurchased parts  category BPurchased parts  category CPurchasing personnelPurchasing systems Purchasing targets
Theme 1 cost reduction)
Theme 2 (improved customer service)increase volume with current supplier
search additional suppliers
turn to makeandbuy
limited downsizing of supplierbase
immediate shift to single sourcing
initiating comprehensive ESI project
outsource on subsystem level (instead of componentlevel)
backward integration with main developer invest in training current purchasing workforce
replace senior buyers
partly training/partly new buyers
introduction of new information system
maintaining the current system one more yeardrastic cost reduction
improved (internal) customer service
reduction of supply risks strategic itemsTable 6.2: Example of a strategy generation table in purchasing
Theoretically, a large number of combinations of alternatives exists, namely (3*2*3*3*2*3). However, in practice many combinations are not feasible and/or desirable. The strategygeneration table can now be used to identify a limited set of feasible alternatives. If we, for example, would decide to focus on achieving improved internal customer service, the alternatives maintaining the current information system and investing in training the current workforce may be considered infeasible if many of the internal customers complaints concern the current information system. Furthermore, introducing a new information system might be better combined with partly hiring new buyers (that are familiar with the new system) rather than investing in training of all current buyers. In this way, many infeasible or undesired paths of alternatives can be cut off early in the process.
Strategy Generation Tables relate supplier selection decisions to other decisions
Strategy Generation Tables very much resemble the AIDAtechnique from Strategic Choice. Consequently, the same comments apply here as well. A Strategy Generation Table provides a structure for linking supplier selection decisions with other decision areas. For example, using table 6.2 as an illustration, the decision whether or not to introduce a new purchasing information system is (also) linked to supplier selection decisions for the purchased parts in category A and category B. The format (i.e. the column headings in table 6.2) can be used as a checklist. The contents of the columns may change but the structure itself can be used again.
An intuitive explanation of Influence Diagrams
Howard (1988) describes influence diagrams as "..an extremely important and useful tool for the initial formulation of decision problems". Influence diagrams consist of ovals, rectangles and arrows. Quantities in the ovals are considered uncertain. Arrows entering circles mean that the quantities in the circles are (probabilistically) dependent on whatever is at the other end of the arrow. The rectangles are decisions under control of the decision makers. Arrows entering such rectangles show the information that is available at the time of the decision.
An example of Influence Diagrams applied to supplier selection
In figure 6.5. an example of an influence diagram is given.
Figure 6.5: Influence diagram
This particular Influence Diagram may reflect the hesitation a purchaser feels regarding whether or not to switch to another supplier for an important component. The Influence Diagram (ID) indicates that this decision is under control of the purchaser (expressed through the rectangled shape) but that a sound decision is dependent on sales projections by Marketing and technology decisions made by R&D. Stable sales figures and sticking to the current technology would be in favour of the current supplier while a significant sales increase and/or a decision to use a new technology in the component would favour another supplier. The ID maps the purchasers view as to how the supplier selection decision interrelates with other actors and their decisions. The ID urges the purchaser to explicate to what extent and in which way, the supplier selection depends on these other actors and their decisions. The ID can then be used to carry out whatif .. analyses with respect to the possible outcomes of the values in the ovals. These analyses may be used to generate alternative (or additional) actions that reduce or eliminate the dependency on the other actors. For example, if the R&D department decides to switch to another technology, can we still use the current supplier? Should we already switch to another supplier that could work with any technology chosen by R&D? These analyses may also be used to be better prepared for the supplier selection.
Influence Diagrams can be seen as structured Cognitive Maps
The ID approach closely resembles Cognitive Mapping in the sense that the purchasers mental perceptions of how various factors influence each other are made explicit. However, IDs provide more structure through the distinction between rectangles and ovals. IDs could thus be used to give further structure to (part of) a Cognitive Map. In that case, IDs will not be used on a daily basis but a completed ID (just as a completed Cognitive Map) can still serve as a reference point or framework for ongoing, daily discussion. Finally, as the ID maps the uncertain (exogenous) factors and actors related to the supplier selection, the ID may provide useful input for a Decision Analysis model (see chapter V) in which probabilities are assigned to the possible values of the variables in the ovals.
An intuitive explanation of a Framework for Formulation of Alternatives (FFA)
Arbel and Tong (1982) present a fivestep framework for arriving at alternatives in a systematic manner. In the first step, all factors that may have a bearing on the problem and its solution are identified. For this purpose, Arbel and Tong propose a generic template consisting of the following categories of relevant factors: the ultimate goal, exogenous decision factors, competitors objectives, competitors potential actions, the decision makers own objectives, general areas of possible actions and finally available resources. The first step results in a hierarchy of relevant decision factors. The second step involves the assessment of the relative importance of each element in this hierarchy. The authors suggest the use of the analytic hierarchy process (see Saaty, 1980) for this step. At this point in the process, the most important decision factors are presented to the decision maker. While recognising these factors, the third step now involves generating a preliminary set of alternatives. The fourth step consists of identifying possible weaknesses in the preliminary set through the execution of sensitivity analysis. The final step in the process consists of providing feedback to the decision maker(s).
An example of FFA applied to supplier selection
A example of the framework applied to a purchasing situation is presented in figure 6.6
Figure 6.6: Example of an application of the framework for option generation
In this example, the framework has been applied to the selection of a supplier for stationary and printed matters. Starting with the overall goal (i.e. reducing the purchasing costs), the framework facilitates a systematic analysis of relevant factors to be taken into account when developing alternatives as well as the relative importance of these factors.
The importance of each factor is expressed in a number (see figure 6.6). For example, in our role as purchasers we regard an easy implementation most important. First, possible alternatives are generated taking into account the set of most important factors. This set is marked with bold arrows in figure 6.6. These are in this example: (1) the downsizing of the purchasing department (2) the possible obstructive attitude of internal customers and (3) an easy implementation. Given these factors, a feasible alternative is a drastic reduction of the range of items purchased and a limited downsizing of the supplier base rather than e.g. a complete outsourcing of the procurement of stationary and printed matters and closing down of the warehouse.
Summarised, a number of more specific variants of the initial idea to reduce the number of suppliers is derived. In addition, other actions leading to the same goal might emerge.
FFA offers a structure for checking the need and feasibility of supplier selection
Similar to WWSanalysis, FFA is a rather structured method. The framework elements (goal, exogenous factors etceteras) serve as a clear and flexible checklist. In addition, the builtin prioritisation through AHP gives further direction to the purchaser. However, unlike WWSanalysis, FFA does not challenge the purchasers goal (and the way this goal is formulated). Furthermore, the framework element competitor does not seem particular useful in the context of purchasing and supplier selection. Instead, the element exogenous decision actor(s) might be more relevant. Given a problem statement, which at first glance implies some action towards suppliers, FFA facilitates the execution of a feasibilitycheck of such an action. In addition, FFA facilitates the search for other possible solutions. If the AHPmethod is used to derive priorities, FFA seems most appropriate for oneoff or longer termdecisions rather than for daily use.
Several approaches aid in generating and evaluating criteria for supplier selection
In this subsection, we respectively discuss Rough Sets (Slowinski, 1992; Pawlak, 1991) and various brainstorming methods (Keeney, 1994). These approaches in particularly support the process of generating criteria as well as evaluating decision criteria.
An intuitive explanation of Rough Sets
Pawlak (1991) developed the theory of Rough Sets. Starting point of any Rough Sets analysis is a socalled information system. In the Rough Setssense an information system simply consists of a collection of objects with certain attributes. For example, such an information system could consist of a group of suppliers with certain attributes like size, turnover, financial stability and approvednon approved status. The Rough Sets approach leads to the definition of a set of objects in terms of socalled lower and upper approximations. A lower approximation is a description of objects (in terms of some of the attributes) that are known with certainty to belong to a certain subset of interest. For example, if all suppliers in our information system with a high level of financial stability turn out to be approved suppliers, the suppliers with that level of financial stability constitute a lower approximation of the set of approved suppliers. An upper approximation is a description of objects which possibly belong to the subset of interest. In our example, most big suppliers may turn out to be approved suppliers, yet not all. Any subset defined through its lower and upper approximations is called a rough set. Rough sets may be a useful approach in evaluating the relevance of criteria (objects attributes) used in a decision making process. Among other things, the rough set approach makes it possible to identify redundant criteria (attributes), i.e. criteria that do not (or only slightly) have discriminating power. In that sense, Rough Sets can be used to evaluate the usefulness of the criteria used in a supplier evaluation/selection process.
A formal notation of Rough Sets
In this subsection we use the definition of Rough Sets as available on the Electronic Bulletin of the Rough Set Community (EBRSC, 1993): Given a set of objects (OBJ), a set of object attributes (AT), a set of values (VAL) and a function f: OBJ*AT> VAL so that every object is described by the values of its attributes, a socalled equivalence relation R(A) is defined where A is a subset of AT:
Given two objects o1 and o2,
o1 R(A) o2 < = > f(o1,a) = f(o2,a), for all a in A
o1 and o2 are said to be indiscernable (with respect to the attributes in A)
Now this relation is used to partition the universe into equivalence classes, {e_0, e_1, e_2, , e_n} = R(A)*. The pair (OBJ, R) form an approximation space with which we approximate arbitrary subsets of OBJ. These are referred to as concepts. Given O, an arbitrary subset of OBJ, we can approximate O by a union of equivalence classes:
The lower approximation of O (also known as the positive region): lower (O) = POS (O) = union {e_i subset O} e_i.
The upper approximation of O: upper (O) = union {e_i \ interset O \ not empty} e_i.
NEG(O) = OBJ POS(O)
BND(O) = upper (O) lower (O)
The most common definition of a rough set is that it is a set O, such that BND(O) is nonempty. In other words: a rough set is defined only by its lower and upper approximation. A set O, however, whose boundary BND is empty is exactly definable. If a subset of attributes, A, is sufficient to create a partion R(A)* which exactly defines O, then A is called a reduct.
An example of Rough Sets applied to supplier selection
A possible application of rough sets in purchasing is illustrated below. The purpose in the example is to identify the possible redundant criteria in the process of qualifying suppliers for a particular group of regularly purchased items. The qualified suppliers are placed on a list of approved suppliers. Suppose that from the past 6 qualification audits, the following information can be obtained:
Qualification (audit) no.Criteria used in the auditOutcome of the auditq1q2q3q4Audit 11111not qualifiedAudit 21213not qualifiedAudit 32222qualifiedAudit 41223qualifiedAudit 52222not qualifiedAudit 62323qualifiedTable 6.3: Information collected from qualification audits
In table 6.3 q1, q2, q3 and q4 represent the criteria that were used to decide upon the qualification of the suppliers. The criteria are explained below:
q1 = 1 if the supplier does not have an ISO 9000 certificate
2 if the supplier has an ISO 9000 certificate
q2 = 1 if the suppliers ROI is below 5%
2 if the suppliers ROI is in the range 510%
3 if the suppliers ROI exceeds 10%
q3 = 1 if the supplier cannot show at least three recent references
2 if the supplier can indeed show at least three recent references
q4 = 1 if the supplier has a solvability of less than 20%
2 if the supplier has a solvability in the range of 2030%
3 if the supplier has a solvability that exceeds 30%
The rough set approach now proceeds as follows. First, the socalled equivalence classes are determined. In this example, we obtain the following result:
The equivalence classes are: {{audit1}, {audit2}, {audit3, audit5}, {audit4}, {audit6}}
If we look at the decision that was made in the various cases, we can construct the set of qualified cases, i.e. {audit3, audit4, audit6], and the set of nonqualified audits, i.e. {audit1, audit2, audit5].
The lower approximation of the set of qualified cases is {audit4, audit6}. This means that if a supplier has a ROI of over 5%, this supplier can show at least three references and has a solvability of at least 30%, this supplier will definitely be qualified. The lower approximation of the set of nonqualified cases is {audit1, audit2}.This means that if a supplier does not have an ISO certificate, and the supplier has a ROI of less than 10% and cannot show at least three references, this supplier will definitely not qualify. In all other cases, i.e. the socalled boundary set, which is {audit3, audit5}, it remains uncertain whether or not the supplier will qualify. The rough set approach can now be used to find the minimum set of attributes (criteria) that yield the same classification, i.e. the identical lower approximations of the qualified and the nonqualified cases. This minimum set is called a reduct and can be found by using the concept of socalled superfluous attributes (see Tanaka et al., 1991). In this case, the reduct consists of {q3, q4}. For the sake of overview, we will not formally explain this concept here but we can easily verify that this is indeed a reduct. Suppose, we remove q1 from the qualification process. The resulting set of equivalence classes is still R(A)* = {{audit1}, {audit2}, {audit3, audit5}, {audit4}, {audit6}}. In addition, suppose we remove q2 as well. The set of equivalence classes remains unchanged. However, if we would also remove q3, the set of equivalence classes becomes {{audit1}, {audit2, audit5, audit6}, {audit3, audit4}}. The corresponding lower approximations are A* (qualified cases) = {(} and A* (nonqualified cases) = {audit1}. In other words: with only q4 as decision criterion, we would not obtain the desired result. The same can be shown for q3. However, the combination of q3 and q4 turns out to be sufficiently discriminating. This implies that the purchaser can focus on evaluating a suppliers references and the suppliers solvability when deciding on whether or not the supplier should be added to the list of approved suppliers.
Rough Sets are especially useful in repetitive supplier audits involving many criteria
The Rough Sets approach clearly differs from the models discussed in the previous section in the sense that this time a supplier selection (and/or evaluation) has already taken place. Rough Sets does not support the initial problem definition and generation of criteria. Rather, is facilitates making existing decision and evaluation processes more efficient by identifying redundant criteria. In addition, the decision rules that result from the Rough Sets analysis offer a means for assessing the consistency of the evaluation/selection of suppliers. The outcome of an (unaided) audit of a new supplier can be compared (checked) with the outcome of the Rough Sets decision rule applied to this supplier. In any case, Rough Sets models require historical information about different (but comparable) cases of supplier selections. Obviously, Rough Sets efficiency potential is highest when (initially) many evaluation criteria are used.
An intuitive explanation of (VFT) brainstorming
There are many forms of brainstorming. In itself, it is ofcourse something we do without considering it to be a decision model or technique. In this subsection, we discuss a somewhat structured version based on the Value Focused Thinking approach developed by Keeney (1994). In VFT a generic set of questions is suggested for eliciting a decision makers values concerning a certain topic or field of interest. The answers to these questions are then rephrased as criteria.
An example of Brainstorming applied to supplier selection
Based on the questions suggested in Keeney (1994) the following questions may be asked to a purchaser considering a particular group of items purchased:
1. Which are the pros and cons of the current supplier?
When comparing two suppliers of this item, what are the most relevant
differences?
3. How would you describe the ideal supplier?
4. How would you describe the nightmare supplier of this item?
5. Which are your best past experiences with the current supplier?
6. Which are your worst pastexperiences with the current supplier?
7. Which goals or aspirations do you have regarding these suppliers?
8. Which restrictions do you pose upon suppliers?
What would other disciplines/managers find important when choosing
suppliers?
Which factors are of specific importance when considering the future supply of this group of items?
The purchaser might give the following answers:
ad.1. Pros are the suppliers control of operations and production flexibility. A major disadvantage of the supplier is his unsatisfactory level of innovativeness.
ad.2. The most relevant differences concern price level and delivery lead times.
ad.3. The ideal supplier is located around the corner and does not cause us any
quality problems.
ad.4. The nightmare supplier makes promises he cant keep.
ad.5. The best experience was the introduction of JIT delivery.
ad.6. The worst experience we had with this supplier was when developing a new
product with him, which completely failed.
ad.7. We would like such suppliers to take a leading role in making our products even more innovative.
ad.8. The supplier should not be located too far away and should be financially sound
ad.9. I dont know.
ad.10. The expected rise in demand.
These answers could then be converted into criteria, as is shown in the table below.
Evaluated through marketresearchEvaluated through field research
Supplier brochures, databases, Internet, archives, etceteras:
. location
. financial status
Quotations:
. price
Visits/audits:
. process control
. production flexibility
. innovativeness
. delivery
. quality level
. reliability
. long term capacityTable 6.4: Criteria resulting from brainstorming
As is done in table 6.4, criteria can be categorised depending on how the evaluation might take place.
Brainstorming can be used to generate qualification and selection criteria
Clearly, brainstorming is one of the few decision models which actually aids the purchaser in generating criteria. After a brainstorm session such as described in the example here it may be necessary to further analyse the raw list of criteria. ISM and Rough Sets could be used for this. Finally, we note that the set of questions in the VFTbrainstorm model can not always be fully used in this form. For example, in case of a New Taskpurchase, it may be difficult to speak of pros and cons of the current supplier or past experience with the supplier. In that case, the current situation might be used instead of the current supplier.
Various decision models for the choice phase provide the properties that were lacking so far
In the previous subsection we discussed several possible approaches for supporting the phase of problem definition in supplier selection. We now turn to approaches within Operations Research that capture some of the properties the current, available formal models for purchasing decisions lack in the choice phase of the decision making process, e.g. multidimensional criteria, noncompensatoriness and multiple decision makers. Throughout this section we will illustrate the various models and methods using a single example. This example is introduced below.
Suppose that an industrial company is looking for a backup supplier in order to ensure the supply of a range of high quality and rather dedicated components. Management has appointed a special task force responsible for recommending one or two suitable suppliers. The taskforce consists of several officers from various functional departments within the company, such as purchasing, engineering, marketing, R&D and production. First, the members of the taskforce organise several meetings in order to agree on a profile of the desired supplier. After several sessions and discussions with management, the following profile emerges:
 The supplier should be a major player in its markets with a high yearly turnover. On the other hand, the supplier should not be too big in order to maintain sufficient commitment on the long term. Preferably, the suppliers turnover approximates $ 9.5 million;
 Because of the JITdriven production system, the supplier should not be located too far away;
 Obviously, a low general cost level is imperative as this range of components significantly impacts the total costs of end products;
 The quality image of the supplier is of significant importance, especially
because of its contribution to the overall quality appeal of the endproducts in which the suppliers components will be used.
Based on previous market research and suggestions of several members within the taskforce, an initial set of 5 candidate suppliers is constructed. Next, the taskforce evaluates these 5 suppliers with respect to the ideal profile. The results of this evaluation are presented in table 6.5.
Criteriasupplier 1supplier 2supplier 3supplier 4supplier 5Turnover (million$)
Distance (km)
Costlevel ($)
Quality image7.5
50
20
moderate8
500
15
excellent11
900
18
good9
200
25
good8
550
11
badTable 6.5: Data available on the suppliers performance
The evaluation of the cost level is based on various sources of information e.g. listprices of comparable components, historical data, supplier estimates etceteras. The set of alternatives clearly consists of suppliers a to e. Even with all these data it is not immediately clear which supplier(s) should be recommended to management: a common problem in practice. In this sections various decision models are applied to this problem. Some of these decision models require normalised, comparable (quantitative) scores on the criteria. A possible transformation of the data available from table 6.5 into such comparable scores is given in table 6.6. All raw scores are transformed into quantitative values on a scale of 0100.
Criteriasupplier 1supplier 2supplier 3supplier 4supplier 5Turnover (million$)
Distance (km)
Costlevel ($)
Quality image0
100
36
5033
47
71
10033
0
50
75100
82
0
7533
41
100
0Table 6.6: Transformed scores on criteria
Finally, we assume that management has agreed on the following weights kj for the criteria (table 6.7):
CriterionTurnoverDistanceCostlevelQuality imageWeight0.20.150.30.35Table 6.7: Weights assigned to the criteria
Several decision models accommodate noncompensatory decision rules
In this subsection, we successively discuss the following models: conjunctive and disjunctive screening models (Hwang and Yoon, 1981), lexicographical methods (Massam, 1980), Maximin methods (Chen and Hwang, 1991), Linear assignment (Chen and Hwang, 1991) and Outranking (Vincke, 1986). Although these models differ in various ways, their common characteristic is that scores (on criteria) are aggregated in such a way that a low score on one criterion cannot be (fully and proportionally) compensated by a (very) high score on another criterion. The descriptions and notation used below are based on the beforementioned sources.
An intuitive explanation of conjunctive and disjunctive models
A conjunctive decision model applies the principle of rejecting an alternative if this alternative does not equal or exceed a minimum score for each criterion. In a disjunctive decision model, an alternative is selected if at least one of its criterionscores exceeds a specified minimum value.
A formal notation of conjunctive and disjunctive models
In formal terms, and using a conjunctive decision model, supplier i is an acceptable supplier only if
EMBED Equation.2
where xij is the score of supplier i on criterion j and xjo is the minimal acceptable level for criterion j. Using a disjunctive decision model, supplier i is an acceptable supplier if
EMBED Equation.2
where xij is the score of supplier i on criterion j and xjo is the minimal acceptable level for criterion j.
An example of Conjunctive and Disjunctive decision models applied to supplier selection
Suppose that in our example, management had specified the following minimum levels: xturnovero = 30, xdistanceo = 40, xcostlevelo = 60 and xqualityo = 70. Using the conjunctive model it then becomes clear that only supplier 2 is acceptable. Using the disjunctive model, we find that all suppliers are acceptable, e.g. supplier 1 satisfies the minimum level for distance and is therefore accepted, although this supplier does not satisfy any of the other minimum levels.
Conjunctive and disjunctive are simple and fully noncompensatory decision models
Both the conjunctive and the disjunctive model are extremely simple decision models. They do not require any computations and/or normalisation of the raw scores on the criteria. Clearly, the conjunctive model is strictly noncompensatory: a (too) low score on one criterion can not at all be compensated for by (very) high scores on other criteria. In that sense, a conjunctive model can be characterised as pessimistic. The disjunctive decision model is less strict: meeting one criterion suffices for the alternative to be accepted. Still, very high scores on other criteria are not taken into account. Furthermore, it is clear that both in the conjunctive and disjunctive decision model, criteria weights do not play any role. Conjunctive and disjunctive decision models seem very suitable for the efficient initial screening of a high number of suppliers. In the conjunctive model, each supplier can simply be checked with regard to its score on one criterion and only if this score is high enough, the supplier has to be evaluated with regard to the other criteria. Any supplier not passing one criterion can be removed from further consideration. In that way, the conjunctive model is sensitive for possible errors in the measurement of supplier performance. The disjunctive model can be used if there are only a few suppliers that would meet all criteria. Conjunctive and disjunctive decision models divide an initial set of suppliers into acceptable and non acceptable suppliers. This means that these models are not particularly useful for making an ultimate choice between a few (acceptable) suppliers.
An intuitive explanation of the lexicographic model
The lexicographical model assumes that the criteria can be ranked from most to least important. The alternatives which satisfy the first criterion are evaluated with respect to the second criterion and if more than two alternatives satisfy this criterion, a third criterion is used and so on down the list of criteria until just one alternative is identified. In the socalled lexicographical semiorder method (see Hwang and Yoon, 1981) basically the same procedure is followed. This method however, allows for a degree of imperfect discrimination so that one alternative (or supplier for that matter) is not judged better, just because it has a slightly higher value on a particular criterion.
A formal procedure for the lexicographic (semiorder) model
Based on Chen and Hwang (1991) we can formulate the procedure as follows:
Compare the alternatives with regard to the most important criterion;
Select the alternative with the highest value on that attribute or with a value not significantly lower than the highest value;
If more than one alternative is selected, compare these alternatives to the next important criterion;
Select the alternative(s) with the highest or near highest value for that criterion;
Proceed in this way until one alternative is left or until all alternatives have been evaluated.
An example of a lexicographic model applied to supplier selection
From table 6.7 we can conclude that criterion 4 (quality image) is most important. We also assume that the minimum levels as defined in the previous example are required as well here. This results in supplier 1 and supplier 5 being removed from further consideration. If we evaluate the remaining suppliers with respect to the second important criterion, i.e. costlevel, only supplier 2 is acceptable as the other two suppliers have scores below the required score of 60.
The lexicographical method is basically a series of prioritised conjunctive models
Similar to the conjunctive and disjunctive models, the lexicographical model does not require computations or any normalisation of the raw scores of the suppliers. Still, if quantitative criteria are used, the lexicographic model might lead to wrongfully discarding (or accepting) a supplier because of the crisp borderline between acceptance and discordance and the possible fuzzy nature of the suppliers scores. In that respect, the lexicographic semiorder model is preferable as it uses a range of values instead of one crisp number. Also, the lexicographical model is strictly noncompensatory: a low score on one criterion cannot be compensated by a high score on another. The lexicographical model takes into account differences in importance of the criteria used. The criteria weights do not have to be quantified, an ordinal ranking suffices. The lexicographical model seems an efficient screening model for situations where a large number of suppliers has to be narrowed to a smaller set of suppliers. In this respect, the lexicographical model resembles the conjunctive and disjunctive models. However, in a lexicographical model, a supplier with a low score on an unimportant criterion might become the ultimately chosen supplier, whereas this is impossible in the conjunctive model.
An intuitive explanation of the maximin and maximax models
The basic idea behind the maximin model is that the overall performance of an alternative is determined by its lowest score on any of the criteria. First, for each alternative, the lowest score (for any of the criteria) is determined. Subsequently, the alternative with the highest of these scores is chosen. Contrary to the maximin method, the maximax model selects alternatives by their highest scores on any of the criteria. Thus for each alternative, the highest score is determined. Subsequently, the alternative with the highest of these scores is chosen.
A formal notation of the maximin model
In the maximin model, we select supplier S* such that
EMBED Equation.2
where xij is the score of supplier i on criterion j. In the maximax model we select supplier S* such that
EMBED Equation.2
where xij is the score of supplier i on criterion j.
Examples of the maximin and the maximax model applied to supplier selection
If we apply the maximin method to our example, we find that supplier 2 is chosen because its lowest score on any of the criteria, i.e. 33, is higher than the corresponding scores of the other suppliers. If we apply the maximax method to our example, we find that all suppliers except for supplier 3 are chosen.
Maximin and Maximax models require normalisation of suppliers scores on the criteria
Obviously, both maximin and maximax models are strictly noncompensatory. An exceptionally high score on one criterion does not matter in the maximin model if a suppliers lowest score is relatively bad. Conversely, in the maximax model an exceptionally low score does not matter if a supplier scores highest on another criterion. Also, no weights are attached to the criteria. Application of the maximax and maximin models requires normalisation of the suppliers scores because scores on different criteria have to be compared. Furthermore, unlike the conjunctive, disjunctive and lexicographical model, the maximin and maximax models always require evaluation of all suppliers on all criteria. The latter two aspects make these models less suitable for the screening of a high number of suppliers. Nevertheless, the normalisation only involves simple calculations and does not require specific software. The maximin model is an appropriate model when we want to select a good allround supplier that performs well on all criteria rather than a supplier that excels in one or two criteria but performs poorly on some other. The model is therefore also relatively insensitive for exceptional high or low scores of suppliers. Such scores could result from misjudgement, measurement errors or mistakes made by the supplier (e.g. misinterpretation of the invitation to tender). However, finding a supplier that excels in a certain aspect is exactly what the maximax decision model facilitates. This may be appropriate if several suppliers together can bring in the required set of competencies.
An intuitive explanation of the linear assignment model
The basic idea of this method is that an alternative deserves a high rank if it has high scores on all criteria. This idea clearly resembles the logic of the maximin model which also tries to find a good allround supplier.
A formal procedure for the linear assignment model
A formal procedure for the linear assignment model is the following (Chen and Hwang 1991):
Rank the alternatives for each criterion;
Assign an importance weight to each criterion;
Create a square (m*m) nonnegative matrix A whose element aik represents the score of alternative ai on the kth criteriawise ranking. The score aik is the summation of the weights of all criteria where ai is ranked k;
Use the linear assignment method to assign a rank to each alternative such that the summation of the scores for that assignment is maximal.
An example of the linear assignment model applied to supplier selection
If we apply the linear assignment model to our example, the ranking of the suppliers looks as shown in table 6.8.
RankTurnoverdistancecostlevelqualityfirst
second
third
fourth
fifthsupplier 4
suppliers 2, 3 and 5
supplier 1supplier 1
supplier 4
supplier 2
supplier 5
supplier 3supplier 5
supplier 2
supplier 3
supplier 1
supplier 4supplier 2
suppliers 3 and 4
supplier 1
supplier 5Table 6.8: Rank order for each criterion
Next, a square matrix is created in which the rows represent the suppliers and the columns represent the ranks. Element aij of this matrix represents the score of supplier ai on the jth criteriawise ranking. This score aij is the summation of the weights of all criteria where ai is ranked j. Using the data from table 6.8 and table 6.6 we obtain the matrix in table 6.9.
rank 1rank 2Rank 3rank 4rank 5supplier 1
supplier 2
supplier 3
supplier 4
supplier 50.15
0.35
0
0.2
0.30
0.5
0.55
0.5
0.20.55
0.15
0.3
0
00.3
0
0
0
0.50
0
0.15
0.3
0Table 6.9: summation of weights
Finally, the procedure involves assigning a rank to each alternative so that the summation of the scores for that assignment is maximal. This may be done as follows. First we pick the supplier which scores highest under rank1. This supplier is will not be considered in the sequel of the procedure. Next, we pick the supplier which scores highest under rank2 and so on. This would mean that we would get the following final rankorder of suppliers: supplier 2, supplier 3, supplier 1, supplier 5, supplier 4.
The linear assignment model applies a quasicompensatory decision rule
Contrary to the models discussed so far in this subsection, the linear assignment model does not employ strictly noncompensatory decision rules. A low score on one criterion (resulting in a low rank on that criterion) can be compensated by very high scores on other criteria (resulting in high ranks on those criteria) as the decisive score equals the summation of the weights of the criteria where a supplier scores best of all. However, unlike pure additive models, the extent to which one supplier performs better (on a criterion) than another supplier does not matter. This also makes the Linear Assignment model insensitive to exceptional high/low scores which may result from measuring errors, misjudgement or misinterpretation. Similar to the lexicographic model, the linear assignment model does not require normalisation of the raw supplier scores. Moreover, criteria scores could easily be qualitative as suppliers need only to be ranked ordinally with respect to each criterion. Although in our example, we used different criteria weights, the linear assignment model can also be used without specification of the criteria weights. If no differences are required, all criteria can be given a weight 1. Also, if differences do exist, the purchaser could be asked to simply rankorder the n criteria. The criterion ranked first would then be given a weight n, the criterion ranked second would be given a weight n1, and so on. The linear assignment model seems especially appropriate in situations where the suppliers scores are difficult to quantify and we want to select a good allround supplier. Also, the model only involves a few basic summation operations. This can easily be handled manually or using a spreadsheet program. Finally, in addition to the linear assignment model shown in the example, extensions are possible, e.g., we could choose the supplier with the highest average weight on the first two ranks.
An intuitive explanation of outranking models
These collection of models are centred around the outranking concept. In general, an alternative a is said to outrank another alternative b if (Roy, 1974): "...given what is known about the decision makers preferences and given the quality of the valuations of the actions and the nature of the problem, there are enough arguments to decide that a is at least as good as b, while there is no essential reason to refute that statement". The arguments in favour of the statement a outranks b are derived from comparing the scores of a (on the criteria) with the scores of b. Basically, for each criterion where as performance is at least as good as bs performance, the weight of that criterion is considered such an argument and the value of the weight is added to the socalled concordance index for the pair of alternatives (a,b). In other words: the concordance index expresses the total strength of the arguments in favour with the thesis a outranks b. If this concordance index is high enough (i.e. exceeds a predefined threshold value) a indeed outranks b, unless for one or more criteria, the performance of a is extremely poor compared to the performance of b on those criteria. In the latter case, the outranking of b is avoided. In the way described above, all pairs of alternatives are evaluated. It should be noted that many (slightly different) outranking models have been developed. The most simple outranking model, ELECTRE I, very closely resembles the basic procedure as described in the foregoing. Over the past decades many more sophisticated outranking models have been developed, e.g. ELECTRE II  IV, PROMETHEE (Brans et al., 1986), REGIME (Nijkamp, 1982), An uncertainty outranking method (D`Avignon and Vincke, 1988) and MELCHIOR (Leclercq, 1984). One of the additional properties of these more sophisticated outranking models is that various degrees of preferences can be modelled. This means that imprecision can be modelled, i.e. the inability of the decision maker to express strong preferences, or maybe even to compare two alternatives at all.
A formal notation of some outranking models
We base the notation used here on Vincke (1986). If gi(a) is defined as the score of alternative a on criterion i and kI represents the weight of criterion i, the concordance index c(a,b) is defined as follows:
Where:
C(a,b) represents the sum of the relative weights for all criteria on which alternative a outperforms alternative b.
The degree to which the outranking of b by a should be refused, is expressed in the discordance index d(a,b), which is defined as:
Where:
EMBED Equation.3
D(a,b) represents the maximum difference in the scores for criteria on which a is not preferred to b. After defining a concordance threshold c*, the outranking relation S is formally defined as:
Or:
depending on the way the discordance was defined. Thus, if the value of c(a,b) is convincing enough (i.e. c(a,b) e" c*) the conclusion is drawn that a outranks b, at least as longs as d(a,b) is small enough.
An assumption in the Electre I model is that a decision maker always feels able to decide that either alternative a is definitely better than b with regard to a criterion or that a and b are equally preferred (i.e. the decision maker is indifferent). Electre III allows the decision maker to have some hesitation concerning the preferability of a over b (i.e. weak preference) or to consider a and b incomparable. The concordance index c(a,b) is now defined as:
and where:
Qj and pj respectively denote the indifference and preference threshold. The definition of the discordance index now requires the specification of a vetothreshold vj(gj(a)) such that outranking of b by a is refused if gj(b) => gj(a) + vj(gj(a)). The discordance index is defined as follows:
In the Electre III model the outranking relation S is then defined as:
Where J(a,b) is the set of criteria for which the discordance is greater than the concordance.
Another family of outranking models are known as the Prometheemodels (see Brans et al., 1986). We briefly show the essence of this approach. The description and notation is based on Brans et al. (1986). For each pair of For each couple of suppliers (a,b) the socalled preferenceindex (a,b) is calculated. This index is defined as follows:
With: k = the number of criteria;
Ph(a,b) = a function which expresses the preference of a over b with respect to criterion h. These values range between 0 and 1 and are indirectly given by the decision makers through the raw performance data and the values of the indifference and the preference threshold.
Wh = the weight of criterion h.
Next, the socalled outranking flows are calculated. The positive outranking flow (also called leaving flow) for alternative a is defined as:
With: n = number of alternatives
A = set of all alternatives
$+(a) represents the strength of alternative a with respect to all other alternatives. The negative outranking flow (also called entering flow) for alternative a is defined as:
$(a) is a measure of the strength of all other alternatives with respect to alternatives a. The netoutranking flow is defined as $(a) = $+(a)  $(a). Using the outranking flows of each alternative, a partial ranking of all alternatives can be established:
a outranks b if: $+(a) > $+(b) and $(a) < $(b);
or: $+(a) > $+(b) and $(a) = $(b);
or: $+(a) = $+(b) and $(a) < $(b);
a and b are indifferent if : $+(a) = $+(b) and $(a) = $(b);
a and b are incomparable in all other cases.
An example of an outranking model applied to supplier selection
In our example, the ideal yearly turnover of a supplier is around $9.5 million.
For actual turnovers differing from this value there is a priori no reason to prefer a turnover that is larger than the ideal to one that is smaller by the same amount. So, the decision makers are indifferent to suppliers having turnovers of $7.5 million and $11.5 million, respectively. It is straightforward now to define a criterion g1 in the following way: given a supplier a, g1(a) = turnover (a)  9.5, where   denotes the absolute value. Clearly, the smaller g1(a) the better. For criteria 2 and 3 it is obvious that g2(a) equals the distance from supplier a to the company and g3(a) denotes the general cost level of supplier a. The scores on the qualitative criterion g4 are included in the set {bad, moderate, good, excellent}. The results of the calculations of the (Electre I) concordance indices for the five suppliers are presented in table 6.10.
Supplier 1Supplier 2Supplier 3Supplier 4Supplier 5Supplier 10.150.150.500.45Supplier 20.851.00.650.70Supplier 30.850.200.650.55Supplier 40.550.350.700.70Supplier 50.500.500.650.30Table 6.10: concordance indices for the 5 suppliers
For example, Supplier 3 performs at least as good as Supplier 5 with respect to criterion g1 while Supplier 3 performs better than Supplier 5 with respect to criterion g4 , hence:
c(3,5) = k1 + k4 = 0.20 + 0.35 = 0.55.
Assume that the taskforce has agreed to refuse the outranking of supplier b by supplier a in the following two cases:
The general cost level of supplier a is at least twice as high as the costlevel of
supplier b (*);
The quality image of supplier a is bad, while the quality image of supplier b is excellent (**).
Discordance with the assertion aSb is defined by means of these two cases.
Now supplier a outranks supplier b if the concordance index c(a,b) exceeds a certain threshold, while at the same time outranking is not refused on the basis of (*) or (**). Outranking of supplier b by supplier a is denoted as:
In case the concordance threshold equals 0.8 we then have:
It is clear from this picture that suppliers 2, 4 and 5 are incomparable. In order to be able to choose between these alternatives, a more precise evaluation of the given criteria and/or other criteria has to be carried out. In case the concordance threshold equals 0.7 we have:
It should be noted that the arrow from supplier 4 to supplier 5 is missing because supplier 4 has a costlevel that is more than twice the costlevel of supplier 5. Now, suppliers 2 and 4 are the most attractive ones. Outranking of supplier 5 by supplier 2 is present now because the strength of arguments for validating aSb has decreased.
The main insight resulting from using the ELECTRE I method in this case is that from now on, the taskforce can focus its attention on the suppliers 2, 4 and 5. Because the exclusion of Supplier 5 depends on whether the value of the concordance threshold is 0.7 or 0.8, the taskforce may decide to conduct a further investigation concerning the supposed preference for Supplier 2 over Supplier 5. However, it seems obvious to recommend to management Supplier 2 and Supplier 4. An ultimate decision on which supplier to choose should then be based on additional information and/or criteria.
Outranking models employ quasicompensatory decision rules
Outranking models are partially compensatory as a low score on one criterion can be compensated by a high score on another criterion. However, just as in the linear assignment model, the extent to which one supplier scores better than another supplier is not reflected proportionally in the overall concordance index which is contrary to the fully compensatory linear weighting models. In such linear weighting models, the overall score equals the weighted sum of the suppliers scores. Hence, the value of the overall score varies proportionally with the separate scores on the criteria. This is not the case in outranking models as only the criteriaweights and not the criteriascores as such are used in the calculation of the overall score. In addition, the outranking of supplier b by supplier a can be explicitly refused if supplier a performs extremely poor on one or more criteria compared to supplier b, irrespective of as higher scores on the other criteria. It also makes the Outranking model insensitive to possible (severe) misjudgements made when evaluating suppliers. Summarised, the family of outranking models offers a flexible tool for supporting a variety of supplier selection situations, both in terms of the imprecision present and the decision rules required. Outranking models seem appropriate for both sorting (relatively) large sets of suppliers based on tentative, rough information as well as ranking the remaining suppliers based on more specific information. However, as outranking models require the evaluation of all pairs of suppliers on all criteria, the use of specific software is necessary in case of a large, initial set of suppliers.
Furthermore, application of more sophisticated models like ELECTRE III will require training to purchasers not familiar with the concept of preference, indifference and vetothresholds.
Other decision models specifically accommodate such aspects like group decision making and imprecision
In this subsection, we discuss several other decision models that cover some of the properties less prominent in the available decision models in the purchasing literature. We successively discuss Topsis and the Distance from target method (Hwang and Yoon 1981), BordaKendall and CookSieford models (Massam 1980), GroupSMART (Lootsma 1996), STEM (Vincke 1986) and Fuzzy Sets (Chen and Hwang 1991). Topsis and Distance from Target (DFT) both assume some kind of ideal supplier profile to be present. BordaKendall (BK), CookSieford (CS) and GroupSmart deal with situations where there is a group of purchasers involved rather than one single decision maker. Finally, STEM is a socalled interactive method. It is based on the idea that the decision maker develops his preference structure while analysing different alternatives rather than specifying a fixed set of criteria weights in advance.
An intuitive explanation of Topsis
An approach that can be used to decide on one of the efficient alternatives is Technique for ordered preference by similarity to ideal solution (TOPSIS, see Hwang and Yoon, 1981). In this approach the decision maker identifies an ideal hypothetical benchmark alternative. The criteria scores are standardised so that the distance between each efficient alternative and the benchmark alternative can be used to classify the efficient alternatives. The alternative that is chosen should have the shortest distance from the ideal alternative and the largest distance from the negative ideal alternative.
A formal procedure for Topsis
The TOPSIS approach proceeds through six steps. The description is based on Hwang and Yoon (1981):
1. Determine the normalised decision matrix (i.e. the matrix with suppliers scores on the various criteria. Let xij be the numerical score of alternative i on criterion j. The corresponding normalised value rij is defined:
EMBED Equation.2
2. Determine the weighted normalised decision matrix. The weighted normalised value vij is defined as follows:
EMBED Equation.2
where wij is the weight attached to criterion j.
3. Determine the ideal and negative ideal alternative. The ideal alternative and the negative ideal alternative, denoted as A* and A respectively, are defined as:
EMBED Equation.2
EMBED Equation.2
where J and J are benefit and cost criteria respectively.
Step 4. In this step the distance si+ between alternative i and A* is determined, as well as the distance si between alternative i and A . In TOPSIS, the ndimensional Euclidean distance is used to calculate these distances, hence
EMBED Equation.2
and
EMBED Equation.2
5. Calculate the relative distance ci* to the ideal alternative, defined as:
EMBED Equation.2
Rank the preference order.
An example of Topsis applied to supplier selection
Applying the first step to the raw scores results in the matrix shown in table 6.11.
Supplier 1Supplier 2Supplier 3Supplier 4Supplier 5Turnover
Distance
Costlevel
quality image0
0.7
0.26
0.320.29
0.33
0.51
0.650.29
0
0.36
0.490.87
0.57
0
0.490.29
0.29
0.73
0Table 6.11: Normalised decision matrix for our example
Executing the next step, we obtain the weighted normalised decision matrix as shown in table 6.12.
Supplier 1Supplier 2Supplier 3Supplier 4Supplier 5Turnover
Distance
Costlevel
quality image0
0.105
0.078
0.1120.058
0.050
0.153
0.2280.058
0
0.108
0.1720.174
0.086
0
0.1720.058
0.044
0.219
0Table 6.12: Weighted normalised decision matrix for our example
In our example A* = {0.174, 0.105, 0.219, 0.228} and A = {0, 0, 0, 0}.
The results of calculating si* and si for the suppliers in our example are given in table 6.13.
Supplier 1Supplier 2Supplier 3Supplier 4Supplier 5si*
si0.2518
0.17200.1449
0.28480.2211
0.21100.2267
0.25870.2629
0.2309Table 6.13: Shortest and longest distances
The results of calculating ci* for the suppliers in our example are: c1* = 0.4059, c2* = 0.6628, c3* = 0.50, c4* = 0.5330 and c5* = 0.4676. From the results of the previous step it follows that supplier 2 would be chosen.
Topsis has intuitive appeal but requires many calculations
Similar to some of the models discussed previously (e.g. the maximin model), Topsis requires quantitative, normalised supplier scores. Contrary to the models from the previous subsection however, Topsis employs a compensatory aggregation of the scores on the various criteria. In that respect, the outcome of a Topsismodel is more sensitive to exceptionally high/low scores. The basic logic of the Topsis model is intuitively appealing: the model identifies the supplier that is closest to the best (virtual) supplier and furthest away from the worst (virtual) supplier. Compared to many of the other models, Topsis requires many calculations. However, these calculations can be easily automated using a simple spreadsheet.
An intuitive explanation of the Distance from Target (DFT) model
Another graphicallyoriented approach is the Distance from Target (DFT) model (Chen and Hwang, 1991). In this model, it is assumed that the decision maker has in mind a set of target levels of the scores on the criteria. That is to say a higher score on a particular criterion does not necessarily imply a higher utility in the perception of the decision maker.
A formal notation of the DFT model
In formal notation, based on Chen and Hwang (1991), an alternative A* is chosen with the shortest distance
where xij is the score of alternative i on criterion j, tj is the target level for criterion j and wj is the normalised weight of the jth attribute.
An example of the DFT applied to supplier selection
Assume that the decision maker in our example has specified the following target levels:
tturnover = 30;
tdistance = 40;
tcostlevel = 60;
tquality = 70.
For the weights we use the data from table 6.7. We can now calculate the distances of the suppliers to the target levels: d1=32.14, d2=18.99, d3=16.75, d4=18.30 and d5=46.87. In this case, we would thus choose supplier 3.
The DFT model involves the definition of an ideal supplier profile
In many aspects, the DFT model resembles the Topsis model. The DFT model also requires the presence of quantitative normalised supplier scores and also employs a compensatory aggregation of scores. The main difference is that this time the ideal supplier profile is not constructed from the maximum scores of the suppliers under evaluation (as in Topsis) but this profile is specified by the purchaser himself. Again, similar to Topsis, the calculations can be easily automated by using a spreadsheet program. The purchaser would only have to provide the suppliersscores and the ideal profile.
An intuitive explanation of the BordaKendall model
In this method for group decision making, each decision maker orders the alternatives from most preferred to least preferred. Next, each alternative is awarded a rank by each decision maker in such a way that the most preferred alternative's rank is the highest and the least preferred alternative the lowest rank. Finally, for each alternative the ranks are summed and the consensus ranking is derived accordingly.
An example of the BordaKendall model applied to supplier selection
An example of this method is given below. Suppose, 10 members of a buying committee express their individual preferences for 5 suppliers as follows: depending on a suppliers rank, a number of points is assigned: 5 points for the first rank, 4 points for the second rank, etceteras.
D1D2D3D4D5D6D7D8D9D10S1
S2
S3
S4
S55
2
3
1
42
3
5
1
4
3
4
1
2
55
2
4
1
34
1
2
5
35
2
3
4
12
5
1
3
45
3
2
4
13
5
1
2
43
2
4
5
1
Table 6.14: D1  D10: team members, S1  S5: suppliers; 1,2,..,5 ordered preferences
Next, for each supplier the total number of points is calculated. The results are shown in table 6.15.
SupplierTotal pointsSupplier 15+2+3+5+4+5+2+5+3+3=37Supplier 229Supplier 326Supplier 428Supplier 530Table 6.15: Results of BordaKendall model
According to the BordaKendall model, supplier 1 would be chosen.
The BordaKendall model is easy to use but only supports the final aggregation of several purchasers preferences
Clearly, the BordaKendall is an easy model in terms of procedures and calculations. It simply requires each team member to rank order the suppliers. It is not necessary to normalise any supplier scores. However, the BordaKendall model does not support these individual rankings. This is left to the individual team member. For these individual ranking many of the models discussed earlier in this chapter might be used.
Also, in the BKmodel the decision makers are assumed to be equally important. Therefore, when using this model, care must be taken when appointing decision makers.
An intuitive explanation of the Cook & Sieford model
This model measures the distance from a certain alternative (which has been evaluated differently by various decision makers) to an (imaginary) alternative that is considered the best by all decision makers. Similarly, the model measures the distance from the alternative to another imaginary alternative that is unanimously considered second best, and so on. Subsequently, it can be determined which supplier is closest to the imaginary supplier unanimously ranked first. This is then the most preferred supplier.
An example of the Cook and Sieford model applied to supplier selection
Again, suppose that ten members of a buying team express their preferences for 5 suppliers as follows:
D1D2D3D4D5D6D7D8D9D10S1
S2
S3
S4
S51
4
3
5
24
3
1
5
2
3
2
5
4
11
4
2
5
32
5
4
1
31
4
3
2
54
1
5
3
21
3
4
2
53
1
5
4
23
4
2
1
5
Table 6.16: D1  D10: team members, S1  S5: suppliers; 1,2,..,5 ordered preferences, 1 is best.
For each supplier the 'distance' is calculated between the actual scores of that supplier and five 'imaginary' suppliers having 10 equal scores of 1, 2, 3, 4 and 5 respectively. These calculations result in the following table:
Rank 1rank 2rank 3rank 4rank 5S1
S2
S3
S4
S513
21
24
22
2011
15
16
16
1211
11
12
14
12
17
11
12
14
1627
19
16
18
20Table 6.17: Distance between actual and imaginary suppliers
For example, the distance between S1 and rank 1(d1) is calculated as follows:
d1 = 11 + 41 + 31 + ... + 31 = 13
and for example, the calculation of d5 :
d5 = 25 + 25 + 15 +...+ 55 = 20
Table 6.17 can now be used to find an ordering which gives the smallest total distance. This might be done as follows. First, we pick the supplier closest to a perfect rank 1. This supplier cannot be chosen again in the sequel of the procedure. Next, we pick the supplier closest to a perfect rank 2 and so on. In this case, the ordering of S1, S5, S2, S3, S4 is the final ordering of the suppliers from most to least preferred. However, there may be alternative orderings which give the same total distance.
The Cook and Sieford model provides a richer result than the BordaKendall model
Compared to the BordaKendall model, the Cook and Sieford model requires somewhat more computational effort, but again, these calculations can be easily automated. The Cook and Sieford model provides a richer picture of how the suppliers perform: it shows the distance of a supplier to all ranks while the BordaKendall model only produces one ranking. However, in most purchasing situations the number one rank will be considered most interesting. A complete ranking is usually not necessary. Still, the richer picture may be helpful in case of a tie between suppliers. Still, the Cook and Sieford model does not support the individual ranking of the suppliers. Again, this is left to the individual buying team member. Finally, also the CSmodel assumes that all decision makers are equally important.
An intuitive explanation of a GroupSMART model
The basic idea behind this model is to extend the original SMARTmodel (which is a basic linear weighting model, see Von Winterfeldt and Edwards, 1985) to a multiple decision maker setting. In this model first (as in the single decision maker version) weights are assigned to the criteria. Next, each decision maker directly rates each supplier on each criterion. The final, overall rating of each supplier is arrived at through aggregating the weighted ratings of the decision makers for that suppliers. To express the differences in power between the decision makers, each decision maker is assigned an additional weight factor. Obviously, the higher this weight factor, the higher the power of that decision maker. These powerweights are also included in the calculation of the final, overall rating of a supplier.
A formal notation of a GroupSMART model
Based on Lootsma (1996) a GroupSMART model can be defined as follows:
EMBED Equation.3
where:
sj = overall score of supplier j
ci = normalised weight of criterion i, i=1,..,m
pd = normalised relative power weight for decision maker d, d = 1,..,g
gijd = grade on criterion i assigned to supplier j by decision maker d
We note that Lootsma also shows how the groupaggregation can be applied to a (multiplicative) AHP model (see Lootsma, 1996). The basic difference is that supplier scores are derived by pairwise comparisons instead of direct rating as in the SMART model.
An example of the Group SMART model applied to supplier selection
Suppose two purchasers (purchaser 1 and purchaser 2) rate three suppliers (supplier 1, supplier 2 and supplier 3) as shown in the table below.
Purchaser 1, p1 = 0.5Purchaser 2, p2 = 0.5criterionPrice QualityDeliveryPriceQualityDeliveryWeight0.50.30.20.50.30.2Supplier 1866766Supplier 2777775Supplier 3668678Table 6.18: ratings given by two purchasers
Application of the Group Smart model, leads to the following overall scores of the suppliers:
S1 = (0.5*0.5*8) + (0.5*0.5*7) + (0.5*0.3*6) + (0.5*0.3*6) + (0.5*0.2*6) + (0.5*0.2*6) = 6.75
S2 = 6.8
S3 = 6.55
Supplier 2 receives the highest overall scores although the difference with the other suppliers is very small.
The GroupSMART does also facilitate the individual ranking of the suppliers
The main difference between this model and the BordalKendall and CookSieford model is that it also supports the purchasers individually in rating the suppliers.
However, in purchasing situations involving crossfunctional team decision making, it may not always be straightforward to achieve agreement on the criteria weights as is assumed in the model.
An intuitive explanation of STEM
As an interactive method, STEM consists of alternating computation steps and dialogue with the decision maker. The first computation step provides a first solution which is presented to the decision maker. This first (compromise) solution consists of an alternative that has (relatively) high scores on all criteria, making it a good allround alternative. The decision maker may already at this point decide to choose this alternative. However, he may also respond by giving extra information about his preferences, especially with regard to the criterion on which he would accept a lower score in order to find an alternative that performs better on at least one other criterion. Using this information, the model provides the decision maker with a new solution. In this way, the procedure continues (Vincke, 1986).
A formal procedure for STEM
Based on Vincke (1989) the general procedure for STEM can be defined as follows:
We define A as the set of alternatives and cj(a) as the score of alternative a on criterion j.
We denote ZA as the image of A in the criteria space. An element z of ZA will be called a compromise solution, i.e. z = (z1,..., zn) = (c1(a),..., cn(a)). Now determine the payoff matrix, i.e. the matrix that contains the numerical values representing the scores of the alternatives on the criteria and calculate the normalisation coefficients (j:
EMBED Equation.3
Let ZA1 = ZA.
1. Determine a compromise solution zh by solving the following problem:
EMBED Equation.3
and where zj** = zj* + (j, with (j and (j are sufficiently small positive values.
2. Present zh to the decision maker.
If the decision maker is satisfied with zh, the procedure ends. If the decision maker is not satisfied with the compromise solution, ask him to indicate on which criterion k he agrees to make a concession and which maximum amount (k he is prepared to sacrifice on that criterion.
3. The set of possible alternatives is reduced.
Define
EMBED Equation.3
and let (k = 0, h = h+1 and go to step 1.
An example of STEM applied to supplier selection
Let us now proceed through these steps using the data from our example.
Step 0.
From table 6.5 we calculate the normalisation coefficients:
(1 = (1000)/100 = 1
Similarly, (2, (3 and (4 are calculated, resulting in (2 = (3 = (4 =1. Hence, (1 = (2 = (3 = (4 = 0.25.
Step 1.
The problem that has to be solved becomes:
MIN (  z1  z2  z3  z4
subject to:
( ( 0.25(101  z1)
( ( 0.25(101  z2)
( ( 0.25(101  z3)
( ( 0.25(101  z4)
and z ( ZA1 .
It should be noted that (j = (j = 1. The problem can be solved by filling in the set of restrictions for each supplier. In this way, we obtain the minimal possible value of ( for each supplier. Subsequently, the value of the goalfunction can be computed for each supplier, e.g. for supplier 1 we have the following set of restrictions:
( ( 0.25(101  0)
( ( 0.25(101  100)
( ( 0.25(101  36)
( ( 0.25(101  50)
This implies that for supplier 1, ( should be at least 25,25. The goalfunction then becomes 25,25  186 =  160,75. In this way we can calculate the value of the goalfunction for the other suppliers. The results are presented in table 6.18.
Supplier 1Supplier 2Supplier 3Supplier 4Supplier 5minimal (25,251725,2525,2525,25value goalfunction160.75234129.75231,75150.75Table 6.18: Results of step 1 in our example
We thus find that supplier 2 minimises the goalfunction and becomes the compromise solution. This makes sense: the minimisation problem finds a supplier that has relatively high scores on all criteria, which is clearly the case in supplier 2.
Step 2.
Suppose that the decision maker is not satisfied with the result (yet) and that he/she is prepared to make a concession (costlevel = 10.
Step 3.
We determine the new set of potential suppliers, ZA2, with (costlevel = 10:
EMBED Equation.3
Apparently, there is no supplier that satisfies these restrictions. However, suppose (for the sake of illustration) that this decision maker chooses (costlevel = 71. In addition, we further relax the problem by removing the condition zj ( zj1. This leads to ZA2 = ZA1. (3 is set to zero and we return to step 1.
Step 1. (revisited)
For supplier 1, 2, 4 and 5, the set of restrictions and therefore the value of the goalfunction remains unchanged. However, because (3 is set to zero, the set of restrictions for supplier 4 becomes:
( ( 0.25(101  100) = 0.25
( ( 0.25(101  82) = 4,75
( ( 0(101  0) = 0
( ( 0.25(101  75) = 6.5
Because ( ( 6.5, the value of the goalfunction for supplier 3 becomes 6.5  257 =  250,5. This means that now supplier 4 would become the compromise solution because this value is lower than  234. However, we stress once again that without relaxing the restrictions, supplier 2 would have been chosen without any further sequences of the procedure.
STEM does not a priori require a complete preference structure
A major difference between STEM and basically all other decision models discussed so far is that STEM offers a dynamic structure to the purchaser for finding out which tradeoffs are acceptable and which are not. STEM, just as the maximin and the Outranking models, is relatively insensitive to exceptionally high or low scores. The STEM procedure seeks to find a supplier that scores well on all criteria. However, it is clear that the procedure requires some form of computer support in order to be practical, especially in case of a large group of suppliers. In case of only a few (2 or 3) suppliers, the STEM procedure does not seem to add much to the immediate overview of the suppliers one has without a decision model. Thus, given adequate computer support, the STEM model seems most useful in identifying and analysing tradeoffs and making a final choice within a fairly large set of efficient suppliers that result from for example a cluster analysis or DEA application. Finally, it is clear that STEM only facilitates quantitative information.
An intuitive explanation of Bonissones fuzzy set model
The term `fuzzy sets` refers to a complete scientific field of its own. It is not a method but rather an approach, based on what usually is referred to as possibility theory. Fuzzy set theory offers a mathematically precise way of modelling vague, imprecise phenomena. In the context of decision making fuzzy set theory may prove to be useful in dealing with what we defined as imprecision (see Chapter III), e.g. imprecise goals, imprecise criteria and imprecise scores of alternatives on these criteria. This then makes fuzzy sets theory also potentially relevant for purchasing decision making. Although fuzzy set theory is a relatively young field in science, the results of a rough scan of relevant literature (Ribeiro, 1996; Carlsson and Fuller, 1996) clearly indicate that over the past ten to twenty years, many fuzzy decision models have been developed, for single as well as multi criteria problems. An excellent overview and discussion of fuzzy multiple criteria decision models can be found in the work of Chen and Hwang (1991). Based on their work, we now use Bonissones method for illustrating the basic idea behind fuzzy sets and its potential in supplier selection. It should be noted however, that this is but one out of many other possible approaches. Bonissones method is chosen because of its simplicity. Alternatives are evaluated in terms of qualitative statements like bad, moderate to excellent. Criteria are also evaluated in terms of qualitative statements, e.g. unimportant, important and very important. Each of these linguistic statements is assigned to a fuzzy number (simply stated: a range of numbers of more or less the same magnitude). Finally, for each supplier the weighted fuzzy total score is calculated.
A formal notation of Bonissones fuzzy model
First, we briefly introduce some necessary formal concepts from fuzzy set theory. Chen and Hwang (1991) define a fuzzy set as follows: Let U be a set of objects, whose generic elements are denoted by x, i.e. U = {x}. A fuzzy set A in U is characterised by a membership function (A(x) which associates with each element in U a real number in the interval [0,1]. The fuzzy set A can then be denoted as A = {(x, (A(x)), x ( U}. For example, the fuzzy set moderately performing suppliers for part Y may be defined by a purchaser as: A = {(supplier A, 0.3), (supplier B, 0.8), (supplier C, 0.6)}. These suppliers may also be member of the fuzzy set suppliers with outstanding performance or the fuzzy set badly performing suppliers. The essence of the fuzzy set approach is the recognition of simultaneous membership of several classes, be it to some degree. This degree is expressed in the membership function. In Bonissones method, U is an infinite set and the membership function is described in terms of four parameters a, b, (, (. This type of fuzzy set can graphically be displayed as a trapezium (see figure 6.6).
Figure 6.7: fuzzy set representation in Bonissones method
Bonissones method proceeds as follows. Let M = (a, b, (, () and N = (c, d, (, (). The arithmetic operations are now defined as follows:
M + N = (a+b, b+d, (+(, (+();
M  N = (ab, bc, (+(, (+();
M * N = (ac, bd, a(+c(((, b(+d(+(();
Using these (approximated) algebraic operations, Bonissone defines the fuzzy utility Ui of an alternative Ai
Ui = EMBED Equation.3
where wj and rij may be crisp or fuzzy numbers represented in the trapezoidal format.
An example of Bonissones fuzzy set model applied to supplier selection
We now turn again to our example. Suppose we feel unable to express the performance of the suppliers with respect to the criteria in exact point estimates. However, we feel that it is possible to attach linguistic appreciations to the suppliers for each criterion. Table 6.19 shows a possible set of such qualitative appreciations.
CriteriaImportanceSupplier 1Supplier 2Supplier 3Supplier 4Supplier 5Turnover
Distance
Costlevel
Quality imageimportant
rather unimportant
very important
very importantmoderate
excellent
moderate
moderategood
moderate
good
excellentgood
bad
moderate
goodexcellent
good
bad
goodgood
moderate
excellent
badTable 6.19: Evaluation of suppliers in linguistic terms
Furthermore, suppose that we define these linguistic appreciations as fuzzy trapezoidal sets as shown in table 6.20 below.
Linguistic appreciationcorresponding fuzzy trapezoidal numberExcellent
Good
Moderate
Bad
very important
important
rather unimportant(0.8, 0.8, 0.2, 0.2)
(0.6, 0.6, 0.2, 0.2)
(0.4, 0.4, 0.2, 0.2)
(0.1, 0.1, 0.1, 0.3)
(1, 1, 0.2, 0)
(0.5, 0.5, 0.2, 0.3)
(0.2, 0.2, 0.2, 0.2)Table 6.20: Definition of fuzzy numbers in our example
The fuzzy utility Ui of each supplier can now be computed. For example, for supplier 1 we obtain the following result:
Usupplier 1 = (0.4*0.5, 4*0.5, 0.4*0.2 + 0.5*0.2  0.2*0.2, 0.4*0.3 + 0.5*0.2 + 0.2*0.3) +
(0.8*0.2, 0.8*0.2, 0.8*0.2 + 0.2*0.2  0.2*0.2, 0.8*0.2 + 0.2*0.2 + 0.2*0.2) +(0.4*0.1, 0.4*0.1, 0.4*0.2 + 1*0.2  0.2*0.2, 0.4*0 + 1*0.2 + 0) +(0.4*1, 0.4*1, 0.4*0.2 + 1*0.2  0.2*0.2, 0.4*0 + 1*0.2 + 0)
=(1.16, 1.16, 0.78, 0.83)
In the same way, the fuzzy utilities for the other supplies can be computed.
The results are presented in table 6.21.
SupplierFuzzy Utilitysupplier 1
supplier 2
supplier 3
supplier 4
supplier 5(1.16, 1.16, 0.78, 0.83)
(1.78, 1.78, 0.96, 0.90)
(1.32, 1.32, 0.60, 0.88)
(1.22, 1.22, 0.78, 1.06)
(1.28, 1.28, 0.68, 1.00)Table 6.21: Fuzzy utilities of suppliers in our example
The results obtained with Bonissones method can also be displayed graphically. This is done in figure 6.8.
Figure 6.8: Graphical representation of results with Bonissones method
In this case, it seems obvious that supplier 2 would be chosen.
Fuzzy Sets models are especially useful in dealing with imprecision
The application of Bonissones method in our example can be seen as formalising the wellknown categorical method (see also chapter V). We would argue that such a fuzzy categorical method is a means for making the purchasers knowledge and experience more explicit, rather than some kind of wonderformula that produces precision out of fuzziness. Besides, the final choice in Bonissones model may not always be as obvious as in our example. Compared to crisp linear weighting models, Bonissones model seems less sensitive to extreme misjudgements and/or measuring errors concerning the supplier performance.
There exist many methods for transforming fuzzy outcomes (such as the outcomes in our example) into a final, crisp number (see also Chen and Hwang, 1991). For the sake of simplicity we will not treat such methods here. In general, Fuzzy Sets theory offers a formal language that can be used to systematically deal with imprecision. In our example, we used Fuzzy Sets in a compensatory model. However, Chen and Hwang (1991) also discuss fuzzy versions of noncompensatory decision models. Thus, the use of fuzzy models is not restricted as far as the type of decision rule and criteria is concerned. The computational effort however might outweigh the advantages, especially in lowimportance situations.
OR offers many useful, complementary decision models for supplier selection
In Chapter V we found that the existing purchasing literature on decision models for supplier selection lacked the required degree of differentiation.
First, decision models for supporting the phase of problem definition in supplier selection were hardly present in the purchasing literature. The literature primarily focuses on the choice phase in supplier selection.
Secondly, the choice models for supplier selection in the purchasing literature typically assume the presence of just one decision maker and quantitative, normalised supplier scores.
Finally, the majority of these models employ compensatory decision rules when aggregating the scores on the various criteria.
The study described in this chapter reveals that Operations Research offers many models and methods (which have so far not been applied in purchasing) that might provide the properties the existing decision models lack. This is illustrated in table 6.22 and table 6.23.
Choice phase Phase of problem definitionOne decision makerCostratio, Categorical, Linear Weighting, Weighted product, AHP, Mathematical Programming, Decision Analysis, DEA, Cluster Analysis, Neural Networks
STEM, Maximin, Linear Assignment, Outranking, Conjunctive/Disjunctive, Topsis, Lexicographic, Fuzzy SetsWeighted product, AHP, ISM
Rough Sets, Cognitive Mapping, Strategic Choice, WWSanalysis, Influence Diagrams, Strategy Generation Table, Framework for Formulation of Alternatives, Value Focused ThinkingGroup decision makingLinear Weighting (Thompson)
BorddaKendall, Cook and Sieford, GroupSMART
Table 6.22: Assessment of existing and newly identified decision models for supplier selection
In table 6.22, the existing decision models for supplier selection (described in chapter V) are shown in italic characters, while the decision models found in this chapter are indicated in bold characters. It is clear that together the existing models and the decision models identified in this chapter have a larger coverage.
Compensatory NoncompensatoryOne dimensionalLinear Weighting, Mathematical Programming, DEA, Weighted product
STEM, SMART, Topsis, Fuzzy SetsLinear Weighting (Willets)
Maximin, Maximax, Fuzzy SetsMultidimensionalCategorical, Linear Weighting (Thompson), AHP
Multiplicative AHP, Fuzzy Sets
Categorical
Linear Assignment, Outranking models, Conjunctive/disjunctive, Lexicographic
Table 6.23: Assessment of existing and newly identified decision models for supplier selection
Similarly, also regarding the dimensionality and the type of decision rule, the newly identified decision models constitute a useful supplementation (see table 6.23).
Summary
In chapter VI we presented the results of an extensive investigation of the (Operations Research) literature regarding possibly useful decision models for supplier selection. Summarised we concluded that OR offers many useful decision models for supplier selection that so far however have not been used for this.
First of all, we found that there are various decision models available for supporting problem definition in supplier selection. Such decision models can be used to investigate the need for supplier selection, generate possible alternatives or aid in generating and evaluating supplier selection criteria.
In addition, we found various decision models for the choice phase in supplier selection which cover the features that were not present in the available decision models for supplier selection (which we mapped in chapter V). Among these features are noncompensatory decision rules, group decision making and handling imprecise data.
All in all, we concluded that OR offers many useful, complementary decision models for supplier selection.
See on the Internet: http://www.cs.uregina.ca/~roughset/
For an elaborate discussion on normalisation methods we refer to the previous chapter.
In case of qualitative criteria, the latter definition is clearly not appropriate. Instead, for each criterion j, a discordance set Dj made of ordered pairs (xj, yj) is defined such that if gj(a) = xj and gj(b) = yj then the outranking of b by a is refused.
Chapter VI: Operations Research offers many useful decision models for supplier selection
PAGE
PAGE 155
increasing downstream competition
increasing need for costcutting
new future product launches
additional supply demands
increasing dependency on suppliers
review of selection criteria
review of list of approved suppliers
higher performance demands on suppliers
fewer, bigger suppliers
trend towards concentration on the supplier market
ever increasing speed of technological developments
d3
d2
d1
c2
c1
b2
b1
c2
c1
b2
b1
a3
a2
a1
d3: partly training, partly replacing buyers
d2: replace all senior buyers
d1: invest in training of current purchasing workforce
c2: outsource on systemlevel
c1: start up ESIproject
b2: shift to singlesourcing
b1: limited downsizing of supplier base
a3: turn to makeandbuy
a2: search for additional suppliers; close contracts for 12 years
a1: increase volume with current supplier
o
o
?
o
o
ok
o
o
?
o
o
o
o
o
o
ok
o
o
x
x
o
o
o
x
o
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ok
x
o
ok
x
o
x
o
o
How might we reduce the cost of nonavailability?
How might we reduce the risk of nondelivery?
How might we find an additional supplier for bottleneck item X?
How might we simplify and standardise our assembly process?
How might we arrive at a more general specification?
How might we ensure the reliability of our suppliers leadtime?
How might we improve our suppliers willingness to cooperate?
How might we allocate
the supply risk to several parties?
Sales figures?
Switch to other technology, yes/no?
Switch to other supplier yes/no?
general purchasing strategy
actual supplier(s) chosen
Available audited suppliers
GOAL: Drastic reduction of administrative costs in the purchasing of stationary and printed matters
Introduction of SAPsystem (0.2)
Downsizing of purchasing dept. (0.6)
Merger with other company (0.2)
EXOGENEOUS DECISION FACTORS:
OWN POTENTIAL ACTIONS:
Drastic reduction of range of items; no. of suppliers down to 3
Restricted catalogue of items; one supplier for stationary
Complete outsourcing of stationary and printed matters purchasing (also closing down of warehouse)
OWN OBJECTIVES:
Quick results (0.2)
Easy implementation (0.5)
Significant savings (0.3)
COMPETITORS POTENTIAL ACTIONS:
Obstructive attitude (fear of getting the administrative burden)
Legal action in case of layoffs.
Demands full participation in whatever project is initiated
Controller (0.3)
Personnel responsible for inventory (0.3)
Internal customers (0.4)
COMPETITORS:
2 (
( 5
( 4
( 3
( 1
( 3
( 5
2 (
( 1
( 4
a (
( b
supplier 2
1
0
2.5
2.0
1.5
(
(
b
a
1
((x)
x
Functional requirements of purchasing decision models
1.0
0.5
EMBED Equation.3
New version yes/no?
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3
((x)
x
Evaluation of the toolbox (X). Conclusions (XI)
Empirical testing of the toolbox (VIII + IX)
Designing a toolbox for supporting supplier selection (VII)
Evaluation of OR and System Analysis models (VI)
Evaluation of available purchasing decision models (V)
Analysing purchasing literature with this framework (IV)
Development of a framework for analysing decision making (III)
Functional requirements of purchasing decision models
Increased price competition
Increased time to market competition
Need to speed up design activities
Switch to other technologies?
Outsourcing?
Hire additional staff
EMBED Equation.3
EMBED Equation.3
EMBED Equation.3
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