Multikriteria Supplier Selection

8/3/2019 Multikriteria Supplier Selection

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A Multiple Criteria Approach to Strategic Supplier Selection

Mohammad Reza AKBARI JOKAR

Yannick FREINLionel DUPONT

Laboratoire GILCO, Institut National Polytechnique de Grenoble

[email protected]

[email protected]

[email protected]

Abstract:

This paper presents some necessary elements for a multiple criteria approach to the

Strategic Supplier Selection (SSS). This approach has to consider the firm strategy, subjectiveand objective criteria, group decision making, supplier probabilistic behavior and supplier and

buyer constraints. In this paper we analyze these necessary elements for a global approach and

develop a two level approach that selects suppliers by considering these characteristics. In the

first level this approach selects the strategic suppliers. In the second level a mathematical

model propose the final solution by considering the objective and subjective criteria.

Keywords: Supplier selection, business strategy, supply chain management.

Introduction

For many firms, the purchasing cost is the most important cost of products. For example, inhigh-tech firms it accounts for up to 80% of total product costs (Burton, 1988). It shows the

importance of purchasing decisions. The supplier selection is probably the most important

purchasing decision (Nydick, 1992; Mobolurin, 1995). It is undoubtedly one of the decisions

that determine long-term viability of the firm (Thompson, 1990).

The Strategic Supplier Selection (SSS) has two different aspects. The first aspect is to

select the number of suppliers. Considering the firm and market characteristics, the business

strategy of the firm can encourage or discourage a large number of suppliers. For example, in

a "Just in time" environment most firms prefer to pursue the strategy of mono supplier or a

small number of suppliers (Ansari, 1986). Today we are in a co-operative logistics period"

(Akbari et al., 2000-a; Akbari et al., 2000-b) in which the firm seeks a high level of co-operation with its important suppliers. Such co-operation requires a small number of suppliers

because co-operation with a large number of suppliers is more difficult than with a few.

Quayle (Quayle, 1998) shows the important factors in mono and multi supplier selection.

The second aspect of SSS is the selection of the best suppliers. In this paper we consider

this aspect of the supplier selection problem. Initially we will present the various supplier

selection criteria. Secondly we present different characteristics of supplier selection. Thirdly

the existing methods in the literature will be presented and analyzed. By considering the

current research gap, we make a contribution to the development of a multiple criteria

approach able to consider different SSS characteristics. A conclusion and some suggestions

for future research complete this paper.


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SSS criteria

Dickson's paper (Dickson, 66) is an interesting and seminal work. He proposes 23 criteria

taken from a case study carried out in 170 firms. Table 1 presents the result of his work, in

which the 23 criteria are ranked according to their weight. At that time (1966), the mostsignificant factors in supplier selection were "Quality", "Delivery ", "Performance History"

and "Warranties and Claim Policies ".

The 23 criteria proposed by Dickson cover the majority of the criteria presented in the

literature, but the importance of these criteria evolve according to the industrial context. For

example Weber (Weber, 1991) shows the extreme importance of supplier location in a "just in

time" environment. A vast study as well as Dicksons work is necessary to identify the

importance of supplier selection criteria in today's industrial environment. As two examples

of recent works, Ellram (Ellram, 1990) proposes 3 main criteria for supplier selection: 1)

financial, 2) organizational culture and strategy and 3) technology issue. For each main

criterion, he proposes several sub criteria. Barbarosoglu (Barbarosoglu, 1997) identifies the 3

following main criteria: 1) Performance, 2) business structure/manufacturing capability and 3)

the quality system. Like Ellram, he proposes some sub criteria for each main criterion.

Rank Criteria Mean rating Evaluation

1 Quality 3.508 Extreme Importance

2 Delivery 3.417

3 Performance history 2.998

4 Warranties and Claim policies 2.849

5 Production Facility and Capacity 2.775 Considerable Importance

6 Price 2.758

7 Technical Capacity 2.545

8 Financial Position 2.514

9 Procedural Compliance 2.488

10 Communication System 2.426

11 Reputation and Position in Industry 2.412

12 Desire for Business 2.256

13 Management and Organisation 2.216

14 Operating Controls 2.211

15 Repair Service 2.187 Average Importance

16 Attitude 2.120

17 Impression 2.054

18 Packaging Ability 2.009

19 Labor Relation Record 2.003

20 Geographical Location 1.872

21 Amount of Past Business 1.597

22 Training Aids 1.537

23 Reciprocal Arrangements 0.610 Slight Importance

Table 1: Decision criteria and their importance according to Dicksons work (Dickson, 1966)

SSS characteristics

The different characteristics of the supplier selection problem are classed as follows:


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Number of decision makers: Single Decision Maker - Group Decision Makers

A supplier selection procedure needs several actors (Mobolurin, 1995). Some decision-

making methods imply several decision-makers (a group) in the supplier selection procedure.

Nature of criteria: Objective (Easy or Difficult) - Subjective

An objective criterion is one, which can be measured, directly in quantitative terms (such

as dollar). An "easy" objective criterion can be measured directly. For example, criterion

"price" is an easy criterion. Finding an "easy" measure for an objective criterion is not always

possible. For example "quality" is a " difficult" criterion because it can't be measured directly:

it must reflect the remaking cost, reject cost, after sale service cost, etc. A subjective criterion

is a criterion that can't be measured quantitatively, for example, "desire expressed by supplier"

or "supplier prestige"(Hoshyar, 92).

Number of criteria: Single Criterion - Multi Criteria

Suppliers can be selected according to one or several criteria. In the multi criteria case,

criteria are often contradictory (such as quality and cost) and thus the best trade-off between

the criteria is sought.

Number of suppliers: Single Supplier - Multiple Suppliers

When the best suppliers cannot satisfy the entire buyer's demands, the latter must resort to

several suppliers. In a multi supplier problem, we are concerned with the following questions:which suppliers should be chosen? And what amount should each one supply? In certain

cases, in spite of the sufficient capacity of the best supplier, the firm prefers to have more than

one supplier (Quayle, 1998).

Aim: Supplier ranking - Supplier selection

In a "ranking" problem, we are concerned with generating a list of suppliers according to

their score. In a "selection" problem, the aim of SSS can be to select the best suppliers without

needing to know their relative score.

In addition, the parameters of an SSS can be deterministic or probabilistic. This means thatsupplier behavior can be expressed by a probability function. Moreover, in a SSS there can be

various constraints concerning the clients or suppliers such as limited capacity, minimum

order size, etc.

SSS Methods

The solution methods can be classed in 5 main categories:


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Elementary MCDM1 methods: Weight-oriented method (Wind, 68) - Categorical

method (Busch, 63)

Modern MCDM method: AHP (Narasimhan, 1983), etc.

In the weight - oriented method, one initially assigns a weight to each criterion according

to its importance relative to other criteria. Suppliers are then compared with respect to each

criterion. In the "categorical method", the weights of the criteria are identical and suppliers

are evaluated with respect to such criteria as Good (+), Neutral (0) or Unsatisfactory (-).

Based on these comparisons a total score is calculated for each supplier.

The Analytic Hierarchy Process (A.H.P.) (Saaty, 1980) is a modern MCDM method that

provides a framework to cope with the multiple criteria situation. There are other modern

MCDM methods such as ELECTRE series (Roy, 1993), etc., but the AHP method is more

utilized than other methods for supplier selection. The AHP first structures the problem in theform of a hierarchy to capture the criteria, sub criteria and the alternatives. All the criteria are

compared in a pairwise fashion to determine their relative weights. Then the alternatives are

compared in a pairwise fashion with regard to each criterion. In the end, the procedure

determines a final score for each alternative. For example, the following works utilize the

AHP in supplier selection. Hoshyar (Hoshyar, 1992) distinguished 3 types of criteria,

"critical" criteria (their presence or absence precludes the supplier from further consideration,

regardless of other conditions that might exist), "objective" criteria (that can be evaluated in

monetary terms) and subjective criteria (which are difficult to quantify). For subjective

criteria, he proposed the A.H.P method suggested for the first time for the supplier selection

problem by Narasimhan (Narasimhan, 1983). Another example for AHP based work is the

work of Korpela (Korpela, 1996) and Barbarosoglu (Barbarosoglu, 1997). They propose an

A.H.P based Decision Support System (DSS).

Cost Based Method

In this model all the costs corresponding to each supplier are calculated and the least

expensive supplier is selected (Timmerman, 1986). The firms which choose a " cost

leadership strategy" (Porter 1980) are interesting for application of this method. Moreover

Verma (Verma, 1998) shows that although company managers declare quality as the most

significant criterion, a significant number of firms select their suppliers' based on cost or

delivery conditions.

Elimination Method: Conjunctive (Crow, 1980) Lexicographic (Wright, 75)

In this method at each level, the suppliers who cannot satisfy supplier selection rule

conditions are eliminated. In a "Conjunctive rule", the suppliers whose score with respect to a

criterion is less than a minimum level will be eliminated. Therefore, one of the suppliers that

satisfies the minimum levels will be selected. In a "Lexicographic rule", suppliers are first

compared with respect to the most important criterion. If a supplier satisfies this criterion

1 Multi Criteria Decision Making


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much better than the other suppliers, then he will be selected. If not, the best suppliers are

compared with respect to the second most important criterion

Mathematical optimization methods: Single Objective (Moore, 73) - Multiple Objective

(Weber, 1993).

The purpose of a mathematical optimization method is to select several suppliers in order

to maximize an objective function subject to suppliers/buyer constraints. The objective

function can be "single" criterion (classical optimization models) or "multiple" criteria (Goal

Programming or Multi Objective Programming). Weber (Weber, 1991) shows that up to 1991

there were 10 papers which used mathematical programming for SSS. Ghodsypour

(Ghodsypour, 1998) presents 7 other papers which were published during 1991-1998. The

methods used were Linear programming, Non-linear programming, Mixed-integer

programming, Multi-objectives Programming. The objectives of the mathematical models

were: Minimization of the total cost, Minimization of the number of defective parts,Minimization of the number of late or early deliveries, or minimization of the distance (or

time) between supplier and buyer, etc. (Weber, 1993).

Scenario Methods: Payoff Matrix (Soukup, 1987) - VPA (Vendor profiles analysis)

(Ellram, 1990).

In the Payoff Matrix method, several scenarios for future supplier behavior are defined.

In each scenario a score is assigned to the suppliers. The selection is made according to the

mean and variance score of suppliers. VPA is a simulation-based decision support system.

For each criterion, a probabilistic function is associated with each supplier. Simulation can

help the decision-maker to estimate the future behavior of a supplier in different conditions.

The characteristics of a global approach

Table 2 shows the advantages and disadvantages of the current methods. Table 3

summarizes the method-characteristics analysis. This analysis shows that current methods

cannot cover the various characteristics of a real SSS. We need a method which can conform

to the characteristics that are often present in a SSS: rules conjunctive, aspect of multiple

decision makers, subjective and objective criteria, supplier and buyer constraints, multi

suppliers and probabilistic characteristic of SSS. Below we present these characteristics whichare essential in an SSS global approach.

Group decision making

The SSS is a problem which requires the intervention of various departments in the firm

(Production, transport, storage, purchase, etc) (Smytka, 1993). In addition, as the majority of

decision criteria are subjective, the consensus of a group of decision-makers with different

opinions prevents the predominance of only one opinion on the final decision. The group

decision making version of AHP (Golden, 1989) can be utilized for this aspect of SSS. This

version of AHP is not present in SSS literature. The members of this group must consider the

interests of all the departments in the firm, which is simplified by a discussion between them.


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Methods Important Advantages Important Disadvantages

Weight oriented

methods

Cost Based method

Elimination

Methods

Mathematical methods

Scenario Methods

Simple

Subjective and objective criteria

Inexpensive

Total supplier performance(considering all

the criteria)

Subjective or human judgment

Does not incorporate the supplier and buyer

constraints in the model

Enormous need for financial information.

Ignores the subjective criteria.Has not a subjective orhuman judgment

Ignores the subjective criteria

Does not find optimal solution

Can be difficult to understanding by manager

Rapid

Simple

Subjective and objective criteria

Inexpensive

Does not consider all the criteria in the final

selection.



Models the probabilistic behaviors of supplier

Multi criteria

Examination of different selections

The supplier and buyer constraints are

incorporated in the model

Does not find optimal solutionDifficult to analyze



Multiple objective

Single Objective Find optimal solutionThe supplier and buyer constraints are

incorporated in the model

.

Ignores the subjective criteria

Single criterion

Table 2: Advantages and disadvantages of the current methods

single criteria

Multi criteria

Single decision maker

multi. decision maker

Supplier selectionSupplier ranking

Objective criteria

Subjective criteria

Single supplier

Multi supplier

Without constraints

With constraints

Deterministic

Probabilistic

Weighted M. Categorical M. AHP Cost Ratio Elimination Single Obj. Prog. Multiple Obj. Prog. ScenarioCharacteristics

Methods

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Table 3: Method-Characteristics comparison

Firm strategies

The decision maker group must know the firms business strategies in as much detail as

possible. This knowledge enables him to adapt to the firm strategy in decision-making

procedure. Such adaptation is essential because this decision has a major influence on the

firms strategic objectives. The strategy determines the activities in which the firm will be

present and allocates resources to these activities (Strategor, 93). This definition identifies two

levels of strategy: 1) corporate strategy determining firm activities. This strategy leads the

firm to begin in one sector or to withdraw from another one, in order to constitute a balanced

business portfolio; 2) business strategy defining the operations which the firm must


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complete for each activity in order to find a favorable position in relation to its competitors

(Porter, 1980).

M. Porter (Porter, 1980) identified 3 basic types of business strategies: 1) cost leadership

strategy 2) differentiation strategy 3) focus strategy. The cost leadership strategy envisages

minimizing product cost. The second strategy aims to create a set of unique characteristics in

the product or in its related services. For example, an original design, an effective distributionnetwork, a fast after sale service, etc. The focus strategy proposes focusing on a specific

segment, for example a specific customer group, a specific range of products, etc. In this

strategy the firm can choose the cost leadership strategy (cost focus) or differentiation strategy

(focused differentiation) for the selected segment. The business strategy of a firm affect

extremely the supplier selection decision. For example a firm having a cost leadership

strategy must select least expensive suppliers. Such selection rule can be tragic for another

firm having a differentiation strategy.

If the firm strategy is not explicitly defined, the decision making group must draw up these

strategies in collaboration with firm management.

Minimal threshold of the criteria.

Failure to comply with the minimal threshold can have negative consequence on the

service or the other constraints or objectives of the firm. A Delphi method (Dalkey, 69) can

be used to fix a minimal threshold for each criterion. In any case, a sensitivity analysis on

these minimal thresholds is necessary to choose a pertinent threshold for each criterion. The

mathematical model developed in this paper offers the possibility of conducting this

sensitivity analysis.

Criteria weights and suppliers' score.

AHP (Saaty, 1980) is a method commonly used for different multi criteria problems(Golden, 1989). It incorporates judgment and personal values in a logical way. In the field of

supplier selection, various authors, such as Narasimhan (Narasimhan, 1983) and Hoshyar

(Hoshyar, 1992) justified the use of this method for SSS. AHP is based on the following three

principles: decomposition, comparative judgment, and synthesis of priorities. AHP starts by

decomposing a complex multi criteria problem into a hierarchy where each level consists of a

few manageable elements, which are then decomposed into another set of elements. The

second step uses a measurement methodology based mathematical consideration to establish

priorities among the elements within each level of the hierarchy. In the third step, through a

mathematical logic, AHP summarizes the judgments into an overall estimate of the relative

priorities of decision alternatives.

As we already showed, SSS requires the intervention of various actors. Therefore we

propose the group decision making version of AHP (Golden, 1989) to determine decision

criteria weight and suppliers' scores. According to Saaty (Saaty, 1980) AHP forms a

systematic framework for group interaction and group decision making. Dyer and Forman

(Dyer, 1992) describe the advantage of AHP in a group setting as follows: 1) both objective

and subjective criteria can be included in an AHP base group decision making. 2) With AHP

discussion in a group can be focused on the objective rather than on alternatives. 3) With AHP

the discussion can be structured so that every factor relevant to the decision is considered in

turn, 4) in a structured analysis, the discussion continues until all relevant information from

each member in the group has been considered and a consensus choice of the decision

alternatives is achieved.


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Analysis of the probabilistic behavior of suppliers

The behavior of a supplier with respect to decision criteria is probabilistic (Soukup, 1987;

Ellram, 1990). Therefore it is difficult to assign a fixed score to the supplier with respect to

the decision criteria. A correct choice requires analysis of the probabilistic behavior of the

suppliers. Simulation can help the decision-makers better understand supplier behavior. This

knowledge helps the decision-maker to assign the pertinent scores to suppliers in AHP

procedures. Moreover, simulation analysis results makes it possible to evaluate the final

choices. Although it is very hard to find the supplier behavior probability function, in the

absence of further data this can be accomplished easily by considering only optimistic,

pessimistic and most probable scenarios. For this, decision-makers can use a numerical scale,

for example from 1 to 10 where 1 is a very low score and 10 is a

probability function is suitable for situations in which you want to consider the probabilistic

behavior of a variable that can be prevented in 3 optimistic, most probable and pessimistic

points. For example, this type of function is widely used to determine time activity in project

management.

Constraints

In a SSS, there is different constraints that must be satisfied. For example, capacity

constraints, demand constraints, etc. On the other hand the combination of different feasible

solutions is very large. These characteristics show the importance of mathematical

optimization methods in a global approach.

Towards a global approach

According to this approach the decision making is made in two stages. With the first stage

we choose the " strategic suppliers " based on the company strategy. The company businessstrategy is the manner by which the company plans to challenge their competitors; therefore

the selected suppliers must be perfectly able to satisfy this strategy.

Alternatives

Pre-selected

Alternatives

mathematical

optimization

modelProposed Solution

strategic Supplier

selection

Company Business strategy

Minimal thresholds

Probability

theoryMultiple Criteria

Decision Making

Figure 1: Proposed approach to Strategic Supplier Selection problem

Another parameter that has to be considered on this level is the minimal thresholds of the

criteria. These are the minimal thresholds that the suppliers must be able to respect. Not torespect these thresholds can cause intolerable consequences on the service quality or other


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company objectives. The suppliers chosen with this stage can support the company strategy

on the one hand and on the other hand they can respect the minimal thresholds of various

criteria. An analysis of sensitivity on these minimal thresholds can help the decision-makers

to choose a suitable threshold for each criterion. In the second stage of this approach a

mathematical optimisation model select the best suppliers and the supplied quantity by

considering the suppliers and buyer constraints. The purpose of this model is to maximise theU function whose coefficients are the supplier scores. This total score can be calculated

based on the objective and subjective criteria by a MCDM method as AHP. In the rest of this

section this mathematical optimisation model is explained.

The mathematical optimization model

Below we explain the mathematical model to select the best suppliers and the order

quantity of each supplier in the second step of proposed approach. This type of mathematical

model is an essential element of any global approach to strategic supplier selection. The

objective function of this model is a utility function whose coefficients are the supplier scores.

This type of objective function is utilized by authors for different problems such as

Ghodsypour's work in supplier selection (Ghodsypour, 1998). As it is showed, the scores of

the suppliers (the coefficients of objective functions) can be calculated from the objective and

subjective criteria by a MCDM method as AHP method. Therefore, the mathematical model

maximizes the total utility of the supplier (all objective and subjective criteria) with respect to

supplier and buyer constraints.

Notation:

F: number of supplier

dp: demand of part p

upf: score of supplier f for part p

cpf min: : minimal order quantity from supplier f for part p

cpf max: maximal order quantity from supplier f for part p

dpf:percentage of late orders from supplier f for part p

dpf: out of delays cost of part p purchased from supplier f

qpf : defect percentage of supplier f for part p

qpf: quality cost of a defect unit of part p purchased from supplier f

ppf : purchasing cost (acquisition + transport +...) of supplier f per unit of part p

d: maximum accepted delays cost

q: maximum accepted quality cost

p: maximum accepted purchasing cost.

v: the total value of product

vp= the value of part p

n:number of suppliers to choose.

Variables:

Xpf: number of units of part p to be ordered from supplier f


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Ypf= 1 if supplier f is chosen for part p, 0 otherwise.

Model:

Max U = upfXpfSubject to:

Xpf= dp

dpfdpfXpf d

ppfppfXpf p

vp Xpf vYpf= np

Xpf 0

Ypf= 0 ou 1

p

p

p f

f

f

f

f=1

p

p, f

p, f

p (1)

c pfmin. Ypf Xpf Ypfcpf max p, f (2)

qpfqpfXpf qp f

(4)

(6)

(5)

(3)

(7)

(8)

(9)

F-1

In this model, the objective function is a utility function whose coefficients are the supplierscores. Constraint 1 ensures that the total quantity of the provided parts is equal to demand.Constraint 2 specifies maximum and minimum order quantity. Constraint 3 ensures that thenumber of late parts from all suppliers does not exceed a threshold. Constraints 4 and 5specify the maximum quality cost and the maximum purchasing costs (buy + transportationcosts +etc.). If we suppose that the Fth supplier is company himself, so the constraint 6 !"#

this constraint ensures that the value of the make parts in the firm will be greater than or equalof the value of the buy parts. For various reasons such as the public image of the firm, it maywish to limit the value of the buy parts(Padilo, 1996). In this paper we do not really wanttreat the make or buy decision. In another paper (Dupont et al, 2001) we showed that themake or buy decision must be approached in 2 levels. The first level can make the decisionfor a lot of the component parts, based on critical /strategic criteria. In the second level thedecision is made based on operational criteria. The mathematical model in this paper can be

used to the second decisional level.Constraint 7 ensures the predetermined number of suppliers. Constraints number 3, 4, 5 ,6

and 7 are optional. Application of these constraints depends on the problem context.

A numeric example

A firm decided to buy a component part. There are 20 potential suppliers for this part. Toencourage competition between suppliers, the firm prefers to select 4 suppliers (n = 4). Themost significant criteria of the firm concerning supplier selection are: delivery, quality, price,and after sale service. These 20 suppliers can support the company strategy and respect the

criteria thresholds. The daily firm demand is 10 000 units. The maximum daily availablecapacities and minimum order size( minimal capacity) of these suppliers are given in table 4.


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The values ofdpf , qpf ,ppf are given in table 5. In this example we have a single componentpart and so we can ignore the p index in the notions.

Supplier Capacity

max.

Capacity

min.

Supplier Capacity

max.

Capacity

min.1 5000 180 11 7000 120

2 8000 150 12 6000 100

3 6000 200 13 4000 200

4 4000 100 14 4500 100

5 8800 120 15 6800 150

6 3000 140 16 9000 200

7 7000 100 17 3200 100

8 6500 110 18 7600 100

9 9000 250 19 5000 100

10 7500 250 20 8200 200

Table 4: The maximum available capacities of suppliers

Supplier dpf qpf ppf Supplier dpf qpf ppf

1 1.0% 2.0% 4.0$ 11 1.05% 0.8% 4.6$

2 2.0% 1.0% 3.2$ 12 1.2% 0.8% 4.5$

3 1.5% 1.0% 3.6$ 13 1.4% 1.0% 3.8$

4 0.9% 1.0% 5.0$ 14 0.8% 1.05%

5.0$

5 1.1% 1.0% 4.0$ 15 3.0% 2.5% 2.9$

6 1.8% 1.0% 3.0$ 16 1.2% 0.9% 4.3$

7 1.2% 0.7% 4.5$ 17 1.1% 1.1% 3.8$

8 2.9% 3% 2.5$ 18 0.8% 0.9% 5.2$9 3.0% 3.0% 2.0$ 19 1.1% 0.95 4.3$

10 2.8% 2.6% 2.8$ 20 1.2% 0.6 4.7$

Table 5: The values ofdpf, qpf, ppf

The cost relating to an out of delay part (dpf )is 0.8 $ and 0.6 $ for a defect(qpf.)The

values of d, q and p are respectively 80 $, 60 $ and 45000 $.

The relative score of each supplier with respect to the criteria is presented in table 6. The

elements of this table are "expected value" of probability distribution function: =(P+4M+O)/6. P is the pessimistic score, O is the optimistic score and M is the most probable

score (the idea of probability distribution function). For example, consider a group of 2decision-makers that want to determine the score of supplier 1 with respect to the delivery


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criterion. The first decision maker considers the following values for the pessimistic, mostprobable and optimistic scores: 7, 9, and 10. The second decision maker assigns values 5, 7and 10 as pessimistic, most probable, and optimistic scores. Therefore, the average of the

pessimistic, most probable, and optimistic scores are 6, 8 and 10 and is equal to 8.According to firm policy, the relative importance of the 4 criteria - delivery, quality,

price and service - are 40%, 30%, 20% and 10%. Based on these data, the relative scoresof suppliers (upf) can be calculated. For example, the score of supplier 1 is u11 = (0.4)(8)+(0.3)(8.1)+(0.2)(5) + (0.1)(7.1)=7.34 These scores are given in table 6.

Supplier Delivery Quality Price Service Total score

1 8 8.1 5 7.17,34

2 5.5 8.3 6.3 7.56,7

3 6.1 8.1 5.6 6.96,68

4 8.1 7.9 4 87,21

5 7 8 5 8.27,02

6 5.9 8.2 6.7 5.56,71

7 6.5 9.1 4.4 7.26,93

8 4 4.2 8 4.54,91

9 4.1 4 10 45,24

10 3.9 5 7.1 5.25

11 6.8 9.3 4.4 66,99

12 6.5 9 4.4 7.16,89

13 6.2 8 5.3 76,64

14 8 8.4 4 87,32

15 3.9 3.8 6.9 64,68

16 6.5 8 4.7 6.96,63

17 7.1 6.8 5.3 6.36,57

18 9 7.8 3.8 9.27,62

19 7 8 4.7 5.16,65

20 6.5 8 4.3 5.5 6,41

Table 6: The total score of each supplier with respect to each criterion

We will now show the advantage of using the mathematical model to treat a SSS.. We willtreat this example using the various methods already existing and then using the mathematicalmodel.

- Directed Method Cost:

In this model, all the costs associated with a supplier are calculated and the least expensive

supplier is selected. We know that the costs relating to an out of delay part and a defect are0.8 $ and 0.6 $. The percentages of the out of delay parts, defect and suppliers prices are


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given in table 5. The cost of each supplier can be calculated from these data. For example, thecost of supplier 1 is calculated as: (0.01*0.8$+0.02*0.6$ + 4$) = 4.002$

The suppliers costs are given in table 7.

Supplier Cost Supplier Cost

1 4.002 11 4.6013

23.202

124.5014

33.602

133.8017

45.001

145.0013

54.001

152.9040

63.002

164.3015

74.501

173.8015

8

2.504

18

5.2012

92.004

194.3015

102.804

204.7013

Table 7: The suppliers costs

According to this table the 4 best suppliers are suppliers numbers 9, 8, 10 and 15. The firmtakes 9000 units of supplier 9 (his maximum capacity), and 250 and 150 of suppliers 10 and15 (their minimum capacity) and 600 units of supplier 8.

- Method of Conjunctive Elimination:

In this approach, suppliers whose score for a criterion is lower than the minimal score areeliminated. Therefore, suppliers that satisfy the minimum level of criteria are selected. Sincethese 20 suppliers respect the minimal thresholds of the decision criteria, there is nodifference between these 3 suppliers. A choice of 5000 units from supplier 1, 4600 units fromsupplier 2, and 200 units from supplier 3 and 200 units from supplier 4, is acceptable.

- Method of lexicographical elimination:

In a lexicographical rule, on the first level, the most important criterion is selected and the

suppliers are compared with respect to this criterion. If a supplier satisfies this criterion muchbetter than the other suppliers do, then he will be selected, if not the suppliers are comparedwith respect to a second criterion. In this example, the most important criterion is deliverywith a weight of 40%. As you see in table 6, supplier 18 respects this criterion much betterthan the other suppliers. Therefore, the firm purchases 7600 units from supplier 18 (itsmaximum capacity). Supplier 4 is in the second position, thus the firm can purchase theremainder of the demand (2400 units) from this supplier. However, 4 suppliers must beselected. We thus take the minimum capacity of the 2 following suppliers who have the bestscores with respect to the delivery criterion. The final result is: supplier 18: 7600 units,supplier 4: 2120 units, supplier 1: 180 units (its minimum capacity), supplier 14: 100 units (itsminimum capacity).


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- Identical weights Method:

In this method, the weights of the criteria are identical and the scores good (+), neutral (0)or unsatisfactory (-) are assigned to each supplier for each criterion. From this comparison, a

total score is calculated for each supplier. From table 6 we will deduce table 8 assuming:Good (+) for a score and 8.

According to table 8, the best supplier is supplier 14, with 3 positive scores. In secondposition are suppliers 1, 4, 5 and 18 with 2 positive scores. Therefore, for example, the firmcan take 4500 units from supplier 14 (his maximum capacity) and an amount of 1833.3 unitsfrom suppliers 1, 4 and 5 equally.

Supplier Delivery Quality Price Service

1 + + 0 0

2 0 + 0 03 0 + 0 0

4 + 0 - +

5 0 + 0 +

6 0 + 0 0

7 0 + 0 0

8 - 0 + 0

9 0 - + -

10 - 0 0 0

11 0 + 0 0

12 0 + 0 0

13 0 + 0 0

14 + + - +

15 - - 0 0

16 0 + 0 0

17 0 0 0 0

18 + 0 - +

19 0 + 0 0

20 0 + 0 0

Table 8: suppliers' scores for each criterion: Good (+), Neutral (0), Unsatisfactory (-)

- A.H.P. method:

Let us assume that an A.H.P. analysis gave the total supplier scores as in table 6. The 4best suppliers are suppliers numbers 18, 1, 14 and 4. The firm will take 7600 units from


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supplier 18 (his maximum capacity), 2200 units from supplier 1, 100 units from 14 (itsminimum capacity), 100 units from 4 (its minimum capacity).

The above-mentioned methods have 2 main disadvantages. Initially they cannot take intoaccount the firm and suppliers constraints. In this small example, we could consider suppliersconstraints (maximum capacity). Consideration of other constraints (constraints relating to l, q

and p), even in this small example, is not easy. The above methods do not consider all criteriaor in other words they do not determine total supplier performance (except A.H.P method).For example, the "cost oriented" method only considers the " cost criterion; thelexicographical elimination method only considers the "delivery" criterion; according to thecategorical method all criteria have the same importance. The significant differencebetween the solutions suggested by these various models shows the importance of " totalperformance " for supplier selection.

- Mathematical model:

Our linear model gets round these 2 main disadvantages of the existing methods. Itconsiders the total performance of the suppliers and selects the best suppliers with respect tothe firm and the suppliers constraints.

The mathematical model solution is in table 9.

Supplier 1 5 6 18

Quantity 180 5294 195.6 4329.6

Table 9: mathematical model solution

Table 10 summarizes the solutions and the performance of the above-mentioned methods.

Cost-oriented

Conjonc. Lexico. Identical A.H.P Mathemat.

S1 0 5000 180 1833.3 2200 180

S 2 0 4600 0 0 0 0

S 3 0 200 0 0 0 0

S 4 0 200 2120 1833.3 100 0

S 5 0 0 0 1833.3 0 5294

S 6 0 0 0 0 0 195.6

S 7 0 0 0 0 0 0

S8 600 0 0 0 0 0

S 9 9000 0 0 0 0 0

S 10 250 0 0 0 0 0

S 11 0 0 0 0 0 0

S 12 0 0 0 0 0 0

S 13 0 0 0 0 0 0

S 14 0 0 100 4500 100 0


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S 15 150 0 0 0 0 0

S 16 0 0 0 0 0 0

S 17 0 0 0 0 0 0

S 18 0 0 7600 0 7600 4329.6S 19 0 0 0 0 0 0

S 20 0 0 0 0 0 0

U252058 70364 75163,6 72484,28 75513,6

72794.76

Diff.3-28% -3% 3% 0,4% 3,7% 0%

Const. d 239.12


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interesting area for future research would be to develop a toolkit that contains differentsubjective tools (such as A.H.P.), objective tools (classical optimization methods) andeffective heuristics for solving the mix integer programming in the large size cases. Asimulation model can be utilized in this toolkit in order to analyze the random behavior ofeach supplier and the stochastic consequences of a solution.

The supplier selection decision is a strategic decision. There are inter-actions between thisdecision and other firm strategic decisions, for example the location of the production site, themake or buy decision, etc. We consider that an opportunity for future research in supply chainmanagement is to develop models and approaches integrating several strategic decisions. Toachieve this goal, it is initially necessary to make an impact analysis between the variousdecisions. Since a feature of strategic decisions is that most of the criteria are subjective, themodels must be able to take into account subjective as well as objective criteria.

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Documents

Multikriteria Supplier Selection