A Model for Group Decision Support for Supplier Selection

Transcription

1 A Model for Group Decision Support for Supplier Selection Abstract: Procurement is one of the critical functions in supply chain management, since it directly impacts the performance of the firm. The domain of supplier selection has been widely studied using a wide variety of quantitative models for decision support. However, there is a gap in existing literature, on decision support models focusing on group decision making. In this study, an application of the Analytic Hierarchy Process has been proposed for leveraging the collective expertise of a group of decision makers, for supplier selection. The Fuzzy extension of the Row Geometric Mean Method has been used in this study whereby the highly consistent consensual decision making vector has been estimated for a group of decision makers. The proposed model for group decision making has been further tested to rank the capabilities of 10 suppliers, in a case study conducted with a steel manufacturing multi-national firm, based in India. Author(s) 1. Arpan Kumar Kar, Faculty, Indian Institute of Management, Rohtak, India. ID: arpan_kar@yahoo.co.in Keywords: Group decision making, Decision support, Procurement management, Analytic Hierarchy Process, Fuzzy set theory.

2 1. Introduction One of the most critical activities in supply chain management is that of procurement management since it is the primary point of contact with most supply-chain partners and also impacts heavily the total expenses incurred by a manufacturing firm, even up to 60% of the total costs incurred. In current times, not only at the strategic level should every firm define the corporate, manufacturing and sourcing strategies but also identify the products and services that should be acquired from outside. Again at the operational level, all the procurement activities, such as to review suppliers, to identify opportunities, and to develop and implement product agreements, should be monitored with the involvement of senior executives. The greater information visibility across processes opens up the scope to improve decision making at every stage through structured quantitative approaches. These decisions taken at the purchasing stage can have a great impact on the overall supply-chain and production planning processes and on the overall performance of the firm. Thus it is extremely important to improve these processes using structured approaches and decision support tools as much as possible, since these models can benefit the decision making process substantially in procurement management. Therefore a review of procurement literature highlights how there has been substantial focus on the decision support models used in identifying appropriate suppliers and apportioning orders among these suppliers. However, it is interesting to note that although it has been established that collective intelligence of a group of decision makers in consensus often is more effective than decision makers working in isolation in the decision making process (Hackman and Morris, 1975), there has been a general lack of focus in existing literature to extend theories for Group

3 Decision Support to the supplier selection problem, despite both domains having a plethora of literature in silos. This stimulated the recognition of the need to integrate these silos of body of knowledge to enrich decision support literature in procurement. The focus of this study is to showcase the application of theories for group decision making, for the supplier selection problem. For doing so, an application of the fuzzy Analytic Hierarchic Process (AHP) has been demonstrated, for providing decision support in consensual group decision making. By using AHP theory, preferences of a group of decision makers, has been aggregated, and subsequently improved to create consensus between the priorities, so that not only individual priorities are consistent, but also, group priorities are also consistent and consensus is achieved. This consensus group decision vector has been used to rank 10 suppliers in a sumproduct approach, using the capability score of the 10 suppliers for 7 criteria which have been used for the evaluation of suppliers. 2. Brief review of literature It has been established through a meta-analysis of literature that supplier selection studies have been considered mostly as multiple criteria decision making problem and studies in decision support for supplier selection have been popular due to the conflicting nature of the goals, complexity of the problem domain and diversity of the evaluation criteria (Weber, Current and Benton, 1991). Therefore many novel approaches involving approaches like interpretive structural modelling, data envelopment analysis, outranking models, cost minimization models, multi-attributedeterministic models, TOPSIS, neural networks, genetic algorithms and agent based models have been utilized for providing decision support in supplier selection problem. However, to the best of our knowledge, none of these studies attempted to

4 provide decision support for group decision making for the supplier selection problem through the same approach. Studies using the AHP started getting popular because of its robustness in being able to analyse consistent data and for its ability to analyse both qualitative and quantitative data. The AHP decomposes the problem into a hierarchy of more easily comprehended sub-problems, each of which can be analysed independently by making binary comparisons. The AHP checks for deviation from consistency in the responses and can measure the deviation. While some of the earlier studies using theories of AHP (Arbel and Seidmann, 1984; Nydick and Hill, 1992; Masella and Rangone, 2000; Rapcsak, Sagi, Toth and Ketszeri, 2000; Tam and Tummala, 2001) adopted a crisp approach to address the supplier selection problem; the more recent studies (Handfield, Walton, Sroufec, and Melnyk, 2002; Zaim, Sevkli and Tarim, 2003; Kahraman, Cebeci and Ulkan, 2003; Hsu and Chen, 2007; Hsu, Lee and Kreng, 2010) proposed the application of AHP further developed using fuzzy set theory. Many studies have integrated AHP with other approaches such as data envelopment analysis (Ramanathan, 2007; Sevkli, Koh, Zaim, Demirbag and Tatoglu, 2007); data envelopment analysis and artificial neural networks (Ha and Krishnan, 2008); genetic algorithm (Basnet and Weintraub, 2008) and linear programming models (Ghodsypour and O Brien, 1998; Cebi and Bayraktar, 2003; Kull and Talluri, 2008; Mendoza, Santiago and Ravindran, 2008; Demirtas and Ustun, 2008, 2009). Despite having a plethora of literature in the supplier selection domain even using AHP, a gap in decision support literature yet to be addressed properly is in the domain of group decision support. Although there has been substantial development

5 of theories for group decision making using AHP (e.g. Dyer and Forman, 1992; Bryson, 1996; Honert, 1998; Bolloju, 2001; Condon, Golden and Wasil, 2003; Escobar, Aguarón, and Moreno-Jiménez, 2004; Escobar and Moreno-Jiménez, 2007; Dong, Zhang, Hong and Xu, 2010), none but one study has applied these theories for the supplier selection problem. Many studies which focused on the theoretical enrichment of the methodology have extended the AHP theory to provide decision support for group decision making through the Eigen Value Method (EVM) and the Row Geometric Mean Method (RGMM). To the best of our knowledge, only Cheng and Tang (2009) attempted to provide decision support for GDM using fuzzy AHP theory but the major focus of this study was on the fuzzy Delphi methodology which was used to finalize the evaluation criteria. Also this study did not focus on estimating group consistency or the degree of consensus between the decision makers, in their approaches and thus did not focus on leveraging the collective intelligence of a group of expert decision makers in consensus. 3. Literature gap and contribution While decision support studies for the supplier selection problem has been a classic area of research and has a plethora of literature, a relatively unexplored area is in the area of application of decision support theories for group decision making. Although Cheng and Tang (2009) explored the application of AHP theory for group decision making briefly, the focus of this study was on the fuzzy Delphi methodology and subsequently on estimating the collective preferences through the simple aggregation of priorities method. In fact, there was no attempt to explore the degree of consensus among the preferences of the decision makers. Thus this study did not

6 attempt to leverage upon the collective intelligence of a group of expert decision makers in consensus, while providing group decision support in procurement. In this paper, we have showcased how the individual preferences of a group of experts may be collected and aggregated using the aggregation of judgements method using the geometric mean approach. After the aggregation of judgements of the experts, it has also been demonstrated how the collective priorities are estimated through consensus building among the decision makers, to estimate the final consensual preference, which has been mapped to the supplier capabilities score in a sum-product approach, to rank suppliers. Not only individual consistencies matter in collective decision making, but also, the group consistency impacts the outcome in a large way, which this study focuses on. 4. Details of the computation methodology In this study, the application of the Row Geometric Mean Method (RGMM) has been demonstrated using which the preferences of a group of decision makers has been estimated. RGMM has been used in our approach instead of EVM since if the individual decision makers are experts, combining their judgments (using EVM) will eliminate estimates from individual expertise but only the final outcome obtained from their individual hierarchies using the geometric mean will provide a better estimate of group preferences (Saaty, 2008). Also the computational time complexity of EVM and RGMM are o(n 2 ) and o(n) respectively. The ranking of suppliers have been estimated through a 5 step approach, which has been described in greater details in the following subsections. 4.1 Estimation of individual judgments

7 In this stage, the relative importance given to the critical criteria for evaluation by the group of decision makers is estimated. Let X= (x 1, x 2, x 3,, x 7 ) be the multidimensional consensus vector for GDM such that x i is the aggregated priority of criteria i estimated as described in the following section such that x i = 1. Let D = (d 1, d 2, d n ) be the set of n decision makers. Let us also assume that each decision maker has a relative importance of ψ i on the outcome of the decision making process. Qualitative linguistic comparative judgments would be coded quantitatively from the scale of responses as described in Table 1. Fuzzy set theory has been used in coding these judgments to accommodate the subjectivity in human decision making process arising due to the complexity of the problem domain. A triangular fuzzy function has been used to receive responses since there is equal probability of the response of the next level as is to the response of the previous level, when a comparative judgment is made by a decision maker. Table 1: The scale for conversion of linguistic preferences Definition Fuzzy sets for the fuzzy AHP (~k) Somewhat equal importance {(1,0.25), (1,0.50), (3,0.25)} Somewhat moderate importance {(1,0.25), (3,0.50), (5,0.25)} Somewhat strong importance {(3,0.25) (5,0.50) (7,0.25)} Somewhat very strong importance {(5,0.25), (7,0.50), (9,0.25)} Somewhat extreme importance {(7,0.25), (9,0.50), (9,0.25)} The pairwise-comparison computation approach for the operations on fuzzy sets has been used in this study, as has been demonstrated for the fuzzy sets for a hypothetical operator used only for illustration, in Eq. 1. =( ) = ( ) ( ) ( ) (Eq. 1)

8 After taking multiple responses from the n decision makers, it would be coded as fuzzy rules to generate the judgment matrix which will be used for obtaining the priority estimates through a judgment aggregation procedure. 4.2 Estimation of individual consistent priorities Let M=( ij ) n n, where ij 0 and ij ji =1 be the judgment matrix for a decision maker d i. In the RGMM, the individual decision vector can be obtained by solving the equation: such that i 0 and i=1. (Eq.2) The solution is obtained by =. (Crawford and Williams, 1985) (Eq.3) where i is the weight of the decision criteria i such that = { 1, 2,, 7} for decision maker i. In the subsequent step, before the crisp aggregation rules are computed, the set of highly consistent decision makers need to be estimated. Thus the Geometric Consistency Index (GCI) for individual priorities needs to be measured and only the highly consistent preferences will be used for the subsequent stage (Aguarón and Moreno-Jiménez, 2003). GCI ( ) = 0.37 for n=7 (Eq. 3) 4.3 Aggregation of judgments for collective preference estimation Aggregation rules which represent the collective preference for deriving the group decision making vector can be estimated by the aggregation of consistent individual judgments as has been defined in the subsequent equation (4). Aggregation of individual judgments: (Eq. 4) After this the collective priority vector is derived using the RGMM approach (Equation 3) whereby w i (c) 2(c),. 7(c) } T is the collective vector such that w i (c) = { 1(c),

9 This would bring out the fuzzy relative weights of the criteria for the group of decision makers. The fuzzy weights could be converted to crisp weights for criteria i, for subsequent usage as shown: w i = [ ) (Eq. 5) 4.4 Estimation of consensus among the collective preferences Subsequently, after the individual consistent preferences are identified, the consensus index for GDM is estimated using the Geometric Cardinal Consensus Index (GCCI). (Dong et al., 2010) GCCI ( ) = (Eq. 6) If GCCI (X i ) for all the n decision makers, consensus is achieved, where is the upper limit for the aggregated priorities ( = 0.37 for n=7) In case, consensus is not achieved among the decision makers, the consensus vector may be further derived by using the cardinal consensus improvement approach (Dong et al., 2010). This aggregated priority vector X= (x 1, x 2, x 3,, x 7 ) will be used for the ranking of suppliers. 4.5 Ranking of suppliers Let supplier i have a performance vector of S i such that S i be a set of performance score against 7 criteria S i = (s i1, s i2, s i7 ). Details on the selection and definition of these 7 criteria have been provided later in the research methodology section. The supplier performance score for supplier i has been estimated by the sum-product approach whereby scalar multiplication of vectors have been done. Si X = (x 1, x 2,, x 7 ) (s i1, s i2, s i7 ) = x 1 s i1 + x 2 s i2 + x 7 s i7 (Eq. 7) Based on this sum-product score, the suppliers may be ranked with any simple ranking approach, to identify the most suitable supplier(s). A higher sum-product

10 score would indicate a supplier who is more suitable and a lower sum-product score would indicate a supplier who is less suitable, based on 2 metrics, the supplier s objective performance against a set of evaluation criteria and the relative priority of these evaluation criteria based on the collective preferences of a group of decision makers in consensus. 5. Research methodology A case study was conducted to evaluate the proposed computational approach. The case study was conducted in one of the largest 10 manufacturers of iron and steel, based out of India, but having a geographically dispersed presence in Europe, South East Asia and the Pacific countries with crude steel production capacity exceeding 30 metric tonnes per annum. First interviews were conducted among the procurement executives of the firm, which indicated that seven criteria were more popularly used for the evaluation of suppliers for most of the commodities, although sometimes suppliers of different commodities were evaluated based on different evaluation criteria specific to the commodity and the context of purchase. These criteria were found already widely used in existing literature among multiple studies including Braglia and Petroni, 2000; and Bottani and Rizzi, These criteria have been defined as follows: 1. Product quality, which depends on meeting the requirement specifications of the buyer firm and the cost of a component rejection by the buyer. 2. Compliance with the agreed date can be computed as the average percentage of in-time deliveries over the last 'n' supplies by the supplier to all his customers.

11 3. Price has been defined as the ratio of the quoted price with respect to the average price of the item to be purchased in the market. 4. The supplier's technological capability is estimated based on the percentage of the total work-force that had technical knowledge about the commodity and the manufacturing process. 5. Production capability may be measured as the ratio of average manufacturing capacity of the supplier and the customer's average consumption per unit time. 6. Financial position of supplier has estimated using 2 financial indicators debt ratio and current ratio. 7. Electronic transaction capability: The supplier is rated on electronic catalogue management, electronic order management, electronic financial settlements and supplier e-skills. Data was collected against each of these seven criteria from 10 suppliers for the same commodity from the firm, by administering a questionnaire through the vendor management cell, within the procurement practice. Subsequently, a questionnaire was administered to 5 decision makers, i.e. procurement executives, who worked in the purchasing department of this firm, to estimate the individual and collective priorities of these evaluation criteria. The analysis of the responses was conducted using the computational approach which has already been detailed earlier. 6. Analysis and Results The preferences of these five decision makers had equal importance. Each of the sub-criteria within the 7 main criteria had equal importance for all the decision

12 makers, and hence the priority break-up has been highlighted at the main criteria level. The individual priorities obtained from the group of 5 decision makers (d i ) and the aggregated preferences are shown in Table 2. Criteria W 1 W 2 W 3 W 4 W 5 Product Delivery compliance Price Technological capability Production capability Financial position E-transaction capability Consistency measures Table 2: Individual and aggregated priorities along with their consistency measures The last row of Table 2 establishes that all the individual priorities of these 5 decision makers were of acceptable consistency, i.e. GCI < The aggregate decision vector in consensus obtained after the aggregation of individual judgments was (0.237, 0.266, 0.143, 0.126, 0.091, 0.087, 0.050). Individual priorities were also in consensus, i.e. the GCCI of the aggregated priorities was (less than 0.37). Next the normalized supplier performance score was estimated from the responses collected from the 10 suppliers, as shown in Table 3. Criteria Criteria Criteria Criteria Criteria Criteria Criteria

13 Supplier A Supplier B Supplier C Supplier D Supplier E Supplier F Supplier G Supplier H Supplier I Supplier J Table 3: Standardized supplier performance score Using both the aggregated preference vector [i.e. (0.237, 0.266, 0.143, 0.126, 0.091, 0.087, 0.050)] and individual preference vectors, individual supplier s total scores were computed. The results of the total score computation exercise are tabulated in Table 4. Performance comparison matrix Aggregated results Supplier number Score Rank Supplier A Supplier B Supplier C Supplier D

14 Supplier E Supplier F Supplier G Supplier H Supplier I Supplier J Table 4: Scores and ranks of the suppliers as per individual priority and group priority Conclusion This paper showcases the application of theories of group decision making, using the AHP, in the supplier selection problem. Considering that there has been indications in literature (e.g. Hackman and Morris, 1975; Saaty, 2008) which postulated that the decision making of a group of experts in consensus is likely to be more effective than the decision making of experts in isolation, following this approach will have a significant improvement of the outcome of supplier selection processes. However, it is important to note that aggregation of preferences of decision makers in consensus is an important criterion for the success of preference aggregation models. If decision makers are not in consensus, simple aggregation of priorities or judgments (either by the EVM or RGMM) is likely to expose the group decision to imprecision arising from extremities of individual priorities. References

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