A fuzzy-Bayesian model for supplier selection - Semantic Scholar

Expert Systems with Applications xxx (2012) xxx–xxx

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A fuzzy-Bayesian model for supplier selection Luciano Ferreira a,⇑, Denis Borenstein b a b

Science and Technology School, Federal University of Rio Grande do Norte, Brazil Management School, Federal University of Rio Grande do Sul, Brazil

a r t i c l e

i n f o

a b s t r a c t The selection supplier problem has received a lot of attention from academics in recent years. Several models were developed in the literature, combining consolidated operations research and artificial intelligence methods and techniques. However, the tools presented in the literature neglected learning and adaptation, since this decision making process is approached as a static one rather than a highly dynamic process. Delays, lack of capacity, quality related issues are common examples of dynamic aspects that have a direct impact on long-term relationships with suppliers. This paper presents a novel method based on the integration of influence diagram and fuzzy logic to rank and evaluate suppliers. The model was developed to support managers in exploring the strengths and weaknesses of each alternative, to assist the setting of priorities between conflicting criteria, to study the sensitivity of the behavior of alternatives to changes in underlying decision situations, and finally to identify a preferred course of action. To be effective, the computational implementation of the method was embedded into an information system that includes several functionalities such as supply chain simulation and supplier’s databases. A case study in the biodiesel supply chain illustrates the effectiveness of the developed method. Ó 2012 Elsevier Ltd. All rights reserved.

Keywords: Supply chain Supplier selection Fuzzy Bayesian networks Influence diagrams

1. Introduction Nowadays, many companies are organized in supply chains (SC), looking for raw-material sources, transforming them into intermediate and final products, and distributing these products to consumers. The concept of supply chain (SC) presents a systemic approach in which the SC is seen as single entity rather than a set of fragmented components. The idea is to synchronize strategies, activities and operations in a unified manner (Bowersox, Closs, & Cooper, 2002). The modern focus on supply chain management (SCM), with emphasis in relationships between suppliers and buyers, escalated the purchasing process to a strategic level. According to Bowersox et al. (2002), the purchase of goods and services represents the largest single cost for any enterprise. It is estimated that for each dollar a company earns on the sale of a product, it spends about 50–60% on goods and services. More capital is spent on the purchase of goods and services to support the business’ operations than on all other expensive items combined. Therefore, much attention now is devoted to supplier selection. Supplier relationship management is a comprehensive longterm approach to managing an enterprise’s interactions with the organizations that supply the goods and services it uses. The goal ⇑ Corresponding author. Tel.: +55 51 3308 4053; fax: +55 51 3308 3991. E-mail addresses: (D. Borenstein).

[email protected]

(L.

Ferreira),

[email protected]

of supplier relationship management (SRM) is to streamline and make the processes between an enterprise and its suppliers more effective. Within this context, supplier selection is a complex decision making process, being multi-objective in nature; that is, several and conflicting criteria should be considered and evaluated during the process (Lin, Chuang, Liou, & Wua, 2009). In addition, in long-term relationships, supplier selection decisions are complicated by the fact that are not static decisions, at opposite, they are severely affected by the dynamics caused by market prices, capacity fluctuation, and uncertain demand. Historically, different approaches have been proposed to evaluate, select and monitor potential suppliers by evaluating multiple criteria, using methodologies and techniques from diverse fields such as operations research, artificial intelligence, and decision analysis theory. Ho, Xu, and Dey (2010) presented a literature review of the multi-criteria decision making approaches for supplier evaluation and selection. The authors pointed out that the most commonly approaches to model the problem are namely data envelopment analysis (DEA), multi-objective programming (MOP), analytic hierarchy process (AHP), case-based reasoning (CBR), fuzzy logic, genetic algorithms (GA), and artificial neural networks (ANN). Chan and Chan (2004) applied AHP to evaluate and select suppliers. Levary (2008) proposed a new AHP model to evaluate disruption risks that a manufacturer’s assembly operation associated with the characteristics of the potential supplier might face. Kull and Talluri (2008) proposed a decision tool for supplier selection in the presence of risk measures and product life

0957-4174/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2012.01.068

Please cite this article in press as: Ferreira, L., & Borenstein, D. A fuzzy-Bayesian model for supplier selection. Expert Systems with Applications (2012), doi:10.1016/j.eswa.2012.01.068

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L. Ferreira, D. Borenstein / Expert Systems with Applications xxx (2012) xxx–xxx

cycles considerations, combining AHP and goal programming. Chen, Lin, and Huang (2006) utilized an extension version of TOPSIS (Chen, 2000) for solving supplier selection problems in fuzzy environment. Linguistic values are used to assess the ratings and weights for different criteria, such as quality, price, flexibility and delivery. Hong, Park, Jang, and Rho (2005) designed a mathematical programming model to consider multiple criteria (quantity, price, quantity and delivery) and to evaluate the change in suppliers’ capabilities over a period of time. According to the authors, the suppliers cannot maintain the same conditions of supplying since the delivery condition, inventory level and market environments change constantly. Narasimhan, Talluri, and Mahapatra (2006) proposed a mathematical model to incorporate the product life cycle perspective into strategic selection of suppliers. Valluri and Croson (2005) utilized agent-based simulation to study the performance of a supplier selection model. The authors used agents to model suppliers who learn to produce at their optimal quality levels through a pre-specified system of rewards and punishments administered by the buyer. Ng (2008) designed a multi-criteria model to maximize the supplier scores. The decision maker must inform the relative importance of each criterion and sort them according with their importance. Awasthi, Chauhan, Goyal, and Proth (2009) presented a supplier selection model where each supplier accepts the order only if the order size lies between the given minimum and maximum limits. The authors presented a heuristic solution and experimental results with a set of randomly generated data. Ordoobadi (2009) presented the utilization of fuzzy logic to elucidate the decision maker’s preferences. These preferences are used as inputs into the selection process where selection criteria are evaluated and suppliers’ performances are measured. These tasks are accomplished by applying fuzzy set theory. However, given the complexity of the problem, several researchers are focusing on the integration of the above cited techniques and methodologies towards effective support tools. Choy, Lee, and Lo (2003) proposed a system called Intelligent Supplier Relationship Management System (ISRMS), using hybrid CBR and ANN techniques to select and benchmark potential suppliers. Amid, Ghodsypour, and O’Brien (2006) presented a multi-objective model for the supplier selection problem, in which an asymmetric fuzzy-decision making technique is applied to enable the decisionmaker to assign different weights to several criteria. Sevkli, Koh, Zaim, Demirbag, and Tatoglu (2008) applied a similar model. Lau, Lee, Ho, Pun, and Choy (2006) applied ANN for benchmarking the potential suppliers and GA to determine the best combination of suppliers. Celebi and Bayraktar (2008) proposed a supplier evaluation method which integrates ANN and DEA. Golmohammadi, Creese, Valian, and Kolassa (2009) developed a model using ANN to select suppliers, while a genetic algorithm was applied to generate weights and network architecture. Lee (2009) proposes a method that integrates fuzzy logic and AHP, taking the following criteria to rank the supplier’s performance into consideration: benefits (quality, flexibility and delivery), opportunities (supplier’s technology, joint growth and relationship building), costs and risks (supply constraints, supplier’s profile and buyer–supplier constraints). The model considers these four criteria simultaneously. Wang and Yang (2009) also integrated fuzzy logic and AHP, however the proposed solution considers a quantity discount from the supplier. Razmi, Rafiei, and Hashemi (2009) developed a fuzzy analytic network process model to evaluate the potential suppliers and select the best one with respect to the vendor important factors, such as price, quality, finish time, company’s rank, company’s antecedents and company’s economic status. Bottani and Rizzi (2008) structured a model that integrates cluster analysis, AHP and fuzzy logic to group and rank alternatives. Ha and Krishnan (2008) outlined a hybrid method, incorporating AHP, DEA, and ANN into the evaluation process. Lin et al. (2009) proposed a method that

utilizes the association rule algorithm of data mining and the set theory to find key suppliers. The set theory is used towards avoiding exhaustive search over all the supplier set. Shih, Hung, and Lin (2009) developed a model with AAN and fuzzy logic to select suppliers, after the training and test of the model, multiple discriminate analyses is applied to compare the accuracy of the classification. Wu, Zhang, Wu, and Olson (2010) developed a fuzzy multi-objective programming model for supply chain outsourcing risk management. An algorithm to solve the proposed fuzzy multi-objective programming model was proposed. A very interesting comparison of three different risk evaluation models namely chance constrained programming (CCP), DEA, and MOP models are presented by Wu and Olson (2008). Based on simulations carried out with these techniques, they concluded that (i) CCP provides the ability to incorporate uncertainty directly into models; (ii) DEA guarantees nondominated solutions, but do not incorporate decision maker preference functions into the models; and (iii) MOP provides flexibility for decision makers to reflect their preferences over different criteria. Although these supplier selection models and tools have useful and interesting principles, the majority of them neglect the dynamic aspects of this problem. Learning and adaptation are key requirements for supplier selection models. Talluri and Sarkis (2002) demonstrated that it is difficult for suppliers to maintain the same capability condition during all supply periods, especially in industries which have seasonal demands and experience a wide fluctuation of capability conditions over periods of time. Dynamic changes of the environment must be supported by an effective supplier selection model. Furthermore, the process of generating criteria, validate them and determine their weights is a challenging task in models such as AHP, ANP, MOP and DEA (Aissaouia, Haouaria, & Hassinib, 2007; De Boer, Labro, & Morlacchi, 2001; Golmohammadi et al., 2009; Ng, 2008). Therefore, there is a space for the development of new approaches towards effective support in the selection of suppliers in SC, mainly for long-term relationships, characterized by the occurrence of several dynamic events. This paper contributes to the state-of-art of the supplier selection problem, presenting a novel approach that combines influence diagram (ID) and fuzzy logic to select suppliers, emphasizing the dynamics characteristics of a long-term relationship with suppliers. ID extends the scope of Bayes network to decision models (Shachter, 1986). The state of each node of the influence diagram can be represented by linguistic fuzzy variables, allowing to overcome the vagueness and imprecision of the information and reduce the model complexity. The first advantage of ID is to model decision problems in a graphical manner. This feature facilitates the validation process and promotes greater understanding by decision makers. The ID’s notation supports the decision maker to choose the structure that best represents his/her perception about the supplier selection process. It is possible to estimate and evaluate the consequences of the weights of each criterion with the use of specialized tools (HuginÒ, for example). The probabilistic nature and hierarchical structure of the IDs is an additional advantage that helps in the simultaneous treatment of learning, adaptation, risk and multiple-criteria, since it represents knowledge in domains of uncertainty and provides a probabilistic approach to learning. As any time, the probability distribution reflects the current belief of the agent about the state of the model. A prior probability distribution reflects the agent’s belief before any observation is made, and a posteriori probability distribution reflects the agent’s belief after observation. Belief updating refers to the computation carried out by the agent to update its prior belief to its posteriori belief (Xiang, 2003). Moreover, probabilistic methods, such as ID, provide consistent requirements for the choice of actions. They are based on normative knowledge, that is, judgments about values,



preferences, and desirability; and represent reliable abstractions of human experience. The remainder of this paper is organized as follows. The next section introduces a brief review of fuzzy sets and influence diagrams. Section 3 presents a complete description of the logical structure of the proposed method. In order to illustrate the effectiveness and applicability of the developed approach, a case study is presented in Section 4. Finally, Section 5 is reserved for conclusions and future works.

Before describing the developed method, we introduce some definitions and notation related to fuzzy logic and influence diagrams. They are widely used in Section 3. 2.1. Fuzzy sets In this section we briefly review some definitions of fuzzy set according to Zimmermann (1991), Ross (2004) and Cheng (1998). e in universe of discourse X is a set of Definition 2.1.1. A fuzzy set A e ¼ fðx; l ðxÞÞjx 2 Xg where l ðxÞ is called memordered pairs A e e A A e bership function or grade of x in A. ~ is defined as Definition 2.1.2. The a-cut of fuzzy number k ~ k ¼ fxi : la~ ðxi P a; xi 2 Xg, where ain½0; 1 e is convex if l ~ ðkx1 þ ð1 kx2 Þ P Definition 2.1.3. A fuzzy set A A minðlA~ ðx1 Þ; le ðx2 ÞÞ; x1 ; x2 2 X; k 2 ½0; 1. Alternatively, a fuzzy set A is convex if all a-levels sets are convex. e is called a normal fuzzy set if Definition 2.1.4. A fuzzy set A 9xi 2 X; le ðxi Þ ¼ 1. Alternatively, a fuzzy set is convex if all a-levels A sets are convex. if

Definition 2.1.6. A linguistic variable is one whose values are not numbers but rather words or sentences in a natural or artificial language, such as ‘‘high’’, ‘‘average’’ and ‘‘low’’. ~ is a convex and Definition 2.1.7. A trapezoidal fuzzy number k ~ ¼ ðn1; n2; n3; n4; 1Þ. The membership funcnormal set defined as k tion, lk~ ðxÞ is defined by Cheng (1998) as

8 L fk~ ðxÞ; > > > > < 1; lk~ ðxÞ ¼ R > > fk~ ðxÞ; > > : 0;

a6x6b b6xPc c6xPd otherwise

fk~L ðxÞ

where : ½a; b ! ½0:1 and fk~R ðxÞ : ½c; d ! ½0:1. Since fk~L is continuous, strictly increasing and its inverse function exists, fk~R is continuous, strictly decreasing and its inverse functional also exists. If ~ is called a triangular fuzzy number. b = c, then k ~ is 0 Þ for a fuzzy number k Definition 2.1.8. The centroid point ð x0 ; y defined by Cheng (1998) as

~ ¼ x0 ðkÞ

Rb

Rc Rd R L ðxf k~ Þdx þ b xdx þ c ðxf k~ Þdx Rb L Rc Rd R ðf~ Þdx þ b dx þ c ðfk~ Þdx a k

a

R1 R1 R L ~ ¼ 0R ðyg k~ Þdy þ R0 ðyg k~ Þdy 0 ðkÞ y 1 1 ðg Lk~ Þdy þ 0 ðg Rk~ Þdy 0 Definition 2.1.9. The distance index between an original fuzzy number and its centroid is defined by Cheng (1998) as

~ ¼ RðAÞ

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðx0 Þ2 þ ðy0 Þ2

ð1Þ

~i , A ~ j 2 S, where S ¼ fA ~1 ; A ~2 ; . . . ; A ~ n g is a Thus, for any fuzzy numbers A set of convex fuzzy numbers, the fuzzy number ranking has the following properties:

2. Theoretical background

~ is normalized Definition 2.1.5. A fuzzy number k supx2X lk ðxÞ ¼ 1, where X is the universe of discourse.

3

~ i Þ < RðA ~ j Þ, then A ~i < A ~j, (1) If RðA ~ i Þ ¼ RðA ~ j Þ, then A ~i ¼ A ~ j , and (2) If RðA ~ i Þ > RðA ~ j Þ, then A ~i > A ~j; (3) If RðA 2.2. Influence diagrams An influence diagram (ID) is a network with directed arcs and no cycles. The nodes represent random variables and decisions. Arcs into random variables indicate probabilistic dependence, while arcs into decisions specify the information available at the time of decision. The diagram is compact and intuitive, emphasizing the relationships among variables and representing a complete probabilistic description of the problem. The influence diagram (ID) has been designed as a knowledge representation to reduce the gap between analysis and formulation, more specifically towards the simplification of modeling and analysis of decision trees. It is intuitive enough to communicate with the decision makers and experts and, at the same time, precise enough for normative analysis (Shachter, 1986). ID can be mathematically defined as a directed acyclic graph G = (N, A), where N represents the nodes. N can be partitioned into sets D, C and V. There is at most one value node m e V, drawn as a diamond, which represents the objective to be maximized. There are zero or more chance nodes in set C, represented by circles (we use rectangles when it is necessary to show the probabilities, as in Fig. 1), representing random variables (or uncertain quantities). Finally, there are zero or more decision nodes in set D, drawn as squares, corresponding to choices available to the decision maker. A represents the set of arcs, indicating dependency between the nodes. Suppose that in the decision maker’s problem there is a variable Xi associated with each node i e N in the graph, and a set Xi of possible values it may assume. If i is a value node, then Xi express the desirability of a state of nature and its domain Xi e R. Each value node i has an associated utility function which represents the expected utility as a function of the values of the conditioning prede~ i is a fuzzy set cessors of node i. If i is a chance node, then X representing the different states that Xi can assume. Each node i has a conditional probability table which quantifies the effect of its parents (or predecessors) on it. For purpose of simplification, we do not utilize decision nodes in the proposed method, since we associate an ID to each supplier. Classical Bayesian decision methods presume that future states of nature can be characterized probabilistically. However, the Bayesian method can be further extended to include fuzzy states ~ ¼ f~ of nature (Ross, 2004). Suppose the new information, X x1 ; ~ x2 ; ...;~ xr g is a universe of discourse. It is possible to define fuzzy events on this information, such as ‘‘good’’ information, ‘‘moderate’’ information and ‘‘poor’’ information. The fuzzy event will have membership function lM~ ðxk Þ; k ¼ 1; 2; . . . ; r. Thus, a probability of a ~ can defined as fuzzy event M


4


leadTime EL VL L A H VH EH

0 0 10.0 20.0 20.0 25.0 25.0 4.35 ± 1.3

complianceWithQuantity EL VL L A H VH EH

0 0 0 26.7 53.3 6.67 13.3 4.07 ± 0.93

ServiceLevel EL VL L A H VH EH

complianceWithDueDate EL VL L A H VH EH

0 0 0 3.00 26.8 43.9 26.3 1.16 ± 1.8

0 0 10.0 10.0 30.0 25.0 25.0 4.45 ± 1.2

Cost EL VL L A H VH EH

0 10.0 10.0 40.0 15.0 15.0 10.0

SupplierPerformance

3.45 ± 1.4 Fig. 1. Example of influence diagram.

~ ¼ PðMÞ

r X

lM~ ðxk Þpðxk Þ

ð2Þ

k¼1

Additionally, let S = {S1, S2, . . . , Sn} be a set of state of nature, the ~ is posterior probability of a state si, given fuzzy information M,

~ ~ ¼ PðMjsi Þpðsi Þ Pðsi jMÞ ~ PðMÞ

ð3Þ

where

~ iÞ ¼ PðMjs

r X

lM~ ðxk Þpðxk jsi Þ

ð4Þ

k1

According to Ross (2004), we can extend the Bayesian approach to consider fuzzy information, provided that the fuzzy events on P the new information universe are orthogonal, i.e., rk¼1 lM~ ðxk Þ ¼ 1, for all xk e X. 3. Developed method 3.1. Supplier selection method The supplier selection in supply chain system is by nature a group multiple-criteria decision making problem, which may be described by means of the following sets, (1) A set of K decision-makers called E = {D1, D2, . . . , Dk}. (2) A set of m suppliers called A = {A1, A2, . . . , Am}. (3) A set of n criteria, C = {C1, C2, . . . , Cn}, with which supplier performance are measured. ~ ¼ ðw ~ 1; w ~ 2; . . . ; w ~ n Þ related to the weight of the (4) A vector W criteria, according with the judgment of the decisionmakers.

(5) A vector of performance ratings of supplier Ai(i = 1, 2, . . . , m) ~ ¼ ð~ with respect to criteria Cj{j = 1, 2, . . . , n} called X xi;j ; i ¼ 1; 2; . . . ; m; j ¼ 1; 2; . . . ; nÞ. Based on the definitions presented in the previous section, and in the formulation of the problem above, we summarize the following steps to evaluate suppliers: Step 1: Translate the company’s strategy into a set of criteria to evaluate suppliers. The main objective is to define a set C of criteria (or attributes) for supplier selection and their hierarchical relationship. This task might require the formation of a multi-disciplinary committee of experts involved on the problem. The definition of the criteria is one of the most difficult tasks in any decision making process. Although there is no universal method described in the literature to generate and structure a set of criteria, Keeney points out important evaluation aspects when carrying out this task as follows: (i) criteria should be meaningful indicators of performance; (ii) the definition of the attribute should be concise and clear; (iii) the set of criteria must address all the critical aspects of a problem; and (iv) the set of criteria should be defined in a such a way that the same dimension is not measured by several different and independent criteria in the criteria structure. A good starting point is to look for support in previous work in the area. Several criteria lists have already been generated by several researchers such as Ho et al. (2010), De Boer et al. (2001), Wu et al. (2010) and Lee (2009). Step 2: Construct an ID, identifying the nodes of chance, the value of nodes and arcs, as defined in Section 2.2. Fig. 1 presents an example of an ID for supplier selection with five criteria as follows, delivery lead time, compliance with promised quality, compliance with the due date, supplying costs, and service level. It should be noticed that the first three criteria influence and characterize the performance of the criterion service level, clearly denoting a hierarchy relationship. Step 3: Determine the number of state for each node and the corresponding linguistic variables to express the performance rat-


5


1.00

EL

VL

L

A

H

VH

EH

0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 0

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 Fig. 2. Example of linguistic terms for defining states in an ID node.

0.60

discrete values identified by the following linguistic terms: extremely important (EI), very important (VI), important (I), moderately important (MI) and unimportant (U). Since there are K experts, the aggregated fuzzy importance of each criterion, whose properties are used to produce a scalar measure of consensus degree (Ross, 2004), is computed by

0.40

~i ¼ w

1.00

0.80

0.20

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1

0.00

Fig. 3. Linguistic terms example for the importance weight of each criteria.

ings. Fig. 2 illustrates the membership functions associated with a node of the ID. The rating of each criterion was represented by a range of seven discrete values identified by the following linguistic terms: extremely low (EL), very low (VL), low (L), average (A), high (H), very high (VH) and extremely high (EH). Step 4: Determine the linguistic variable for the importance weight of a criteria. Fig. 3 illustrates a possible choice, in which the importance of each criterion was represented by a range of five

K 1X ~ ik ; w K k¼1

8i 2 C

ð5Þ

~ ik is the weight of criteria i defined by the decision maker k. where w Step 5: Calculate the ratings of each criteria and the supplier performance using an algorithm based on Shachter (1986). This author proposed a method to evaluate an ID quickly, without convert it into a decision tree. The method involves four basic transformations as follows: barren node removal, arc reversal, conditional expectation, and maximization. Shachter demonstrated that the several proposed transformations are consistent with the original diagram and do not affect the choice of the optimal policy. The developed algorithm utilizes some of Shachter’s transformations to structure the logic of the proposed solution. First, the algorithm computes the marginal probabilities of the barren nodes (or sink nodes, if it has no successors) by Eq. (2). Second, the conditional probabilities of the intermediate nodes are calculated by Eq. (4). Third, the desirability of the value node is calculated by Eq. (5). The algorithm can be outlined as follows

Procedure updateBeliefs (Node m , Vector weight) Begin If (barrenNode (m ) is False)then Begin For all parents P of node m do updateBeliefs (P, weight) End //Condition expectation updateConditionalProbability (m , Parents (m )) End Else //barren node removal updateMarginalProbability (m ) If (valueNode (m ) is True)then Maximization (m , weight) End

//recursive call

//uses Eq. (4)

//uses Eq. (2) //uses Eq. (5)


6


The function Maximization (m , weight) calculates the expected value of a node m as

VðmÞ ¼

X

~ i ÞÞ RððNi w

by Fuzzy Module. These new values are used for estimating the posteriori probability.

ð6Þ

4. Case study

i

~ ¼ max Xi , i. e., is the most where R is defined as in Definition 2.1.9, N i ~ i is the weight of the likely state of node i predecessor of m, and w ~ and w ~ i are linguistic variables whose values node (or criteria) i. N i are described by trapezoidal fuzzy numbers (Definition 2.1.7).

This section demonstrates the applicability of the method proposed in this work. The case study was motivated by some planning and operational problems raised by a biodiesel plant installed in Rio Grande do Sul, the southernmost state of Brazil. Biodiesel is the name given to a renewable diesel fuel that is produced from fats and oils through different processes, such as cracking, esterification or transesterification (Hass, McAloon, Yee, & Foglia, 2006). Fig. 5 presents a general view of the configuration of the biodiesel supply chain in Brazil. The mass balance for the production using vegetable oil is also presented in the figure. Besides biodiesel, glycerin and residues are also produced. After production, biodiesel is sold to fuel distributors and is then mixed to mineral diesel (according to government-stipulated percentages) before being distributed for consumption. According with the Brazilian Law, distribution can only be carried out by companies licensed by the Petroleum Brazilian Agency (PBA). Thus, biodiesel cannot be directly sold to retailers, but rather to regional distribution bases controlled by this agency. Biodiesel has received a lot of attention from Brazilian government that launched in December 2004 the National Biodiesel Production and Use Program (NBPUP), towards stimulating the introduction of the biofuel in the national energetic matrix. The refineries and distributors are authorized to add 2% bio-fuel to the mineral fuel (B2), requiring a production superior to 800 million liters of bio-fuel per year. In 2013, the tax will increase to 5%, corresponding to 2.5 billion annual liters. The government addresses Biodiesel as a strategic driver for the future development of the country due to the following reasons: (i) it is an alternative to reducing the dependence on petroleum by-products, helping diversify on the Brazilian energy matrix; (ii) it will open a new market for oil plants; (iii) it will increase the participation of the agribusiness in the GDP; (iv) it will reduce air pollution, contributing to a better environment; and (v) it will created new jobs in poorer regions of the country by providing the Social Fuel Stamp. Particularly, the Social Fuel Stamp is part of Brazilian NBPUP. It attempts to deal with the question of social sustainability of biofuels by providing tax incentives and better financing conditions for biodiesel producers to purchase raw material from small family farms. Companies that have the Social Fuel Stamp may use the certificate to differentiate their brand, highlighting the importance of the social responsibility principles in production.

3.2. Computational implementation Fig. 2 presents a modular view of the developed method and its integration with different sources of data, characterizing the architecture of the selection supplier system. All modules were implemented in Java language, facilitating integration with other models. The Purchasing Strategy Module (PSM) assists decision makers in the representation of knowledge about the problem, facilitating the execution of steps 1–3 of the method. Graphical facilities are provided to draw the inference diagram, to define fuzzy numbers, to input conditional probabilities and so forth. The PSM is important to align the organizational strategy with the selection supplier process. The Decision Network Module (DNM) implements the procedures and functions, and the corresponding data structure for solving the algorithm described in step 4 of the method. These modules are related to three sources of data: (1) Database Model, (2) Enterprise Database, and (3) Fuzzy Module. The Database Model provides the necessary data for calculating the probabilities and training the ID. The Fuzzy Module converts the output of the simulation model and the Enterprise Database to fuzzy values. The Supply Chain Simulator (SCS) has as its main function to analyze the dynamic behavior of the supply chain under different strategies and operational scenario, offering technical performance data such as productivity, production costs, and inventory levels. Given the complex characteristics of some supply chains, and in order to get the best response and total control of the model, it was necessary to develop our own simulation model (described in Ferreira and Borenstein (2011)), in instead of using a commercial package. The simulation output is used for training and learning of the parameters of our method as well as to evaluate the model effectiveness of the method suggestions. The first results generated by the DNM are based on historic data. The initial values are used for calculating the prior probabilities. However, new data are generated in each simulation run, whose numerical values are converted and stored in the Database Model

criteria, performance, Purchasing Strategy network structure Module

Decision Network Module training cases, observations, probabilities

Membership functions, linguistic terms

Supply Chain Simulator

Data from simulations

Fuzzy Module

Fuzzy data

Database Model

Historical data

Enterprise database

Suppliers informations

Fig. 4. Supplier selection system architecture.


7


Methanol

Sugarcane production

Ethanol Fuel Distributors

Inputs

Rearing bovine animals

Animal Fat

Oilseed production

Vegetable oil

Biodiesel Production Plants

Gas Stations

Fuel refineries

Production coefficients Oil + Alcohol → Biodiesel + Glycerin + Residue 100 16 90 11 15 Fig. 5. Biodiesel supply chain.

As presented in Fig. 5, there are several different sources of rawmaterials to produce biodiesel in Brazil. In recent survey of the PBA the raw materials most used by biodiesel production plant are as follows: soybean oil (78%), animal fat (16%), cotton oil (3%), methanol (63%), and ethanol (29%). The most used combination of raw materials for biodiesel production in Brazil is therefore soybean oil and methanol. The choice of suppliers in the biodiesel supply chain has been presented several particularities: (i) the sector is regulated; (ii) it is part of a wider government program in sustainability and social inclusion; and, (iii) there is a great diversity of raw-materials available for production, with different properties, costs, energetic efficiency and production scale. The lower cost of supplying is only used for supplier selection of biodiesel by ANP through auctions. However, the biodiesel producer should have the Social Fuel Stamp to participate in auctions, buying 30% of the necessary oil from small family farms (according with the Brazilian Law). The volume of remaining oil (70% oil) can be acquired from other sources. It is also necessary an alcohol supply to complete the production of biodiesel. There are two possibilities as follows: (i) methanol, used worldwide to produce biodiesel; and (ii) ethanol, produced on a large scale in Brazil from sugarcane. The choice of alcohol is related to the following criteria: cost of supplying; interest in export development; (2) reaction time, the metha-

nol rate is twice than ethanol; and, (3) environmental advantage, the use of ethanol generates an ‘‘100% green’’ biodiesel. Therefore, to define the set of suppliers in the biodiesel supply chain is a complex task that requires analysis and consideration of several and contrasting criteria, involving economic, technological and social issues, since the lowest cost solution is not applicable due to the long-term relationship with the involved suppliers and the Social Fuel Stamp issue. The main objective of the experiments is to determine the type of oil to supply for the biodiesel production. This can be considered one of the most important decisions for a biodiesel plant, since the oil supply is responsible for an estimated 88% of the overall biodiesel production cost (Hass et al., 2006). Moreover, a ‘‘proper’’ oil supply provides a continuous flow of production, the essence of any SCM. We evaluated four potential vegetal oil supplying alternatives as follows: soybean oil supplier (SBS), sunflower oil supplier (SFS), canola oil supplier (CS) e castor oil supplier (CBS). This kind of supplying decision establishes a long-term relationship among the biodiesel plant and their effective suppliers that demands a more careful analysis. As a consequence, two different contexts were analyzed. First a decision making process was carried out without considering possible dynamic events that can disturb the decision making process. Next, some dynamic events were

Table 1 Criteria and sub-criteria definitions. Criteria

Sub-criteria

Definition

Economic

Pressure over the food market Availability of raw-material Transportation costs Storage costs Structure of cooperatives General demand Supplying costs

Raw-material employed in the food industry Balance between production, stock, consumption, importation and exportation. Transportation cost related to each raw-material Storage cost related to each raw-material Ability to operate with a raw-material Need for expanding the planted area The purchase cost of a raw-material

Social

Financing availability Planted area Profitability

Facility to obtain production financing Total planted area Profitability of the producer per planted area

Technological

Productivity Energy efficiency Crushing costs Producer knowledge Assistance knowledge

Amount obtained per planted area Conversion rate from grain to oil Oil cost production Level of knowledge of the producers related to a raw-material production process Level of knowledge of technical assistance related to a raw material


8


Fig. 6. Influence diagram for selection supplier of oil.

Table 2 Importance weight of the criteria from decision-makers. Criteria/sub-criteria

E1

E2

E3

E4

E5

~ ik w

1. Economic Pressure over the food market Availability of raw-material Transportation costs Storage costs Structure of cooperatives Producer demand Cost of supplying

C1 C11 C12 C13 C14 C15 C16 C17

EI MI EI I I EI U EI

EI I EI VI EI EI VI EI

EI VI EI EI EI EI EI EI

EI VH EI EI EI I MI EI

VI EI EI MI MI VI EI EI

(0.76; (0.40; (0.80; (0.56; (0.60; (0.68; (0.48; (0.80;

0.82; 0.47; 0.85; 0.64; 0.67; 0.75; 0.56; 0.85;

0.88; 0.54; 0.90; 0.72; 0.74; 0.82; 0.64; 0.90;

0.98) 0.62) 1.00) 0.82) 0.84) 0.92) 0.74) 1.00)

2. Social Financing availability Planted area Producer Income

C2 C21 C22 C23

I EI I MI

I I I U

I EI VI VI

MI EI I EI

EI EI VI EI

(0.44; (0.72; (0.48; (0.48;

0.53; 0.78; 0.58; 0.56;

0.62; 0.84; 0.68; 0.64;

0.72) 0.94) 0.78) 0.74)

3. Technological Productivity Energy efficiency Cost of crushing Producer knowledge Assistance knowledge

C3 C31 C32 C33 C34 C35

VI EI EI I I I

I I VI EI MI VI

VI EI VI EI EI EI

EI EI VI EI VI EI

VI EI EI I EI EI

(0.60; (0.72; (0.68; (0.64; (0.56; (0.68;

0.69; 0.78; 0.76; 0.71; 0.64; 0.75;

0.78; 0.84; 0.84; 0.78; 0.72; 0.82;

0.88) 0.94) 0.94) 0.88) 0.82) 0.92)

introduced, emphasizing both the learning aspects of the developed method as well as the importance of the architecture presented in Fig. 4. 4.1. Experiments settings In this section we describe the required parameters to conduct the experiments. The necessary data were determined based on a review of the prior literature (Demirbas, 2009; Hass et al., 2006; Ho et al., 2010) and semi-structured interviews undertaken with experts from a Brazilian biodiesel production plant, emulating a real-world decision making process. Based on the list of criteria discussed in the literature and the evaluation of the experts, Table 1 presents the final set of criteria for the evaluation of the most appropriate vegetal oil supply. After defining the criteria, a sample of five interviewers validated the hierarchical structuring of the decision model and the weights of criteria, estimated from a sample of empirical data, using the software HuginÒ. Fig. 6 shows the structuring of the hierarchy of the ID proposed, which includes three levels. The top level of hierarchy (Supplier Performance node) represents the ultimate goal of

the problem, while the second level consist of three main supplier selection criteria, which are namely economic, technological and social. At the third level, these criteria were decomposed into various sub-criteria that may affect the choice of a particular supplier. Table 2 shows the importance weights of the criteria determined by the same five experts (E1, E2, E3, E4 and E5). The values ~ ik Þ were obtained by Eq. (5). The same pattern in the last column ðw presented in Fig. 3 was used.

4.2. Results and managerial implications After defining the initial parameters needed to structure the model, Table 3 presents the prior probabilities for each alternative. The ratings of the criteria C11, C15, C16, C21, C34 and C35 were estimated from data collected in the interviews. The ratings for C12, C22, C23, C31 and C32 were estimated from the average production of each oilseed in the last 4 years, while for C13, C14, C17 and C33 were calculated from the average quote of the last 18 months. All these data were stored in Database Model. We imported data about vegetal oil supplying, provided by the biodiesel


9

L. Ferreira, D. Borenstein / Expert Systems with Applications xxx (2012) xxx–xxx Table 3 Prior probabilities for the experiments. State

Economic criteria C11

Social criteria

Technological criteria

C12

C13

C14

C15

C16

C17

C21

C22

C23

C31

C32

C33

C34

C35

Soybean oil EH 0.2 VH 0.6 H 0.2 A 0.0 L 0.0 VL 0.0 EL 0.0

0.7 0.2 0.1 0.0 0.0 0.0 0.0

0.0 0.25 0.5 0.25 0.0 0.0 0.0

0.0 0.1 0.1 0.6 0.2 0.0 0.0

0.1 0.3 0.6 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 1.0

0.0 0.4 0.6 0.0 0.0 0.0 0.0

0.0 0.1 0.6 0.3 0.0 0.0 0.0

1.0 0.0 0.0 0.0 0.0 0.0 0.0

0.7 0.3 0.0 0.0 0.0 0.0 0.0

0.4 0.6 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.75 0.25 0.0 0.0

0.0 0.0 0.0 0.65 0.35 0.0 0.0

0.0 0.0 1.0 0.0 0.0 0.0 0.0

0.0 0.0 1.0 0.0 0.0 0.0 0.0

Sunflower oil EH 0.2 VH 0.6 H 0.2 A 0.0 L 0.0 VL 0.0 EL 0.0

0.0 0.0 0.0 0.2 0.6 0.1 0.1

0.1 0.6 0.3 0.0 0.0 0.0 0.0

0.0 0.1 0.7 0.2 0.0 0.0 0.0

0.0 0.0 0.0 0.3 0.4 0.3 0.0

0.0 0.0 0.0 0.0 0.7 0.2 0.1

0.0 0.0 0.3 0.7 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.9 0.1 0.0

0.0 0.0 0.0 0.0 0.1 0.9 0.0

0.0 0.0 0.0 0.0 0.3 0.6 0.1

0.0 0.0 0.3 0.7 0.0 0.0 0.0

0.0 1.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.9 0.1 0.0 0.0 0.0

0.0 0.0 0.0 1.0 0.0 0.0 0.0

0.0 0.0 0.0 1.0 0.0 0.0 0.0

Castor oil EH VH H A L VL EL

0.0 0.0 0.0 0.0 0.1 0.2 0.7

0.0 0.0 0.0 0.0 0.5 0.3 0.2

0.1 0.6 0.3 0.0 0.0 0.0 0.0

0.0 0.1 0.1 0.6 0.2 0.0 0.0

0.0 0.0 0.0 0.0 0.3 0.5 0.2

0.0 0.0 0.0 0.0 0.2 0.6 0.2

0.8 0.2 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.3 0.7 0.0

0.0 0.0 0.0 0.0 1.0 0.0 0.0

0.0 0.0 0.0 0.0 0.1 0.6 0.3

0.0 0.0 0.0 0.0 0.0 1.0 0.0

1.0 0.0 0.0 0.0 0.0 0.0 0.0

0.26 0.74 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 1.0

0.0 0.0 0.0 0.0 0.0 0.0 1.0

Canola oil EH VH H A L VL EL

0.2 0.6 0.2 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.7 0.2 0.1

0.0 0.2 0.6 0.2 0.0 0.0 0.0

0.0 0.1 0.1 0.6 0.2 0.0 0.0

0.0 0.0 0.0 0.0 0.3 0.5 0.2

0.0 0.0 0.0 0.0 0.2 0.6 0.2

0.0 0.4 0.6 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.1 0.8 0.1 0.0

0.0 0.0 0.0 0.0 0.0 1.0 0.0

0.0 0.0 0.0 0.0 0.3 0.6 0.1

0.0 0.0 0.35 0.65 0.0 0.0 0.0

0.0 0.0 1.0 0.0 0.0 0.0 0.0

0.0 0.0 0.85 0.15 0.0 0.0 0.0

0.0 0.0 0.0 0.0 1.0 0.0 0.0

0.0 0.0 0.0 0.0 1.0 0.0 0.0

plant, from the Enterprise Database module (Fig. 4). The decision makers were happy with the pattern shown in Fig. 2. The goal of the first experiment was to determine the best vegetable oil supplying, demonstrating the strength of the proposed solution to rank and evaluate possible alternatives. Table 4 summarizes the results obtained from the prior probabilities pre-

sented in Table 3. The value of the line corresponding to V(SP) in Table 4 is related to the final performance of each supplier, i.e., node Supplier Performance of the ID presented in Fig. 6. This means that the soybean is the best raw-material to produce biodiesel in Brazil, followed by sunflower, castor beans and canola, respectively. These results are in total concordance with the Brazilian

Table 4 Ranking of the alternatives. C/A

SBS

SFS

CS

CBS

N i

~ iÞ RðN i w

N i

~ iÞ RðN i w

N i

~ iÞ RðN i w

N i

~ iÞ RðN i w

C11 C12 C13 C14 C15 C16 C17

H VH H A H EL H

0.56 0.75 0.51 0.56 0.67 0.73 0.54

H L VH H L L A

0.56 0.54 0.48 0.52 0.53 0.58 0.59

EL L VH H VL VL EH

0.56 0.54 0.51 0.52 0.48 0.66 0.54

H L H H VL VL H

0.46 0.54 0.48 0.52 0.48 0.66 0.47

V(C1)

4.35

C21 C22 C23

3.81

N i

RðN i

H EH EH

V(C2)

1.62

C31 C32 C33 C34 C35

N i VH A A H A

V(C3) V(SP)

2.96 8.94

3.83

3.63

N i

~ iÞ RðN i w

N i

RðN i

~ iÞ w

0.57 0.59 0.45

L VL VL

0.50 0.47 0.56

EL L VL

0.50 0.47 0.56

N i L VL VL

~ iÞ RðN i w 0.67 0.56 0.55 0.57 0.60

N i A VH H A A

~ iÞ RðN i w 0.56 0.67 0.51 0.54 0.55

N i VL EH VH EL EL

~ iÞ RðN i w 0.56 0.60 0.51 0.50 0.51

N i A H H L L

~ iÞ w

1.53

2.85 8.20

1.53

2.71 8.08

~ iÞ RðN i w 0.46 0.50 0.56

1.52 ~ iÞ RðN i w 0.48 0.74 0.48 0.46 0.46

2.63 7.80


10


Fig. 7. Evolution of the alternatives of vegetable oil supplying.

reality that is dependent on soybean to produce biodiesel in large scale. The goal of the second experiment was to demonstrate the ability of continuous learning and adaptation of the model by processing new evidences from the Database Model and by updating the posterior probabilities. In this case, we started the simulations without defining the prior probabilities, i.e., the probabilities of Table 3 were initialized to zero. During the experiments, new evidences were gradually stored in the Database Model by the Supply Chain Simulator. According to Fig. 7, in the first steps of the simulation the suppliers presented the same performance, so the demand of oil was divided proportionately among them. In the 110th simulation step, the CBS alternative posterior probabilities were updated with new evidence stored in the Database Model during the simulations, getting a performance higher than others alternatives. The oil demand graph demonstrates the preference change of the biodiesel production plant in relation to the previous simulations steps. The same situation occurs in the 220th, 330th and 440th simulation steps, demonstrating the preference chance for canola, sunflower and soybean, respectively. Thus, until the 550th simulation steps, approximately, alternative CBS is preferred to SFS (CBS SFS), SFS is preferred to CS (SFS CS) and CS is preferred to CBS (CS CBS). Finally, considering that the production of biodiesel has an important role in social inclusion and the canola was cited by interviews as the most appropriate crop for small family farms, we simulated the following government incentives for canola production from 550th simulation steps onward: (i) subsidies to reduce the production cost and transportation (C22 and C27), (ii) investments in infrastructure (C23 and C24), (iii) increased availability of funding (C27), and (iv) technical training (C34 and C35). Based on the new data generated by the Supply Chain Simulator, the performance of alternative CS increased to 9.04. This rating value is obtained when the following changes happens in the criteria values: C22 = A; C23 = A; C24 = EH; C27 = L; C29 = VL; C34 = L; and C35 = L. Therefore, according to the new values calculated, alternative CS is preferred to SBS, CBS is preferred to SFS and SFS is preferred to CBS.

The case study demonstrated that the developed method can be effectively used by biodiesel plants to define the best vegetal oil supplying. The method can be also used to further determine the best suppliers in each oil category. However, the model can also be employed by the Brazilian government as an aid in the establishment of policies to stimulate the production of new sources of raw-material. Nowadays, 78% of the biodiesel production plant of Brazil utilize soybean as main raw-material in the manufacturing process. However, as this option is related to large producers, it is important to carry out studies to evaluate the best alternatives of production by small family farms, since the biodiesel producers need to purchase their production to maintain the Social Fuel Stamp. The developed framework presented in Fig. 4 can play a vital role in this difficult task.

5. Concluding remarks In this work, we presented a novel method based on the integration of influence diagram and fuzzy logic to rank and evaluate suppliers in a supply chain context. This approach presents the following advantages: (i) modeling of uncertainty and vagueness of information. The method uses linguistic variables to assess ratings and weights of criteria; (ii) exploiting probabilistic learning in supplier selection problem through Bayesian learning; (iii) representing explicitly the decision maker’s knowledge in influence diagrams, eliminating redundant criteria, storing historical data about purchasing decision making process, and facilitating the communication of the outcomes of the decision-making process; and (iv) supporting long term relationships with suppliers, incorporating learning and dynamic environmental changes in the customer preferences. We used the biodiesel supply chain in order to illustrate the main features of the proposed solution. Notwithstanding the short experimentation time, the tests carried out clearly demonstrate that the developed method has enormous potential as an effective prescriptive tool in real-world supplier selection, particularly in long term relationships. The method was able to capture dynamic events and to reevaluate preferences to reanalyze the decision



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