Lean and Green Supplier Selection Problem: A Novel Multi Objective Linear Programming Model for an Electronics Board Manufacturing Company in Turkey

Abstract

Even though various studies are proposed to evaluate and determine the best suppliers, studies generally consider similar factors such as cost, quality, delivery time etc. in the supplier selection problem. Nowadays, some lean and green issues such as on time (JIT) delivery, waste reduction, avoidance and treatment of hazardous materials, energy efficiency, occupational health and safety, corporate social responsibility, etc. started to be addressed together with the supplier selection process. Lean and Green Supply Chain Management (L-GSCM) is a dynamic field for companies to gain advantages in the competitive business market place. In the light of these concepts a new supplier selection process is developed for an electronics board manufacturing company in Turkey. We present an integrated approach which consists of three stages. In the first stage, the Fuzzy Analytic Hierarchy Process (FAHP) method is applied in order to determine the weights of the lean and green criteria with respect to different experts’ judgments using linguistic terms. At the second stage, linguistic judgments related to qualitative drivers are provided from decision makers. Then these fuzzy, judgements are aggregated by means of fuzzy group decision making and deffuzzified to crisp scores. The outputs of this stage are the quantitative data of a Multi-Objective Linear Programming (MOLP) model. In the third stage, a novel Fuzzy Weighted Additive Max-Min approach with Group Decision-Making (F-WAMG) is proposed and applied to guarantee that satisfaction degrees of each objective functions in the MOLP model are greater than or equal to their own weights. The proposed model and solution approach is applied to an electronics board manufacturing company in Turkey. The results point out that the proposed F-WAMG approach yields consistent satisfaction degrees with respect to weights of objectives that represent decision makers’ preferences and judgements.

Appendix: Questionnaire for FAHP

1.1 Questionnaire Form Is Used to Determine of Importance of Criteria

With respect to (W.r.t.) the criterion “Cost (Price)”

• Q1. How much is C1 more important than C2?

• Q2. How much is C1 more important than C3?

• Q3. How much is C1 more important than C4?

• Q4. How much is C1 more important than C5?

Table 12

1.2 Zimmermann (1978) Approach

After Zimmermann (1976) combined the fuzzy set theory with conventional linear programming, several authors developed new fuzzy programming approaches. Zimmermann (1978) proposed the max–min approach:

$$ \max \lambda \vspace*{-15pt} $$

$$ subject\ to \vspace*{-15pt} $$

$$ \lambda \le {\mu}_{Z_j}(x)\kern1.75em j=1,\cdots, J \vspace*{-15pt} $$

$$ \lambda \in \left[0,1\right]\kern2.25em x\in X. $$

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where j defines the number of fuzzy goals, μ_j(x) refers to the satisfaction degree of the objective j, and λ shows the minimum satisfaction level of objectives and is defined in the range [0, 1].

1.3 Tiwari et al. (1987) Approach

The weighted additive model was proposed by Tiwari et al. (1987) and it is given below (Amid et al. 2006; Shaw et al. 2012):

$$ \operatorname{Max}\ \sum_{j=1}^J{w}_j\cdot {\lambda}_j+\sum_{k=1}^K{\beta}_k\cdot {\gamma}_k \vspace*{-12pt} $$

$$ {\lambda}_j\le {\mu}_{Z_j}(x)\kern1.75em j=1,2,\dots, J \vspace*{-12pt} $$

$$ {\gamma}_k\le {\mu}_{g_k}(x)\kern1.25em k=1,2,\dots, K \vspace*{-12pt} $$

$$ {g}_p(x)\le {b}_p\kern1.75em p=1,2,\dots, M \vspace*{-12pt} $$

$$ {\lambda}_j,{\gamma}_k\in \left[0,1\right]\kern1.75em j=1,2,\dots, J\ \mathrm{and}\ k=1,2,\dots, K \vspace*{-12pt} $$

$$ \sum_{j=1}^J{w}_j+\sum_{k=1}^K{\beta}_k=1\kern2em {w}_j,{\beta}_k\ge 0 $$

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1.4 F-WAMG Approach

The steps of the proposed F-WAMG approach are given in the following:

Step 1

The first step involves a meeting that consists of experts at the electronics board manufacturing company, and then identifies decision-makers for evaluation of suppliers.

Step 2

In the second step, evaluation criteria are given to the decision-makers. Then, each decision-maker chooses the appropriate criteria based on their expertise.

Step 3

In the third step, pairwise comparison matrices are constructed for all decision-makers to provide their opinions.

Step 4

In the fourth step, the consistency of the pairwise comparison matrices is calculated. Following Saaty’s (1980) approach consistencies are evaluated. If the results of the comparisons are consistent, the weights of the criteria are calculated using a FAHP method. Otherwise, the decision-makers are required to reassess their judgments.

Step 5

In the fifth step, all decision-makers assign a fuzzy score to each qualitative criterion to be converted into quantitative data. In this study, a five-point Likert-type scale was used to obtain experts’ opinions.

Step 6

In the sixth step, using the aggregated fuzzy decision matrix, fuzzy scores are defuzzified and crisp scores are obtained.

Step 7

In the last step, the following fuzzy multi-objective supplier selection model is solved. Here, w _j defines the weight of objective functions, where j defines the priority order of objective functions.

$$ \operatorname{Max}\ \sum_{j=1}^J{w}_j\cdot {\lambda}_j $$

$$ {\lambda}_j\le {\mu}_{Z_j}(x)\vspace*{-12pt} $$

$$ {\lambda}_j\ge {w}_j\vspace*{-12pt} $$

$$ {\lambda}_j\le {w}_{j-1}\kern1.75em j=2,\dots, J \vspace*{-12pt}$$

$$ {\lambda}_j\in \left[0,1\right]\kern1.75em j=1,2,\dots, J\vspace*{-12pt} $$

$$ \sum_{j=1}^J{w}_j=1\kern1.25em {w}_j\ge 0\vspace*{-12pt} $$

$$ {x}_i\ge 0\kern1.5em i=1,2,\dots, N $$

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