Today green supply chain is considered all around the world and supplier selection has been changed regarding these green and carbon emission criteria, so green supplier selection has been a major problem in this area. In this study we use fuzzy time function to assist managers in green supplier selection under uncertainty and ambiguity. This function will consider derivation from the goal during the time and by using it, and we will be able to have the best supplier in every period after having some modification in legal limitations for green supplier selection criteria. We use a fuzzy TOPSIS to have better initial weighting in TODIM, a discrete multicriteria method based on prospect theory in uncertainty (known as TODIM in Portuguese) decision making method. The results indicated that our proposed approach can easily and effectively accommodate criteria with gains and loss functions during time and also by using this method we will have a more reasonable predict of our suppliers ranking in future and that will help us in future investment in these suppliers. Finally it has been shown in car industries in Iran.
In recent years, the European Union (EU) has established various environmental policies, including the RoHS (Restricted Use of Hazardous Substances in Electronics and Electrical Equipment) as well as WEEE (Waste Electronics and Electrical Equipment) directives. So far, environmental management has evolved to include boundary-spanning activities in the upstream and the downstream supply chains. Sirvastava defined green supply chain management (GSCM) as a combination of environmental and supply chain management activities, including product design, material selection, manufacturing process, final product delivery, and end-of-life product management. With GSCM, firms can select from a wide variety of suppliers and leverage resources throughout the firm to eliminate the environmental impact of supply chain activities, Tseng [
Firms typically expect their suppliers to surpass environmental compliance and to develop efficient and green product design. In addition, suppliers are expected to assess the life cycle of a product. Although the qualitative criteria are littered with subjective perception because the GSCM evolution criteria tend to be subjective, qualitative, or described with linguistic information. Thus, it is extremely difficult for the decision makers to express their preference using exact numerical values, Zhang et al. [
A fuzzy set is a class of objects with grades of membership. A membership function is between zero and one, Zadeh [
There are some kinds of fuzzy numbers. Among the various shapes of fuzzy number, triangular fuzzy number (TFN) is the most popular one. It is represented with three points as
Fuzzy time function is an approach to considering time as an important factor in uncertainty. In many situations we have to change our approach because of the uncertainty and changes in criteria during time. Sometimes these kinds of changes cause extra cost for organization. With fuzzy time function we could predict when some new factors like technology will be used in our system and how they could affect our decisions. de Figueiredo and Perkusich, [
A fuzzy time function consists of three sections, optimistic, normal, and pessimistic related to time and these lines do not cross each other’s (Figure
Fuzzy time functions.
In fact, this function in each time represents a fuzzy triangular number (
According to (
For computing the FTF in this paper we introduce two ways.
To get precise decisions, it is recommended to use the separate functions for each period of time.
In some cases which fuzzy time function has more complicated function, we must use the combination of these two methods.
TOPSIS, one of the classical multicriteria decision making methods, was developed by Hwang and Yoon [
In the following, Chen’s fuzzy TOPSIS method is explained. Chen [
Linguistic variable representing triangular fuzzy numbers.
Fuzzy evaluation scores for alternatives | |
---|---|
Linguistic terms | Fuzzy score |
Very poor (VP) | (0, 0, 1) |
Poor (P) | (0, 1, 3) |
Medium poor (MP) | (1, 3, 5) |
Fair (F) | (3, 5, 7) |
Medium good (MG) | (5, 7, 9) |
Good (G) | (7, 9, 10) |
Very good (VG) | (9, 10, 10) |
In this study the linguistic variables used for each criterion and we will make FTF for each criterion during times. At the beginning weights of the criteria and fuzzy ratings of alternatives with respect to each criterion have been calculated, and the fuzzy multicriteria of decision-making problem can be expressed in matrix format as
The above normalization method preserves the ranges of normalized fuzzy decision matrix as
According to the weighted normalized fuzzy decision matrix
The distance of each alternative from
Obviously, when
TODIM is a discrete multicriteria method founded on prospect theory. The TODIM method has been successfully used and empirically validated in different applications. This is an experimental method based on how people make effective decisions in risky conditions. The shape of the value function of TODIM is identical to prospect theory’s gain and loss function. The global multicriteria value function of TODIM aggregates all measures of gains and losses by considering all criteria. Gomes and Rangel [
In previous methods used in TODIM or other MCDM methods, data have been collected based on alternative and criteria comparisons, but we use interval-valued triangular fuzzy numbers which consider the criteria with respect to alternatives in a deterministic time and these data collection will be continued in other times which are important for decision makers, or when we have some changes in criteria or alternatives. Table
Corresponding TFNS for linguistic preferences.
Linguistic preferences | Interval-valued TFNS |
---|---|
Very poor | [(0, 0), 0, (1, 1.5)] |
Poor | [(0, 0.5), 1, (2.5, 3.5)] |
Medium poor | [(0, 1.5), 3, (4.5, 5.5)] |
Fair | [(2.5, 3.5), 5, (6.5, 7.5)] |
Medium good | [(4.5, 5.5), 7, (8, 9.5)] |
Good | [(5.5, 7.5), 9, (9.5, 10)] |
Very good | [(8.5, 9.5), 10, (10, 10)] |
Let
The TFN is based on a three-value judgment: the minimum possible value
An interval-valued TFN.
Given
The distance between the reference value and each comparison value can be calculated by using definition (
These calculations are used to determine the distance between the reference value and the comparison value in the interval; after calculation we have a new interval TFN for every TFN as
The value function used in the prospect theory is described in the form of a power law expressed as
TODIM value function.
The TODIM method uses pairwise comparisons between the criteria by using technically simple resources to eliminate occasional inconsistencies resulting from these comparisons. TODIM allows value judgments to be performed on a verbal scale using hierarchy of criteria, fuzzy value judgments, and interdependence relationships among the alternatives. The decision matrix consists of alternatives and criteria. The alternatives
TODIM then calculates the partial dominance matrices and the final dominance matrix. The first calculation that the decision makers must define is a reference criterion (typically the criterion with the greatest importance weight). Therefore, wrc indicates the weight of the criterion
The dominance of an alternative over the other is as follows:
The term
Ordering the values
In this study we first use Fuzzy TOPSIS for weighting the criteria considering time factor and then we use this data to combine with data from TODIM which calculate from comparisons between alternatives regarding to criteria, and finally we will able to determine which alternative will be more reliable and more effective in any duration of time.
We use the abovementioned method to find out the best supplier in green supply chain management considering time variations as follows (Figure
Flowchart of the method.
A group of decision makers identified the criteria in GSCM which are important and also will be changed during time horizons.
Collect the opinion of decision makers with linguistic variables (Table
Use fuzzy TOPSIS to evaluate the criteria during time and initial weight of each criterion.
Collect the opinion of decision makers on alternatives, respectively, with linguistic variables (Table
Use TODIM for evaluating the final weight of each criterion against alternatives and the relationship between them.
Combine the results of TODIM and fuzzy TOPSIS to find out which supplier will be more effective from our company’s imagination now and in the future regarding the condition changes.
In this section we study on green supplier selection problem based on time factor in a Tier company in Iran. In this company regarding the expert researches we have 6 important criteria. The data have been collected from three expert decision makers who have more than 10 years of experience in this area and also have the ability to predict the market and its requirements in future. Table
Criteria for green supply chain.
Annual growth in green products ( |
|
Cost of revenue: extent that it remains flat to decreases each year ( |
|
Industry leadership: green market share ( |
|
Customer retention/percentage of growth with existing customers ( |
|
Customer acquisition: the number of new green customers/total revenue to new green customers ( |
|
Life cycle assessment ( |
Experts data collection.
Criteria | 10 months | 20 months | 30 months |
---|---|---|---|
|
P, MP, VP | MP, F, MP | MG, MP, F |
|
MP, VP, F | F, MP, MP | MP, F, MG |
|
VP, F, G | MP, MP, G | F, MG, VG |
|
F, G, F | MP, VG, G | MG, G, MP |
|
G, F, P | G, VG, G | P, F, F |
|
F, MP, G | G, F, F | MP, MP, P |
The data in Table
Criterion 1
(0.33,1.3,3)
(1.6,3.6,5.6)
(3,5,7)
The FTF from (
To get precise decisions, it is recommended to use the separate functions for each period of time. For example for criterion 1, using the function between 10 and 20 months is more exact than considering the FTF for any time. Calculations for finding the best green supplier in our study for the 15th and 25th months are presented in Table
Green supply chain criteria considering time.
15 months | 25 months | |
---|---|---|
|
(3.64, 5.58, 7.97) | (4.97, 7.08, 9.825) |
|
(1.82, 4.16, 6.32) | (5, 8.66, 8.99) |
|
(2.83, 5.16, 6.99) | (9.5, 10.82, 11.66) |
|
(8.33, 9.82, 10.49) | (0.33, 2.84, 5.51) |
|
(9.82, 11.4, 11.6) | (0, 0, 0) |
|
(13.5, 15.5, 17.23) | (0, 0, 0) |
By using FTF, we will have the variance for calculations that is useful in some other analysis which could not be achieved by ordinary triangular fuzzy numbers.
We use the first method for
Table
Criteria weights using fuzzy TOPSIS considering time periods.
15 months | 25 months | |
---|---|---|
|
0.5412 | 0.5322 |
|
0.55 | 0.533 |
|
0.5437 | 0.52 |
|
0.5256 | 0.55 |
|
0.523 | 0 |
|
0.51 | 0 |
By using the fuzzy TOPSIS method we have Table
As shown in Table
Criteria ranking for green supply chain considering time.
15 months | 25 months | |
---|---|---|
|
3 | 3 |
|
1 | 2 |
|
2 | 4 |
|
4 | 1 |
|
5 | 5 |
|
6 | 5 |
Table
Interval-valued TFNs decision matrix.
Criteria/alternative |
|
|
|
---|---|---|---|
|
[(5.5, 7.5), 9, (9.5, 10)] | [(4.5, 5.5), 7, (8, 9.5)] | [(4.5, 5.5), 7, (8, 9.5)] |
|
[(5.5, 7.5), 9, (9.5, 10)] | [(8.5, 9.5), 10, (10, 10)] | [(0, 1.5), 3, (4.5, 5.5)] |
|
[(4.5, 5.5), 7, (8, 9.5)] | [(2.5, 3.5), 5, (6.5, 7.5)] | [(4.5, 5.5), 7, (8, 9.5)] |
|
[(5.5, 7.5), 9, (9.5, 10)] | [(0, 1.5), 3, (4.5, 5.5)] | [(2.5, 3.5), 5, (6.5, 7.5)] |
|
[(8.5, 9.5), 10, (10, 10)] | [(5.5, 7.5), 9, (9.5, 10)] | [(4.5, 5.5), 7, (8, 9.5)] |
|
[(4.5, 5.5), 7, (8, 9.5)] | [(0, 0), 0, (1, 1.5)] | [(8.5, 9.5), 10, (10, 10)] |
Use TODIM methods; see Tseng et al. [
By applying TODIM approach, first
Matrix of alternative scores with respect to criteria.
|
|
| |
---|---|---|---|
|
0.4232 | 0.6933 | 0.6933 |
|
0.4232 | 0.1155 | 1.4598 |
|
0.6933 | 1.0532 | 0.1155 |
|
0.4232 | 1.4598 | 1.0532 |
|
0.1155 | 0.4232 | 0.6933 |
|
0.6933 | 1.9204 | 0.1155 |
Criteria weights.
|
|
|
|
|
| |
---|---|---|---|---|---|---|
|
0.144 | 0.159 | 0.148 | 0.233 | 0.098 | 0.217 |
After calculating weight of each criterion, the data must be normalized for calculation dominance weight of criteria. The normalized data is shown in Table
Normalized scores.
|
|
| |
---|---|---|---|
|
0.2338 | 0.3831 | 0.3831 |
|
0.2118 | 0.057 | 0.73 |
|
0.3723 | 0.5657 | 0.062 |
|
0.1441 | 0.4972 | 0.358 |
|
0.0937 | 0.3435 | 0.562 |
|
0.254 | 0.7037 | 0.0423 |
Equation (
Final weight of criteria by using TODIM.
|
|
|
|
|
| |
---|---|---|---|---|---|---|
|
−0.59 | −0.44 | −0.99 | −0.52 | −1.083 | −0.711 |
Normalization | 0.41 | 0.56 | 0.01 | 0.48 | 0 | 0.3 |
Negative numbers explain losses from goal.
Considering results in Table
Now the final conclusion will be conducted from Tables
By combination of Fuzzy TOPSIS which represents the weight of criteria of green supply chain with respect to time and TODIM method which shows the weight of alternatives according to criteria of supply chain we will have weights of criteria and alternatives in Tables
Criteria weight’s changes during time.
|
|
|
|
|
| |
---|---|---|---|---|---|---|
|
0.22 | 0.38 | 0.005 | 0.252 | 0 | 0.153 |
|
0.21 | 0.29 | 0.005 | 0.264 | 0 | 0 |
Alternative weights during time.
|
|
| |
---|---|---|---|
15 months | 0.47 | 0.86 | 0.98 |
25 months | 0.32 | 0.56 | 0.84 |
This study represents a new way to select supplier during time periods by using a hybrid MCDM. Using fuzzy TOPSIS to have more accurate weighting method for TODIM and then combining it with fuzzy time function (FTF) helped us to rank the criteria and alternatives in several time periods. The important aim of this study was to use fuzzy time function with a new approach to consider time for each triangular fuzzy number that helped us to find out which supplier in the future according to criteria is suitable for our green supply chain and when we should change our supplier. According to the results shown in Table
The authors declare that there is no conflict of interests regarding the publication of this paper.