Green supplier selection and order allocation in a low-carbon paper industry: integrated multi-criteria heterogeneous decision-making and multi-objective linear programming approaches

Abstract

The low-carbon supply chain is one of the predominant topics towards a green economy and it establishes the opportunity to reduce carbon emissions across the product value chain. This paper focuses on recycling and optimized sourcing in the paper industry as a case company. The main objective is to engage the case company with their supplier networks to diminish the greenhouse gases (GHG) emissions and cost in their production process. It proposes a model to support the selection of the best green supplier and an allocation of order among the potential suppliers. The proposed model contains a two-phase hybrid approach. The first phase presents the rating and selection of potential suppliers by considering economics (cost), operational factors (quality and delivery), and environmental criteria (recycle capability and GHG emission control) using Fuzzy Technique for Order of Preference by Similarity to Ideal Solution (Fuzzy TOPSIS) methodology. The second phase presents the order allocation process using multi-objective linear programming in order to minimize cost, material rejection, late delivery, recycle waste and $\mathrm{CO}_{2}$ emissions in the production process. A case study from a paper manufacturing industry is presented to elucidate the effectiveness of the proposed model. The results demonstrate a 26.2 % reduction of carbon emission by using recycle products in the production process. The firm benefits by forming a systematic methodology for green supplier evaluation and order allocation. Finally, a conclusion and a suggested direction of future research are introduced.

Appendices

Appendix 1

Summary of MCDM approaches for supplier selection and order allocation

MCDM approach	Author
Category: supplier selection; single approach
Case-based reasoning (CBR)	Choy et al. (2003a)
Neural networks	Choy et al. (2003b)
Genetic algorithm (GA)	Ding et al. (2005)
AHP	Haq and Kannan (2006)
ANP	Gencer and Gurpinar (2007), Bhattacharya et al. (2014)
DEA	Wu et al. (2007)
Fuzzy TOPSIS	Kannan et al. (2009)
ISM	Kannan et al. (2010)
Fuzzy extent analysis	Kannan and Murugesan (2011)
Category: order allocation; single approach
Mathematical programming	Wang et al. (2004)
Category: order allocation; integrated approach
FAHP and MOLP	Shaw et al. (2012)
Category: supplier selection and order allocation; integrated approach
MAUT and LP	Sanayei et al. (2008)
ANP and MOMILP	Demirtas and Üstün (2008)
AHP and MO Possibilistic LP	Özgen et al. (2008)
CBR and MIP	Faez et al. (2009)
FANP and MOLP	Lin (2009)
AHP and Dynamic programming	Mafakheri et al. (2011)
Shannon entropy and LP	Ghorbani et al. (2012)
FAHP and Fuzzy TOPSIS	Zouggari and Benyoucef (2012)
AHP and GP	Erdem and Göçen (2012)
Category: green supplier selection; single approach
Knowledge based system	Humphreys et al. (2003b)
FEAHP	Lee et al. (2009)
Multi-objective goal programming	Yeh and Chuang (2011)
Grey theory	Tseng (2011)
Fuzzy TOPSIS	Kannan et al. (2014a)
Category: green supplier selection; integrated approach
Rough set theory and Grey system	Bai and Sarkis (2010)
DEMATEL, ANP and TOPSIS	Büyüközkan and Çifçi (2012)
Category: green supplier selection and order allocation; integrated approach
AHP and MODP	Mafakheri et al. (2011)
FAHP, Fuzzy TOPSIS and MOLP	Kannan et al. (2013)

Appendix 2

1.1 The proposed FAHP method for group decision making in MCDM

AHP was first developed by Saaty (1980) to determine the comparative importance of events in MCDM problem by examining the pair-wise comparisons of decision criteria. The pair-wise comparison matrix yields weight from the information of DMs and sometimes the information is uncertain and vague. The FAHP was developed to overcome the uncertainties in AHP and FAHP proposed by Zeng et al. (2007) used in this paper; the steps are presented as follows:

By following the initial condition of MCDM problem as described in the Sect. 3.2 (step 1 to 3), the steps of FAHP are

Step 1: The aggregation of the individual DMs TrFN preferences on each alternative with respect to each criterion in to group TrFN is defined by

$$\begin{aligned} \tilde{P}_{ij} =p_{ij}^1 \otimes \alpha ^{1}\oplus p_{ij}^2 \otimes \alpha ^{2}\oplus \ldots p_{ij}^l \otimes \alpha ^{l}, \;\; i=1,2,..,m;\;\; j=1,2,\ldots ,n; \;\; l=1,2,\ldots ,L \end{aligned}$$

where $\tilde{P}_{ij}$ is the aggregated TrFN preference of criteria $C_j$ on alternative $A_i$, $p_{ij}^l$ is the individual TrFN preference of criteria $C_j$ on alternative $A_i$ by $M^{l}$ and $\alpha ^{l}$ is the crisp weight of DM.

Step 2: The pair-wise comparison matrix of individual DMs TrFN preferences on each criteria is constructed as follows:

$$\begin{aligned} \tilde{A}^{l}=\left[ {\tilde{a}_{ij}^l } \right] _{n\times n} \end{aligned}$$

where $\tilde{a}_{ij}^l$ is the TrFN pair-wise comparison of criteria $C_i^l$ with $C_j^l$ where $i=1,2,..,n; j=1,2,\ldots ,n$

In this study, the following scale is used for pair-wise comparison of linguistic preferences on selected criteria by DMs. For example, if VH preference is compared with H preference, then preference VH is moderately strong over H preference and reciprocal for reverse comparison. Likewise, VH preference is essentially strong over MH preference and H preference is moderately strong over MH preference.

 Linguistic scale for fuzzy pair-wise comparisons

Comparison variable	Trapezoidal fuzzy scale	Trapezoidal fuzzy reciprocal scale
Equally strong	(1, 1, 1, 1)	(1, 1, 1, 1)
Moderately strong	(2, 2.5, 3.5, 4)	(0.25, 0.29, 0.4, 0.5)
Essentially strong	(4, 4.5, 5.5, 6)	(0.17, 0.18, 0.22, 0.25)
Very strong	(6, 6.5, 7.5, 8)	(0.13, 0.13, 0.15, 0.17)
Extremely strong	(8, 8.5, 9, 9)	(0.11, 0.11, 0.12, 0.13)

Step 3: The aggregation of pair-wise comparison of criteria can be calculated by:

$$\begin{aligned}&\tilde{a}_{ij} =\tilde{a}_{ij}^1 \otimes \alpha ^{1}\oplus \tilde{a}_{ij}^2 \otimes \alpha ^{2}\oplus \ldots .\oplus \tilde{a}_{ij}^l \otimes \alpha ^{l},\quad i=1,2,..,m;\\&\quad j=1,2,\ldots ,n;\quad l=1,2,\ldots ,L \end{aligned}$$

Step 4: In order to convert the aggregated TrFN of criteria into matching crisp values that can adequately represent the group preferences, a proper defuzzification is needed. After defuzzification, the crisp pair-wise comparison matrix between $C_i^l$ and $C_j^l$ is constructed as follows:

$$\begin{aligned} A=a_{ij} ={ \begin{array}{ccccc} &{} {C_1 }&{} {C_2 }&{} {\ldots }&{} {C_n } \\ {C_1 }&{} 1&{} {a_{12} }&{} {\ldots }&{} {a_{1n} } \\ {C_2 }&{} {1/{a_{12} }}&{} 1&{} {\ldots }&{} {a_{2n} } \\ {\ldots }&{} {\ldots }&{} {\ldots }&{} {\ldots }&{} {\ldots } \\ {C_n }&{} {1/{a_{1n} }}&{} {1/{a_{2n} }}&{} {\ldots }&{} 1 \\ \end{array} }, \quad i,j=1,2,\ldots ,n \quad \hbox { where } a_{ii} =1,\quad a_{ji} =1/{a_{ij} } \end{aligned}$$

Calculate the consistency ratio (CR) of the pair-wise comparison to check the consistency of the judgment made by the DMs. Saaty (1980) indicates that if the CR value equal to 0 then the judgments are perfectly consistent, and if it is more than 0.1 then the judgments may be inconsistent.

Step 5: The priority weights of criteria in the matrix A can be calculated by using the arithmetic averaging method.

$$\begin{aligned} w_j =\frac{1}{n}\sum \limits _{j=1}^n {\frac{a_{ij} }{\sum \nolimits _{k=1}^n {a_{ij} } }} \quad i,j=1,2,\ldots ,n \end{aligned}$$

where $w_j$ is the relative weight of criteria $C_j$

Step 6: The final group priority weight of each alternative $\left( {\tilde{F}S} \right) _i$ is calculated by

$$\begin{aligned} \left( {\tilde{F}S} \right) _i =\sum \limits _{j=1}^m {\tilde{P}_{ij} .w_j } \end{aligned}$$

Step 7: The matching crisp value $\left( {FS} \right) _i$ of group priority weight can be calculated and the best alternative are those that have higher value of $\left( {FS} \right) _i$.

1.2 The proposed FSAW method for group decision-making in MCDM

FSAW is simple in application and is used for solving MADM problems (Hwang and Yoon 1981; Virvou and Kabassi 2004). It consists of two basic steps (Hwang and Yoon 1981; Kabassi and Virvou 2004; Chou et al. 2008): (1) Compare the values of all attributes by proper scale. (2) Sum up the values of all the attributes for each alternative. The procedural steps of FSAW develop by adopting the initial condition given in Sect. 3.2 (step 1–3), and it is described as follows:

Step 1: The individual preference weight of each criterion by each DM is converted to a group preference weight for each criterion by

$$\begin{aligned} \tilde{w}_j =\left( {\tilde{w}_j^1 \otimes \alpha ^{1}} \right) \oplus \left( {\tilde{w}_j^2 \otimes \alpha ^{2}} \right) \oplus \ldots \oplus \left( {\tilde{w}_j^l \otimes \alpha ^{l}} \right) \hbox { where} \quad j=1,2,\ldots ,n; l=1,2,\ldots ,L \end{aligned}$$

Step 2: The fuzzy group preference weight of each criteria is converted in to matching crisp value by proper defuzzification, and the normalized group weight of each criterion $C_j$ can be calculated by

$$\begin{aligned} w_j =\frac{d\left( {\tilde{w}_j } \right) }{\sum \nolimits _{j=1}^m {d\left( {\tilde{w}_j } \right) } },\quad j=1,2,\ldots ,m \end{aligned}$$

Step 3: The aggregated fuzzy decision matrix of DMs’ preferences on each alternative with respect to j criteria can be constructed as

$$\begin{aligned} \tilde{P}=\left[ {\tilde{p}_{ij} } \right] _{m\times n} \hbox {with}\quad i=1,2,..,m \quad \hbox { and }\quad j=1,2,\ldots ,n \end{aligned}$$

Step 4: The normalization decision matrix for alternative evaluation based on benefit and cost criteria is constructed by:

$$\begin{aligned} \bar{{S}}= & {} \left[ {{\begin{array}{cccc} {\tilde{S}_{11} }&{} {\tilde{S}_{12} }&{} {\ldots }&{} {\tilde{S}_{1n} } \\ {\tilde{S}_{21} }&{} {\tilde{S}_{22} }&{} {\ldots }&{} {\tilde{S}_{2n} } \\ .&{} . &{}&{} .\\ .&{} . &{}\ldots &{} .\\ {\tilde{S}_{m1} }&{} {\tilde{S}_{m2} }&{} {\ldots }&{} {\tilde{S}_{mn} } \\ \end{array} }} \right] \\ \tilde{S}_{ij}= & {} \left\{ {\frac{\tilde{p}_{ij} }{\mathop {\max }\limits _i \left\{ {d_{ij} } \right\} }} \right\} \end{aligned}$$

where $\max \left\{ {d_{ij} } \right\} \ >\ 0,\ \tilde{S}_{ij}$ denotes the transformed fuzzy rating of fuzzy benefit $p_{ij}$

$$\begin{aligned} \tilde{S}_{ij} =\left\{ {\frac{\mathop {\min }\limits _i \left\{ {a_{ij} } \right\} }{\tilde{p}_{ij} }} \right\} \end{aligned}$$

where $\min \left\{ {a_{ij} } \right\} \ >\ 0,\ \tilde{S}_{ij}$ denotes the transformed fuzzy rating of fuzzy cost $p_{ij}$

Step 5: The total fuzzy scores of individual alternatives are determined by multiplying the normalized decision matrix with the weight vector of each criteria as given by:

$$\begin{aligned} \bar{{F}}= & {} \bar{{S}}\otimes w^{T}=\left[ {{\begin{array}{cccc} {\tilde{S}_{11} }&{} {\tilde{S}_{12} }&{} {\ldots }&{} {\tilde{S}_{1n} } \\ {\tilde{S}_{21} }&{} {\tilde{S}_{22} }&{} {\ldots }&{} {\tilde{S}_{2n} } \\ .&{}.&{}&{}.\\ .&{}.&{}\ldots &{}.\\ {\tilde{S}_{m1} }&{} {\tilde{S}_{m2} }&{} {\ldots }&{} {\tilde{S}_{mn} } \\ \end{array} }} \right] \otimes \left[ {{\begin{array}{l} {w_1 } \\ {w_2 } \\ . \\ . \\ . \\ {w_n } \\ \end{array} }} \right] \\= & {} \left[ {{\begin{array}{c} {\tilde{S}_{11} \otimes w_1 \oplus \tilde{S}_{12} \otimes w_2 \oplus \ldots \oplus \tilde{S}_{1n} \otimes w_n } \\ {\tilde{S}_{21} \otimes w_1 \oplus \tilde{S}_{22} \otimes w_2 \oplus \ldots \oplus \tilde{S}_{2n} \otimes w_n } \\ . \\ . \\ . \\ {\tilde{S}_{m1} \otimes w_1 \oplus \tilde{S}_{m2} \otimes w_2 \oplus \ldots \oplus \tilde{S}_{mn} \otimes w_n } \\ \end{array} }} \right] =\left[ {{\begin{array}{c} {\tilde{f}_1 } \\ {\tilde{f}_2 } \\ . \\ . \\ . \\ {\tilde{f}_m } \\ \end{array} }} \right] =\left[ {\tilde{f}_i } \right] _{m\times 1} \ \end{aligned}$$

where $\tilde{f}_i =\left( {r_i ,s_i ,t_i ,u_i } \right) ,i=1,2,..,m$

Step 6: The matching crisp value $f_i$ of each alternative weight can be calculated and the best alternatives are those that have a higher value of $f_i$.