Sustainable supplier selection model with a trade-off between supplier development and supplier switching

Abstract

Due to growing concerns regarding sustainability, purchasing decisions are challenging and difficult tasks for decision-makers. This difficulty has compelled purchasing companies to know and understand the whole purchasing process and to give importance to purchasing associated decisions. A long-term relationship and investment are required for purchasing decisions because they impact significantly on a company’s performance and supply chain. Hence, supplier selection and sourcing strategy selection decisions are among a firm’s most important problems. In this study, sourcing strategy decisions include supplier development, which helps suppliers to improve their performance, and supplier switching, which searches for more proficient alternatives for supply. To solve these problems, this study provides an integrated multi-criteria decision-making (MCDM) model. The model contains four stages. First, the right set of sustainable key performance indicators (SKPIs) for evaluating the performance of suppliers is identified through a literature survey and discussions with the decision-making team. Second, the best worst method-measurement of alternatives and ranking according to the compromise solution method (BWM-MARCOS) approach is applied to determine the priority weights of SKPIs and the priority weights of incumbent and new suppliers based on identified SKPIs. Third, a bi-objective mathematical model is developed to determine which optimum sourcing strategy and potential supplier should be chosen based on the priority of incumbent and new suppliers while optimizing cost and sustainable performance. Fourth, the mathematical model is solved using Epsilon constraint method and min–max fuzzy approach. The applicability and efficiency of the proposed integrated MCDM model is demonstrated with a real case study from a home appliance manufacturing company. The key findings reveal that the proposed model can be utilized for strategic and effective sourcing planning. One of the important contributions of this work is to provide suggestions for deciding the appropriate sourcing strategy for suppliers using the outputs of the mathematical model.

Appendices

Appendix A

1.1 A.1 Multi-criteria decision making (MCDM)

MCDM is the study of methods that are applied to make decisions in the presence of multiple, usually conflicting, criteria (Törn, 1980). MCDM has become a powerful tool to solve design problems that involve multiple conflicting quantitative and qualitative criteria. It includes different perspectives and varied knowledge domains of the decision makers (DMs) so that all the criteria are properly catered for optimizing the problem and attaining appropriate decisions as per the objective (Mousavi-Nasab, and Sotoudeh-Anvari, 2017). Hence, MCDM methods are best utilized in situations where conjoint decision analysis is required and the conflicts among conjoint DMs are needed to transform into priority weights (Chowdhury & Paul, 2020). Ching and Kwangsun (1981) have classified the problems of MCDM broadly into two categories: 1) Multiple Attribute Decision Making (MADM), 2) Multiple Objective Decision Making (MODM). The aim of the study is to utilize the combined efficiencies and effectiveness of both MODM and MADM. The combined approach is extremely beneficial in decision making problem situations that include the multi-dimensions of sustainability objectives. It facilitates an efficient framework to model the complexities while formulating the supply chain problems and enables DMs for participating actively in decision making. The key concepts of MODM and MADM techniques used in the study are briefly described below.

1.1.1 A.1.1 Multiple attribute decision making (MADM)

MADM methods are applied to evaluate and solve discrete problems with limited number of predetermined alternatives (Zavadskas & Turskis, 2011). Evaluating a limited number of alternatives inherent in a range of attributes is difficult; prioritizing them adds further complexity. To solve such arrays of problems, MADM methods are best suited. In MADM, the final selection of the alternative is decided by various alternatives’ comparisons with respect to each inter- and intra-attribute. The comparisons may include explicit or implicit tradeoffs. The MADM methods BWM and MARCOS applied in this study to evaluate the supplier performance are explained briefly below while we provide the advantages of both over other MADM methods.

1.1.1.1 A.1.1.1 Best–worst method

The best worst method (BWM) is a MADM method that has been proposed by Rezaei (2015). BWM is based on pairwise comparisons; the advantages of this method over other MCDM methods are: 1) it requires less pairwise comparison data entries as compared to other full pairwise comparison based MADM methods, and 2) the consistency of results generated from BWM are better than the other full pairwise comparison-based MADM methods. Given the above advantages of BWM, it has become a popular MADM technique and is extremely useful in various applications such as supplier selection (Rezaei et al., 2016), social sustainability assessment of supply chains (Ahmadi et al., 2017), sustainable Manufacturing (Malek & Desai, 2021), R&D performance evaluation of firms (Salimi & Rezaei, 2018), facility location selection (Kheybari et al., 2019), sustainable manufacturing barriers prioritization (Malek & Desai, 2019), risk analysis (Yazdi et al., 2020), and Lean six sigma enablers prioritization (Singh et al., 2021).

As discussed previously, a set of SKPIs $\{{SKPI}_{1}, {SKPI}_{2},\dots ,{SKPI}_{U}\}$ are divided into three categories. The sets of economic, environmental, and social sub-SKPIs $\{{SKPI}_{1}^{Eco},{SKPI}_{2}^{Eco},\dots ,{SKPI}_{L}^{Eco}\}$, $\{{SKPI}_{1}^{Env}, {SKPI}_{2}^{Env}, \dots , {SKPI}_{M}^{Env}\}$, and $\{{SKPI}_{1}^{Soc}, {SKPI}_{2}^{Soc}, \dots , {SKPI}_{N}^{Soc}\}$ respectively are chosen for sustainable evaluation of suppliers. The steps of BWM for finding the importance of ranking of SKPIs are structured as follows:

Step 1: Determine the best and worst SKPI:

The best economic ${SKPI}^{Eco}$ $\left({SKPI}_{B}^{Eco}, B\in \left\{\mathrm{1,2},\dots ,L\right\}\right)$ i.e., the most important economic SKPI and the worst economic ${SKPI}^{Eco}$ $({SKPI}_{W}^{Eco}, W\in \left\{\mathrm{1,2},\dots ,L\right\}))$ i.e., the least important economic SKPI are identified by each of the k DMs.

Step 2: Compute the preference of ${SKPI}_{B}^{Eco},$ over all the other SKPIs:

Using a scale of 1–9, the preference of ${SKPI}_{B}^{Eco}$ over each ${SKPI}_{h}^{Eco}$ is calculated for kth DM, denoted as ${a}_{Bh}^{k} \mathrm{with }{a}_{BB}^{k}=1 .$ This results in the best-to-others (BO) vector ${A}_{B}^{k} = ({a}_{B1}^{k}, {a}_{B2}^{k}, \dots , {a}_{BL}^{k})$

Step 3: Compute the preference of ${SKPI}_{W}^{Eco}$ over all the other SKPIs:

Using the same scale, the preference of each ${SKPI}_{h}^{Eco}$ over worst KPI ${SKPI}_{W}^{Eco}$ is calculated for kth DM, denoted as ${a}_{hW}^{k} \mathrm{with }{a}_{WW}^{k}=1.$ This results in the others-to-worst (OW) vector ${A}_{W}^{k} = ({a}_{1W}^{k}, {a}_{2W}^{k}, \dots , {a}_{LW}^{k})$

Step 4: Calculate the optimal weights of each ${SKPI}^{Eco}$ for each DM.

To determine the unique optimal weighting vector $\left({w}_{1}^{k*},{ w}_{2}^{k*},\dots ,{w}_{L}^{k*}\right)$ of the set of SKPIs for kth DM, the following maximum absolute difference is to be minimized:

$$ max\left\{ {\left| {w_{B}^{k*} - a_{Bl}^{k} w_{l}^{k*} } \right|,\left| {w_{l}^{k*} - a_{lW}^{k} w_{W}^{k*} } \right|;l = 1, 2, \ldots ,L} \right\} $$

This is achieved by the following optimization model:

$$ \begin{aligned} & min\mathop {\max }\limits_{l} \{ |\frac{{w_{B}^{k*} }}{{w_{l}^{k*} }} - a_{Bl}^{k} \left| , \right|\frac{{w_{l}^{k*} }}{{w_{W}^{k*} }} - a_{lW}^{k} |\} \\ & {\text{Subject to}} \\ & \mathop \sum \limits_{l} w_{l}^{k*} = {1} \\ & w_{l}^{k*} \ge 0,\quad \forall l \in \left\{ {1 ,2, \ldots ,L} \right\} \\ \end{aligned} $$

(P1)

The above fractional programming problem formulation (P1) is transformed into a linear programming problem formulation as given below (Rezaei, 2016):

$$ \begin{aligned} & \min {\upxi }^{k} \\ & {\text{Subject to}} \\ & \left| {w_{B}^{k} - a_{Bl}^{k} w_{l}^{k} } \right|\} \le {\upxi }^{k} \quad \forall l \in \left\{ {1, 2, \ldots ,L} \right\} \\ & \left| {w_{l}^{k} - a_{lW}^{k} w_{W}^{k} } \right|\} \le {\upxi }^{k} \quad \forall l \in \left\{ {1, 2, \ldots ,L} \right\} \\ & \mathop \sum \limits_{l} w_{l}^{k} = {1} \\ & w_{l}^{k} \ge 0, \quad \forall { }l \in \left\{ {1, 2, \ldots ,L} \right\} \\ \end{aligned} $$

(P2)

Problem (P2) provides a unique optimal weighting vector $\left( {w_{1}^{k*} , w_{2}^{k*} , \ldots ,w_{L}^{k*} } \right)$ and optimal value $\xi^{k*}$ for kth DM. The desirable value of $\xi^{k*}$ is closer to zero as it indicates a high consistency and high reliability.

Problem (P2) is solved to compute the optimal weighting vector for each DM. Further, for computing the final weights of each $SKPI^{Eco}$, the average of all the attained optimal weights for DMs is calculated by given formula.

$$ w_{l}^{Eco} = \frac{{\mathop \sum \nolimits_{k = 1}^{K} w_{l}^{k*} }}{K}\quad \forall l = 1,2, \ldots ,L. $$

(11)

The final optimal weighting vector ($w_{1}^{Eco} , w_{2}^{Eco} , \ldots ,w_{L}^{Eco} )$ is determined and provides the priority weights of each $SKPI^{Eco}$. Similarly, this procedure is performed for $SKPI^{Env}$ and $SKPI^{Soc}$ to determine the optimal weighting vectors ($w_{1}^{Env} , w_{2}^{Env} , \ldots ,w_{M}^{Env} )$ and ($w_{1}^{Soc} , w_{2}^{Soc} , \ldots ,w_{N}^{Soc} )$ respectively.

Further, the procedure is repeated for three categories (economic, environmental, and social) and determines the optimal weighting vector $\left( {w^{Eco} , w^{Env} , w^{Soc} } \right)$.

To compute the global weights of each SKPI $w_{1}^{SKPI} , w_{2}^{SKPI} , \ldots ,w_{U}^{SKPI}$, the weight obtained for each SKPI belong to each category is multiplied by the weight of the category.

1.1.1.2 A.1.1.2 MARCOS

Measurement of Alternatives and Ranking according to Compromise Solution (MARCOS) is a MADM technique developed by Stevic, Pamučar, Puška, and Chatterjee (2020). The main advantage of this method over other MADM methods is its consideration of ideal and anti-ideal alternatives at the initial stage of the evaluation process. The closer determination of utility degree with respect to ideal and anti-ideal solutions provides greater stability while considering a large set of criteria and alternatives. The steps of the MARCOS method for computing the priority weights of incumbent and new suppliers with respect to SKPIs are described as follows:

Step 1: Develop an initial decision-making matrix

In this step, a decision matrix is developed for incumbent suppliers with respect to each DM. The opinions of all DMs are included to form a decision matrix for supplier evaluation with respect to SKPIs. DMs are asked to evaluate the U SKPIs for each incumbent supplier on the scale of five degrees: 1,3,5,7 and 9, where 1 = very poor, 3 = poor, 5 = average, 7 = good, 9 = very good. The evaluation decision matrix filled by kth DM is

$$ T^{k} = \left[ {\begin{array}{*{20}l} {x_{11}^{k} } \hfill & {x_{12}^{k} } \hfill & \cdots \hfill & {x_{1U}^{k} } \hfill \\ {x_{21}^{k} } \hfill & {x_{22}^{k} } \hfill & \cdots \hfill & {x_{2U}^{k} } \hfill \\ \cdots \hfill & \cdots \hfill & \cdots \hfill & \cdots \hfill \\ {x_{I1}^{k} } \hfill & {x_{I2}^{k} } \hfill & \cdots \hfill & {x_{IU}^{k} } \hfill \\ \end{array} } \right] $$

(12)

In group decision-making, evaluation decision matrices formed by members of expert panel are aggregated into initial decision-making matrix by taking the average of evaluation decision matrices. The initial decision-making matrix is

$$ T = \left[ {\begin{array}{*{20}l} {x_{11} } \hfill & {x_{12} } \hfill & \cdots \hfill & {x_{1U} } \hfill \\ {x_{21} } \hfill & {x_{22} } \hfill & \cdots \hfill & {x_{2U} } \hfill \\ \cdots \hfill & \cdots \hfill & \cdots \hfill & \cdots \hfill \\ {x_{I1} } \hfill & {x_{I2} } \hfill & \cdots \hfill & {x_{IU} } \hfill \\ \end{array} } \right] $$

(13)

Step 2: Form an extended initial matrix

To extend the initial decision-making matrix, the ideal (AI) and anti-ideal (AAI) solutions are computed. The AI solution is the best incumbent supplier with respect to SKPIs, whereas the AAI solution is the worst incumbent supplier with respect to SKPIs. Based on the nature of the SKPIs, AI and AAI are defined as follows:

$$ AI = \mathop {\max }\limits_{i} x_{iu } \, if\,u\epsilon Ben\,and\, \mathop {\min }\limits_{i} \,x_{iu} \,if\,u\epsilon Cos $$

(14)

$$ AAI = \mathop {\min }\limits_{i} x_{iu} \, if\,u\epsilon Ben\,and\,\mathop {\max }\limits_{i} \,x_{iu } \,if\, u\epsilon Cos $$

(15)

where Ben: a benefit group of SKPIs, and Cos: a group of cost SKPIs.

The extended initial matrix X is performed as follows:

(16)

Step 3: Normalize the extended initial matrix

The extended initial matrix X is normalized to obtain normalized extended initial matrix $Y = \left[ {y_{iu} } \right]_{I \times U}$ by using the following equations:

$$ y_{iu} = \frac{{x_{ai} }}{{x_{iu} }} \,if\, u\epsilon {\text{Cos}} $$

(17)

$$ y_{iu} = \frac{{x_{iu} }}{{x_{ai} }}\,if\, u\epsilon Ben $$

(18)

where $x_{ai}$ and $x_{iu}$ are the elements from the initial decision matrix.

Step 4: Determine the weighted matrix

The weighted matrix $Z = \left[ {z_{iu} } \right]_{I \times U}$ is computed by multiplying the normalized matrix Y with the weight coefficient of the SKPI $w_{u}^{SKPI}$, using the following expression:

$$ z_{iu} = y_{iu} \times w_{u}^{SKPI} $$

(19)

Step 5: Calculate the utility degree of suppliers

The utility degree of each incumbent supplier with regard to anti-ideal and ideal solution are computed using the following expressions:

$$ P_{i}^{ - } = \frac{{Q_{i} }}{{Q_{aai} }} $$

(20)

$$ P_{i}^{ + } = \frac{{Q_{i} }}{{Q_{ai} }} $$

(21)

where $Q_{i}$ represents the sum of the elements of the weighted matrix Z using following expression:

$$ Q_{i} = \mathop \sum \limits_{i = 1}^{I} z_{iu} $$

(22)

Step 6: Determine the utility function of alternatives

The utility function of each incumbent supplier with regard to the ideal and anti-ideal solution is determined using the following expression:

$$ f\left( {P_{i} } \right) = \frac{{P_{i}^{ + } + P_{i}^{ - } }}{{1 + \frac{{1 - f\left( {P_{i}^{ + } } \right)}}{{f\left( {P_{i}^{ + } } \right)}} + \frac{{1 - f\left( {P_{i}^{ - } } \right)}}{{f\left( {P_{i}^{ - } } \right)}}}}; $$

(23)

where $f\left( {P_{i}^{ - } } \right)$: the utility function with regard to the anti-ideal solution and $f\left( {P_{i}^{ + } } \right):$ the utility function with regard to the ideal solution. These are computed by using the following expression:

$$ f\left( {P_{i}^{ - } } \right) = \frac{{P_{i}^{ + } }}{{\left( {P_{i}^{ + } + P_{i}^{ - } } \right)}} $$

(24)

$$ f\left( {P_{i}^{ + } } \right) = \frac{{P_{i}^{ - } }}{{\left( {P_{i}^{ + } + P_{i}^{ - } } \right)}} $$

(25)

Step 7: Compute the weightage of alternatives

The priority weights of incumbent suppliers are computed by normalizing the final utility function values. For each incumbent supplier, it is desirable to achieve highest utility function value.

This procedure is repeated for the set of new suppliers to determine their priority weights.

1.1.2 A.1.2 Multiple objective decision making (MODM)

The Multiple objective decision making (MODM) technique is best suited for continuous decision spaces and associated with the problem where the alternatives are non-predetermined (Zavadskas et al., 2014). The aim of considered problem is to design the 'best' alternative under consideration of a set of quantifiable objectives and a set of well-defined designed constraints. MODM facilitates a process of obtaining some tradeoff information, implicit or explicit, between the stated quantifiable objectives and also between stated or unstated nonquantifiable objectives.

Real world decision-making problems generally have multi-objectives that cannot be optimized simultaneously due to inherent incommensurability and conflict between these objectives. Thus, to get the best compromise solution, achievement of trade-off between these objective plays a main role. Several methodologies are proposed for solving MODM problems in the existing literature (Hwang et al., 1993).

Mathematically, MODM problems can be expressed as follows:

$$ \min F\left( x \right) = [f_{1} \left( x \right),f_{2} \left( x \right), \ldots ,f_{O} \left( x \right)]^{T} $$

s.t.

$$ x\epsilon S = {\text{\{ }}x{|}g_{h} \left( x \right){)}\left\{ { \ge , = , \le } \right\}0, h = 1,2, \ldots ,H\} $$

where $S \subseteq R^{n}$ is the feasible space (Steuer, 1986).

The problem consists of H constraints and O objectives. $f_{o} \left( x \right)$ and $g_{h} \left( x \right)$, can be linear or non-linear.

As discussed earlier, optimization of all the objectives simultaneously is not possible. In this case, the concept of non-inferiority i.e., known as efficiency or Pareto optimality is utilized to obtain the solution to the MODM problems. This concept is based on the following definitions (Hsiao et al., 1994):

Definition 1

The feasible region S is the set of state vectors x that satisfy the constraints: $S = {\text{\{ }}x{|}g_{h} \left( x \right){)}\left\{ { \ge , = , \le } \right\}0, h = 1,2, \ldots ,H\}$.

Definition 2

A point $\check{x}\epsilon S$ is a local non-inferior point if there exists an $\rho > 0$ such that in the neighborhood $N\left( {\check{x},\rho } \right)$ of $\check{x}$, there exists no other point x such that (i) $f_{o} \left( x \right) \le f_{o} \left( {\check{x}} \right),o = 1,2, \ldots ,O$ and (ii) $f_{{o^{{\prime }} }} \left( x \right) < f_{{o^{{\prime }} }} \left( {\check{x}} \right),$ for some $o^{{\prime }} \epsilon \left\{ {1,2, \ldots ,O^{{\prime }} } \right\}$.

Definition 3

A point $\check{x}\epsilon S$ is a global non-inferior point if and only if there exists no other point x such that (i) $f_{o} \left( x \right) \le f_{o} \left( {\check{x}} \right),i = 1,2, \ldots ,O$ and (ii) $f_{{o^{{\prime }} }} \left( x \right) < f_{{o^{{\prime }} }} \left( {\check{x}} \right),$ for some $o^{{\prime }} \epsilon \left\{ {1,2, \ldots ,O^{{\prime }} } \right\}$.

A non-inferior solution of a MODM problem is one in which any improvement of one objective function can be achieved only at the expense of at least one of the other objectives. In general, there are an infinite number of (global) non-inferior points for a given MODM problem; this makes the task of finding the collection of such points called the non-inferior set extremely difficult.

For generating an entire non-inferior set, there are few methods such as the weight sum method, kth-objective method, and the Epsilon constraint method. In the current study, the Epsilon constraint method, applied to solve the proposed optimization model, is discussed in detail as follows.

1.1.2.1 A.1.2.1 Epsilon constraint method

The Epsilon constraint is a MODM approach, proposed by Haimes (1971), to generate Pareto optimal solutions. These solutions provide a clear understanding of the Pareto optimal set. In this method, initially the primary objective function and secondary objective functions are decided (Engau & Wiecek, 2007). Further, the MODM problem is transformed into single objective problem by shifting the other objectives in constraints with some allowable amount $\varepsilon$ (Nouri et al., 2018). The advantages of $\varepsilon$-constraint method over other MODM methods are such as (i) Weighting approach results in merely Pareto optimal extreme solutions for linear models, whereas non-extreme solutions can be produced through applying ε-constraint method. (ii) Unlike the weighting approach, in multi-objective problems via integer programming as well as mixed-integer linear programming ones, unsupported Pareto optimal solutions can be produced by ε-constraint method. (iii) Weighting approach highly depends on the scaling of objective functions while this issue is not important in the ε-constraint method. (iv) The controlled number of Pareto optimal solutions can be produced in ε-constraint method by effectively tuning the number of grid points in the range of each objective function.

Based on $\varepsilon$-constraint method, a single-objective model of problem (P3) is represented as follows:

$$ \begin{aligned} & {\text{Objective}}\,{\text{Function}} = Min f_{1} \left( x \right) \\ & s.t. \\ & f_{o} \left( x \right) \ge \epsilon_{o} ,o = 2,3, \ldots ,O \\ & x\varepsilon S = {\text{\{ }}x{|}g_{h} \left( x \right){)}\left\{ { \ge , = , \le } \right\}0, h = 1,2, \ldots ,H\} \\ \end{aligned} $$

For generating the Pareto optimal solutions, the $\varepsilon_{o}$ are altered from minimum to maximum amount of $f_{o} \left( x \right)$ and the goal is obtained.

1.2 A.2 Fuzzy decision

For deciding the best compromised solution, max–min fuzzy method is utilized in this study. This method a fuzzy membership function in the interval [0,1] to each solution in the Pareto front (Cao et al., 2019). The fuzzy membership functions for oth objective function are as follows:

$$ \mu_{o}^{r} = \left\{ {\begin{array}{*{20}l} 1 \hfill & {\theta_{o}^{r} \le \theta_{o}^{min} } \hfill \\ {\frac{{\theta_{o}^{max} - \theta_{o}^{r} }}{{\theta_{o}^{max} - \theta_{o}^{min} }}} \hfill & {\theta_{o}^{min} \le \theta_{o}^{r} \le \theta_{o}^{max} } \hfill \\ 0 \hfill & {\theta_{o}^{r} \ge \theta_{o}^{max} } \hfill \\ \end{array} } \right. $$

(26)

where $\mu_{o}^{r}$: the optimality degree of the rth solution of oth objective function.

In the oth objective function $f_{o}^{min}$ and $f_{o}^{max}$ are the minimum and maximum values of Pareto solutions. Then, per unit quantities are compared and the minimum value is selected based on Eq. (17). Finally, the best point as trade-off solution for multi-objective solution is the maximum amount of all the minimums Eq. (18).

$$ \mu^{r} = \min \left( {\mu_{1}^{r} , \ldots ,\mu_{o}^{r} } \right);\forall r = 1,2, \ldots .Rp $$

(27)

$$ \mu^{max} = \max \left( {\mu^{1} ,\mu^{2} , \ldots ,\mu^{Rp} } \right). $$

(28)

Appendix B

See Table 5.