1 Introduction

The supplier selection decision-making process is a fundamental activity in supply chain management, since purchasing costs account for more than fifty percent of all firms’ expenses (Khan et al. 2018; Chang 2017). Supplier selection is often a complex, multi-criteria decision-making problem that requires thorough performance evaluation to create the most efficient supply network. Despite the financial imperative, other evaluation criteria should be considered such as reliable delivery, which can enhance production flow and decrease the overall (operational) cost. Dickson (1966) highlighted 23 criteria that can be considered by decision makers for supplier assessment, Ha and Krishnan (2008) expanded on this work, totalling 30. However, the most popular traditional business criteria are quality, cost, and delivery reliability; the most popular green criteria are: environmental management system, resource consumption, eco-design and waste management. Further supplier selection criteria can be found in Weber et al. (1991); Govindan et al. (2015); Mohammed 2020; Aissaoui et al. (2007) and Lorenc and Lerher (2019).

With the recognition of resource depletion, companies are ever increasingly required to consider the environmental impact of their supply chain (Koberg and Longoni 2018; Rezaei et al. 2017; Nujoom et al. 2018, 2019; Mohammed and Wang 2017; Mohammed et al. 2019a, b). Green supply chain management understands and accounts for the full range of purchasing, production, marketing, packaging and logistical activities from an environmental perspective (Burinskiene et al. 2018; Mohammed et al. 2018a, b; Sarkis 1999). Unfortunately, suppliers typically represent inevitable sources of external risk (Alikhani 2018; Jamshidi et al. 2018; Kaur and Singh 2016). It has been indicated that purchasing managers consider traditional and recently green criteria when assessing suppliers but neglecting resilience aspects (Ivanov 2017; Kannan et al. 2013). Christopher and Peck (2004) defined supply chain resilience “the ability of a [supply chain] to return to its original state or move to a new, more desirable state after being disturbed”. Resilience which was also defined as the capability of a system to efficiently adopt expected disruptions and back to its normal process, is a vital aspect of any supply chain management (Torabi et al. 2015). During the Japanese earthquake (2011), Apple’s iPad 2 production was negatively affected due to a lack of flash memory and super-thin battery (BBC News, 18 Mar 2011). This event also interrupted the automotive sector and retail supply chains in the UK (Hall, 16 Apr 2010). Recently, hurricane Sandy led to massive disruptions in US supply networks (Ortega and Taṣpınar 2018; Torabi et al. 2015). Therefore, designing a resilient supply chain is necessary to protect a business from unexpected events (Sáenz et al. 2018). Resilience criteria are mainly represented by a supplier’s capability to cope with risk and unexpected events more efficiently and quickly than other suppliers. The current work considers resilience criteria identified and analysed by Purvis et al. (2016). The work proposed a framework for the development and implementation of a resilient supply chain strategy, which illustrates the relevance of various management paradigms. The authors considered four pillars (enablers) as key factors to improve supply chain resilience including: robustness, agility, leanness and flexibility (RALF). Nevertheless, visibility (V) was also incorporated as a resilience sub-criterion suggested by the purchasing manager for this case study.

Since additional criteria such as environmental sustainability and resilience are paramount in designing a successful and competitive supply chain, supplier selection complexity has increased and the necessity for new methodologies is evident. These should be able to tackle this complexity by incorporating three main criteria: traditional business, green and resilience. The vast majority of current literature considers the green and resilient aspects of supplier selection separately. Realizing the fact that environmental sustainability works towards a system that can sustain its service considering traditional business responsibilities and complying with green development regulations. On the other hand, resilience works to avoid or mitigate an expected or unexpected disruption, or at least mitigate its negative impact towards an ideal goal of environmental sustainability. Hence, resilience and greenness are an ultimate goal of a healthy supply chain management since to obtain a supply chain that could sustain its sustainability, resilience aspect should also be considered simultaneously. Furthermore, the literature support and evident the connections between resilience and environmental sustainability. Derissen et al. (2011) investigated this relationship describing sustainability and resilience as normative and descriptive aspects respectively. Rose (2011) argued that sustainability practices support the improvement after a severe disruption. These practices would not be available without owning deep-rooted resilience linked to disruption recovery. Lebel et al. (2006) presented resilience aspect as a key factor for sustainability, and to cope with green development effectively, resilience management is paramount. Ivanov (2017) analysed the intersections between sustainability and resilience in supply chains aiming to design a resilient supply chain along with uncertainty reduction and sustainability improvement. Giannakis and Papadopoulos (2016) and Ivanov (2017) discuss that the development of environmentally sustainable and resilient supply chains can be improved via the modelling and development of decision support systems from sustainability and resiliency perspectives.

This paper aims to address this need and contributes to the related literature by proposing a unified supplier selection and order allocation approach that considers traditional, green and resilience criteria simultaneously. The evaluation criteria were identified from the literature (e.g., Ha and Krishnan 2008; Govindan et al. 2015; Aissaoui et al. 2007) and in collaboration with the purchasing manager of the real case under study. This includes: traditional (T) criteria (i.e. cost, quality, delivery reliability, operating capacity, turnover, and performance history and lead time); green (G) criteria (i.e., environmental management system, waste management and environmental certificate); resilience (R) criteria (i.e., RALF). The development of this approach can be subsumed into four phases. In phase one, the main traditional, green and resilience criteria and their sub-criteria were identified in a unified framework. AHP was used to integrate judgments from decision makers aiming to determine the weights of the criteria and sub-criteria as a second phase. In the third phase, TOPSIS was applied to evaluate and rank suppliers based on their TGR performance. In the fourth phase, the obtained weights from AHP and TOPSIS were then integrated into a developed multi-objective programming model (MOPM) used to obtain an order allocation plan. This supports decision makers’ evaluation regarding suppliers’ performance in which the order allocation plan is set considering suppliers’ gresilience performance. The MOPM was solved by using the ε-constraint method and TOPSIS was finally used to select the final Pareto solution. The usability of the developed approach was validated within a real case study. The real-world application of the developed approach with a manufacturing company is a practical impact of the current study. This study also contributes to enhancing the supplier selection strategy by incorporating traditional, green and resilience (Gresilience) criteria. The majority of existing literature includes traditional and green supplier selection criteria but not resilience requirements.

The rest of this paper is structured as follows. In the next section, the related literature review is presented as green supplier selection and resilience supplier selection. In Sect. 3, steps followed for applying AHP, TOPSIS are shortly explained. In Sect. 4, the MOPM developed for obtaining a green and resilient supplier selection and order allocation planner is described. In Sect. 5, the developed approach was applied within a real case study. Conclusions, managerial implications and future works are drawn in Sect. 6.

2 Literature review

2.1 Green supplier selection

Previous research studies on traditional criteria are more extensive than the less established green supplier selection (Koberg and Longoni 2018; Brandenburg and Rebs 2015; Govindan et al. 2015). An important work in the area of green supplier selection is Büyüközkan and Çifçi (2012) where they used fuzzy decision-making trial and evaluation laboratory (DEMATEL), fuzzy analytic network process (ANP) and fuzzy TOPSIS in the evaluation of green suppliers for a major manufacturing company, namely Ford Otosan. Recently, Govindan et al. (2015) reviewed published research from 1997 to 2011 on multi-criteria decision making (MCDM) algorithms and mathematical modelling used for green supplier selection problems. Khan et al. (2018) proposed a MCDM approach aimed at evaluating suppliers’ sustainable performance. The Fuzzy-Shannon Entropy approach was applied to quantify the sustainability criteria relative importance followed by the application of fuzzy-Inference system to evaluate and rank suppliers. Akman (2015) suggested a two-step supplier-assessment framework to evaluate green suppliers. Kannan et al. (2015) investigated a green supplier selection problem in a plastics manufacturing company using a fuzzy axiomatic design approach. Govindan and Sivakumar (2016) developed an integrated multi-criteria decision-making and multi-objective linear programming approach as an aid to select the best green supplier. Banaeian et al. (2018) compared TOPSIS, visekriterijumska optimizacija i kompromisno resenje (VIKOR) and grey relational analysis (GRA) methods to rank suppliers in the agri-food industry by considering economic and environmental criteria. Hamdan and Cheaitou (2017) applied TOPSIS together with AHP for supplier selection and order allocation based on green criteria. Trapp and Sarkis (2016) proposed a programming model that concurrently considers supplier selection with respect to economic and environmental responsibilities. Song et al. (2017) proposed an integrated approach for evaluating suppliers with respect to economic, green and social criteria using the merit of pairwise comparison method in determining relative importance. The strength of DEMATEL algorithm is in manipulating the complex and intertwined problems with fewer data, and the rough number’s advantage in flexibly dealing with vague information. Amorim et al. (2016) proposed an integrated framework to solve supplier selection problems in the processed food industry. As outlined in the literature, different algorithms were used to determine supplier selection and order allocation. However, Chai et al. (2013) and Govindan et al. (2015) show that AHP, VIKOR, TOPSIS and multi-objective programming are the most commonly used techniques.

2.2 Resilient supplier selection

Supply chain management includes a variety of complex activities which may be subjected to unexpected disruptions and resilience is crucial for mitigating them (Wang et al. 2016a, b; Torabi et al. 2015). The reviewed literature suggests that studies using quantitative approaches to solve resilient supplier problem are limited. Mitra et al. (2009) and Sawik (2013) identified several pillars and criteria that should be considered for selecting resilient suppliers. Haldar et al. (2014) developed a fuzzy MCDM approach for supplier selection considering the importance degrees of specific attributes as linguistic variables formulated by triangular and trapezoidal fuzzy numbers. Torabi et al. (2015) proposed a fuzzy stochastic bi-objective optimization model to solve a SS/OA problem to improve the supply chain resilience under operational and disruption risks. Sahu et al. (2016) proposed a supplier evaluation decision support system using VIKOR considering both general and resilience criteria. Pramanik et al. (2016) presented a fuzzy MCDM approach as an aid to developing a resilient supplier selection. Rajesh and Ravi (2015) applied AHP and ANP to supplier selection in resilient supply chains. Klibi and Martel (2012) formulated a mixed integer programming model for handling supplier selection and order allocation problem. Sawik (2013) designed a mixed-integer programming model to solve a supplier selection problem in a supply chain under disruption risks. Table 1 lists further studies conducted to solve the supplier selection problem considering green or resilience aspects.

Table 1 Related traditional green/traditional resilient supplier selection studies
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The literature review highlights a gap in presenting a unified supplier selection and order allocation approach that considers traditional, green and resilience criteria simultaneously. This can support decision makers in coping with green development and unexpected disruptions. This need has inspired the authors to develop a unified traditional business, green and resilient supplier selection and order allocation approach. It is realized from the abovementioned, analysis in literature review and to the best of our knowledge, the proposed study delivers the first study of using the MCDM algorithms to determine the quantitative importance model.

3 Allocation planning: methods

As discussed by Chai et al. (2013) and Govindan et al. (2015) AHP, TOPSIS and multi-objective programming are the most commonly used techniques for the selection of suppliers. This was also supported by Fallahpour and Moghassem (2012) mentioning that AHP and TOPSIS are the popular techniques in tackling evaluation problems. With regards to AHP, the decision makers have the ability to incorporate qualitative and quantitative criteria in the unified evaluation framework. Within the context of this work, AHP and TOPSIS are being used to validate the evaluation outcome obtained via TOPSIS.

3.1 AHP

AHP is a multi-criteria decision making algorithm developed for considering both qualitative and quantitative aspects of decisions (Saaty 1977). It aims to analyse the complex decisions to a series of pairwise comparisons and then reveals the final weight. In this work, AHP was applied to determine the importance weight for each TGR criteria and sub-criteria and Table 2 shows the evaluation scale in terms of linguistic variables that were used to perform pairwise comparisons. Decision makers need to give their opinion regarding the importance of each criteria/sub-criteria with respect to the others. Steps toward the solution of an AHP process can be found in Mathiyazhagan et al. (2015), Bhagwat and Sharma (2007) and Handfield et al. (2002).

Table 2 Criteria evaluation scale
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3.2 TOPSIS

Hwang and Yoon (1981) developed TOPSIS to select an alternative based on its distance to the ideal solution and the negative ideal solution. In this work, TOPSIS was applied to evaluate and rank suppliers with respect to their TGR performance. The linguistic variables presented in Table 3 were used to evaluate suppliers towards each criterion. Decision makers need to give their opinions about the performance of every supplier based on their TGR performance. In order to find the solution of a decision making problem using TOPIS, we refer to Behzadian et al. (2012), Opricovic and Tzeng (2004) and Wang et al. (2016a, b).

Table 3 Linguistic variables and their equivalent scale used for evaluating suppliers
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4 Allocation planning: research methodology

A laboratory instrumentation Original Equipment Manufacturer (OEM) plans to develop a resilient supplier selection and order allocation strategy for evaluating its current suppliers in order to react for unexpected events. Additionally, the company is keen to take ownership of its environmental responsibilities. This research supports the company through development of a supplier selection approach to facilitate evaluation and selection of suppliers based on their performance with respect to traditional, green and resilience criteria. Figure 1 shows a hierarchal framework, established for identifying traditional, green and resilience sub-criteria. The three criteria include traditional criteria with sub-criteria of cost, quality, delivery reliability, operating capacity, turnover, performance history and lead time, the green criteria with sub-criteria of environmental management system, waste management and environmental certificate, and the resilience criteria with sub-criteria of visibility, robustness, agility, leanness and flexibility (V-RALF). It is worth mentioning that in addition to the mentioned criteria in the literature, the purchasing manager has suggested additional traditional criteria i.e. lead time and turnover to be included as it will be shown in application Sect. 5. The purchasing manager clarified further in relation to traditional criteria: lead time is very important for the company to be considered because it is related to inventory management and demand forecasting; and turnover represents an indicator for the supplier’s capability to cope with the company’s demand. AHP was used to determine the importance weight for each criterion and sub-criterion based on linguistic expert’s assessment. Next, TOPSIS was adapted towards the evaluation of suppliers based on their performance in TGR criteria shown in Fig. 1. Subsequently, the ranking order of suppliers was determined based on evaluation derived from TOPSIS. Afterwards, a MOPM was developed, incorporating the weights obtained from AHP and TOPSIS to determine the optimal order allocation among suppliers. This integration helps the purchasing team to purchase products from suppliers taking into account their weight (i.e. derived from TOPSIS) with respect to the relative weight of each gresilience criterion (i.e. derived from AHP) based on decision makers’ opinion. Figure 2 shows a framework in terms of the processes followed for developing the green and resilient supplier selection and order allocation approach.

Fig. 1
figure 1

A hierarchal criteria framework for the gresilient supplier selection and order allocation

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Fig. 2
figure 2

Schematic representation of the gresilient supplier selection and order allocation approach

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4.1 The order allocation planning

This section presents the order allocation planner, which was obtained through the development of a new multi-objective programming model. It was used to support decision makers to order the optimal quantity of products from suppliers considering TGR aspects. Three objective functions were formulated: minimization of related costs (RC), environmental impact and maximization of resilience purchasing.

The MOPM was formulated based on the following sets, parameters and decision variables.

\( C_{i}^{p} \):

purchasing cost per unit of product ordered from supplier i

\( C_{i}^{t} \):

fixed unit transportation cost per mile from supplier i

\( C_{i}^{a} \):

fixed administration cost per unit of supplier i

di:

transportation distance (mile) of product from supplier i

TC:

transportation capacity (units) per lorry

Si:

supply capacity (units) of supplier i

Dmin:

minimum demand of the manufacturer

Dmax:

maximum demand of the manufacturer

CO2i:

CO2 emission in gram per mile for each lorry travelling from supplier i

IWt:

importance weight of traditional criteria revealed via AHP

IWg:

importance weight of green criteria revealed via AHP

IWr:

importance weight of resilience criteria revealed via AHP

\( iw_{i}^{t} \):

importance weight of supplier i revealed via TOPSIS towards traditional performance

\( iw_{i}^{g} \):

importance weight of supplier i revealed via TOPSIS towards green performance

\( iw_{i}^{r} \):

importance weight of supplier i revealed via TOPSIS towards resilience performance

Decision variables

q i :

quantity of products ordered from supplier i

Objective function 1 (RC)

Equation 1 shows the first objective function that is formulated for minimizing the sum of the purchasing, administration (e.g., ordering) and transportation costs. Furthermore, the importance weight of traditional criteria obtained via AHP and traditional suppliers’ weight obtained via TOPSIS were integrated in the first term to reflect the traditional performance of each supplier in the order allocation. The RC function is formulated as follows:

$$ Min\quad RC = IW^{t} \left( {\mathop \sum \limits_{i \in I} iw_{i}^{t} q_{i} } \right) + \mathop \sum \limits_{i \in I}^{{}} C_{i}^{p} q_{i} + \mathop \sum \limits_{i \in I} C_{i}^{a} q_{i} + \mathop \sum \limits_{i \in I} mC_{i}^{t} q_{i} d_{i} $$
(1)

where m is a multiplicative inverse of the transportation capacity per lorry (TC).

Objective function 2 (EI)

Equation 2 shows the second objective function that is formulated for minimizing the EI in terms of CO2 emissions throughout the transportation process from suppliers to the company. Furthermore, the weights of green criteria obtained via AHP and the green suppliers’ weight obtained via TOPSIS were integrated in the first term to further express the trend towards the supplier with highest green performance. The minimisation of EI can be expressed as follows:

$$ Min\;EI = IW^{g} \left( {\mathop \sum \limits_{i \in I} iw_{i}^{g} q_{i} } \right) + \mathop \sum \limits_{i \in I} mCO_{2i} q_{i} d_{i} $$
(2)

Objective function 3 (Res)

Equation 3 shows the third objective function that is formulated for maximizing the resilience value of purchasing. To achieve this aim, suppliers’ weights in resilience criteria obtained by TOPSIS were used as a coefficient for suppliers. Also, the overall weight of resilience criteria were multiplied by the formula to further express the trend towards resilience purchasing. The maximisation of Res can be expressed as follows:

$$ \begin{aligned} & Max\quad \text{Re} s = IW_{{}}^{r} \sum\limits_{i \in I} {q_{i} iw_{i}^{r} } \\ & {\text{Subject}}\,{\text{to:}} \\ \end{aligned} $$
(3)

Supply capacity constraints

These constraints ensure that the quantity of product ordered from supplier i should not exceed its capacity. It can be formulated as follows:

$$ q_{i} \le S_{i} ;\quad i = 1,2, \ldots ,I $$
(4)

Demand constraints

These constraints ensure that the demands of the company are fulfilled from supplier i. It can be formulated as follows:

$$ \sum\limits_{i \in I} {q_{i} } \ge D_{\hbox{min} } $$
(5)
$$ \sum\limits_{i \in I} {q_{i} } \le D_{\hbox{max} } $$
(6)

Non-negativity constraints

These constraints ensure that the quantity of all products throughout the supply chain are non-negative:

$$ q_{i} \ge 0\quad \forall i $$
(7)

4.1.1 Solution approach: ε-constraint

In this study, the ε-constraint method is used to obtain Pareto solution derived from optimizing the three objective functions (Eqs. 1–3) simultaneously. This method transforms the multi-objective model to a mono-objective model by keeping one of the functions as an objective function (in this study, minimization of expected cost), and treating other functions (in this study, minimization of environmental impact and maximization of resilience purchasing) as constraints limited to ε values (Marler and Arora 2004). Assuming the following multi-objective optimization problem:

$$ \begin{aligned} & \hbox{max} \left( {o_{1} \left( x \right),o_{2} \left( x \right), \ldots , o_{i} \left( x \right)} \right), \\ & {\text{Subject}}\,{\text{to}} \\ & X \in S; \\ \end{aligned} $$
(8)

where i denotes the number of objective function o, X is the decision vector and S refers to the feasible solution. In this method, one objective function is optimized, in which others are shifted to the constraint set as follows:

$$ \begin{aligned} & \hbox{max} \quad o_{1} \left( x \right) \\ & {\text{Subject}}\,{\text{to:}} \\ & o_{1} \left( x \right) \ge \varepsilon_{1} \\ & o_{2} \left( x \right) \ge \varepsilon_{2} \\ & o_{3} \left( x \right) \ge \varepsilon_{3} \\ & o_{i} \left( x \right) \ge \varepsilon_{i} \\ & X \in S \\ \end{aligned} $$
(9)

It should be noted that here we have a maximization objective; in case we have a minimization objective the shifted objective would need to be less than or equal epsilon value. In this work, the equivalent solution formula is given by:

$$ Min_{{}} RC = IW_{{}}^{t} \left( {\sum\limits_{i \in I} {iw_{i}^{t} q_{i} } } \right) + \sum\limits_{i \in I}^{{}} {C_{i}^{p} q_{i} } + \sum\limits_{i \in I} {C_{i}^{a} q_{i} } + \sum\limits_{i \in I} {mC_{i}^{t} q_{i} d_{i} } $$
(10)

Subject to:

$$ EI \le \varepsilon_{1} $$
(11)
$$ Max \, \text{Re} s \ge \varepsilon_{2} $$
(12)

In addition to Eqs. 4–7.

Where every assignment of ε1 and ε2 values in Eqs. 11 and 12 would reveal a pareto solutions. For instance, 20 ε values should be assigned to Eqs. 11 and 12 individually to obtain 20 Pareto solutions.

5 Application: a real case study

To validate the applicability and effectiveness of the developed approach, it was applied on a manufacturing company (Company A, henceforth) that assembles measurement equipment in the UK. Company A is an SME that represents one of the world-leading developers and manufacturers of scientific instruments for analysis of organic compounds. Products designed and manufactured by Company A are used in a variety of application areas such as: environmental monitoring, detection of chemical warfare agents, quality control and safety of food products, aroma profiling and environmental forensics. Company A aims to develop a purchasing strategy that supports evaluation of their current suppliers with respect to green and resilience performance in addition to the traditional criteria such as cost and quality. Currently, the main aim of the company is to meet their growth target by 2020. The current and potential turnover has not been revealed upon the company’s request. In this respect, the developed approach is applied in this case study to help the purchasing manager to (1) develop a unified TGR purchasing strategy and (2) evaluate their current system resilience in term of the performance of current suppliers.

Three buyers (i.e., B1. B2 and B3) who work in the purchasing department were invited to evaluate the importance of identified criteria illustrated in Fig. 1 using linguistic variables shown in Table 2. B1 has more than 10 years of work experience compared to B2 and B3 has four years of work experience. With regards to weighting the three buyers’ opinions, although, the first buyer is the purchasing manager with 10 years of purchasing experience, however, he has joined Company A 4 months ago whereas buyers 2 and 3 have been with the company 4 years. Thus, the purchasing manager has limited knowledge about the company and its suppliers. As a result of changes in the company, it was decided (by the authors and the purchasing manager) to weight their opinions equally (i.e., have the same weight). Two in-depth discussions (each discussion lasted around 2 h) were held with buyers individually to explain, constructively discuss and evaluate the TGR criteria and sub criteria. For the purpose of evaluation, the following definitions were used in discussions with the buyers:

  • Supply chain resilience “the ability of a [supply chain] to return to its original state or move to a new, more desirable state after being disturbed” Christopher and Peck (2004).

  • Robustness measures the ability to withstand disruptions to elements within the supply network, either through the immediate availability of alternative suppliers or being capable of quickly planning the incorporation of new suppliers.

  • Agility evaluates the ability to respond in a quick and well-coordinated manner to comparatively small market opportunities, through having a partner able to handle unexpected/volatile demand.

  • Leanness assesses the absence of excess/waste and hence the ability to fulfil predictable, base-line, demand in an efficient manner.

  • Flexibility gauges the ability to respond easily to disturbances in the supply network, whilst maintaining control of costs and lead-times. This involves having processes in place that enable effective response when disturbances in the supply chain are sensed.

  • Visibility refers to sharing relevant information, which would improve sensing of unexpected orders and fulling them. In other words, it is the ability of suppliers to see the light at the end of tunnel and run towards it based on their flexibility and agility.

5.1 Revealing the weight of TGR criteria: AHP

AHP was implemented as follows to determine the importance weight for each TGR criterion and sub-criterion:

  • Step 1 Three buyers were invited to perform a pairwise comparison among TGR criteria and sub-criteria (see Fig. 2) using the linguistic variables presented in Table 2.

  • Step 2 A pair-wise comparison matrix among TGR criteria and sub-criteria was built as shown in Tables 4, 5 and 6.

    Table 4 Decision matrix among TGR criteria
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    Table 5 Decision matrix among traditional criteria
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    Table 6 Decision matrix among green and resilience criteria
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  • Step 3 Table 7 shows the importance weights of the traditional criteria, green criteria and resilience criteria as well as their sub-criteria.

    Table 7 Weights of TGR criteria and sub-criteria obtained by AHP
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According to the calculations shown in Table 7, the weight of traditional criteria (IWt) is 0. 362 compared to 0.112 and 0.525 for the weight of green criteria (IWg) and resilience criteria (IWr) respectively. Subsequently, the resilience criteria obtained the highest weight followed by the traditional criteria, while the green criteria obtained the lowest weight from the perspective of buyers. Thus, resilience criteria are the most important compared to the other criteria of both green and traditional criteria. This complies with the ultimate target of company A in improving their supply chain resilience which represents their current main concern. In the context of traditional criteria, quality has obtained the highest weight of 0.214 compared to the lowest criterion weight for the operating capacity with a weight of 0.079. Also, the resilience criterion of flexibility obtained the highest weight of 0.278. This could be expected as the purchasing manager mentioned during the interview that they have a main issue with some suppliers in having the ability to respond easily to disturbances in the supply network, whilst maintaining control of lead-times.

5.2 Evaluating and ranking suppliers: TOPSIS

In this section, the five suppliers were evaluated and ranked using TOPSIS, based on their TGR performance. After determining the importance for each TGR criterion, TOPSIS was implemented to obtain the ranking order of suppliers, based on their TGR performance.

  • Step 1 The buyers were again invited to evaluate the performance of five suppliers (S1–S5), that were selected by the purchasing manager, with respect to each sub-criterion using the scale previously presented in Table 3. However, the third buyer evaluated the first supplier only, clarifying that he does not work with the others. Table 8 presents the evaluation of five suppliers based on three buyers’ opinions. In this context, weights of their opinions were considered equally for the reason mentioned previously.

    Table 8 Evaluation of suppliers based on their TGR performance
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  • Step 2 Table 9 shows matrix of normalized numbers and weighted normalized numbers which was obtained by multiplying the sub-criteria weights obtained by the AHP with the normalized matrix.

    Table 9 Normalized and weighted normalized decision matrices
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  • Step 3 he distance of each supplier from the positive ideal solution (\( d_{i}^{ + } \)) and the negative ideal solution (\( d_{i}^{ - } \)) are calculated. The closeness coefficient (CC) for each supplier is determined based the obtained distances. The results are reported in Table 10.

    Table 10 Closeness coefficient and distances from the positive ideal/negative ideal solutions related to suppliers
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5.3 The order allocation planner: MOPM

After quantifying the suppliers’ performance towards TGR criteria, decision makers in Company A need to know who to order the metal sheet from and what the optimal order quantity from each supplier is. This is based on their performance and consideration of the three objectives (i.e., minimization of expected cost, environmental impact and maximization of resilience purchasing). Thus, to support them in ordering the right quantity from the right supplier, the MOPM developed in Sect. 4 was applied as follows:

  • Step 1 Table 11 presents collected data related to each supplier from the purchasing manager. However, data related to TGR weights and TGR suppliers’ weights were taken from AHP and TOPSIS, respectively.

    Table 11 Date of the current case study related to the implementation of the MOPM
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  • Step 2 The ε-constraint presented in Sect. 4.1.1 was implemented to solve the three objectives optimization problem in terms of obtaining Pareto solutions. In this work, the expected cost minimization was kept as an objective function. Minimization of environmental impact and maximization of V-RALF are moved to ε-based constraints.

  • Step 2.1 Objective functions two and three were solved individually to obtain the upper and lower values for each objective. The values between upper and lower for the two objectives were divided into segments. The segment values were assigned individually to ε1 and ε2.

  • Step 3 Fig. 3 depicts Pareto frontiers among the three objective functions output that were developed based on 130 solutions. For the sake of simplicity, Table 12 shows selected 18 Pareto solutions associated with the selected suppliers and the order allocation plan for the 18 solutions. For instance, solution 2 required minimum costs of 387514.47, reveals minimum CO2 emissions of 2037586.82 and leads to maximum resilience value of purchasing 3240.07. Also, this solution is associated with a selection of suppliers 2, 3, 4 and 5 (0 1 1 1 1) in which 1853 units should be ordered from supplier 1483 units from supplier 3, 3000 units should be ordered from supplier 4 and 2500 units should be ordered from supplier 5. It is worthy to mention that more Pareto solutions can be obtained by varying epsilon values within the defined range.

    Fig. 3
    figure 3

    Pareto frontiers

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    Table 12 Selected Pareto solutions
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  • Step 4 Each of these solutions is associated with a different order allocation plan as shown in Table 12. Thus, the purchasing manager has asked to select one solution to get the final order allocation. However, selecting a solution out of 18 was a challenge decision. Thus, TOPSIS was applied again to help the purchasing manager in selecting the final solution that is closest to the ideal solution and furthest from the worst solution. Accordingly, solution number 9 was selected as the final solution to get the optimal order allocation as it showed the highest closeness coefficient (CC = 0.5821). Based on this solution, the minimum total cost is 431520.03; the minimum CO2 emissions is 3167654.78 and the maximum value of resilience pillars (V-RALF) is 3572.44. Also, this solution is obtained via an allocation of ε1 = 3167737.23 and ε2 = 3572.27. Based on the selected solution, the optimal order allocation plan is illustrated in Fig. 4. As shown in this figure, the buyers should order 3332 units from supplier 1, 1146 units from supplier 3, 3000 units from supplier 4 and 2500 units from supplier 5. It is noticed that all solutions lead to select less than 5 suppliers. It is noteworthy that this complies with the long-term purchasing strategy to reduce the administration costs by having less than 5 suppliers (current scenario). The purchasing manager commented that this will provide more time to buyers seeking and evaluating new suppliers. This also complies with the purchasing manager’s short-term plan (to be achieved by 2018) to have an average of 3 suppliers to satisfy all demands rather than five.

    Fig. 4
    figure 4

    The optimal order allocation for the case under study

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The developed MOPM was coded in Python and solved using GUROBI solver. The computational (run) time is neglected as it was in a few seconds since we have small-sized case study.

5.4 Sensitivity analysis

Sensitivity analysis is conducted to investigate how the changes of input data may affect the results of the decision-making model. In this study, a sensitivity analysis is performed to study the effects of changing the weight of TGR criteria on the ranking of suppliers. Eight different scenarios of weights (see Table 13) are assigned to TGR criteria in Eq. 10. Table 14 shows the closeness coefficient (CC) for each supplier related to each scenario. As shown in Table 14, the analysis shows that the evaluation and ranking process is slightly sensitive to variation in the TRG criteria weight. For instance, in scenario 6, the ranking order has been changed to S4 > S1 > S2 > S3 > S5 compared to the original order of S4 > S5 > S1 > S3 > S2. This could be related to the resilience criteria as S1 has reasonable traditional and green performance but an average of medium resilience performance which made it as the third suppliers in the original evaluation since the resilience criteria revealed highest weight based on decision makers’ evaluation. However, once an almost equal weight allocated for the TGR criteria as in the sensitivity analysis, S1 revealed a high overall performance putting it as the second-best supplier. Generally, suppliers 4 and 1 are always ranked first and second in all scenarios respectively.

Table 13 Eight different scenarios of TGR criteria weights allocated for TOPSIS individually
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Table 14 Ranking order of suppliers revealed via the sensitivity analysis
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5.5 Managerial implications

This research delivers the purchasing team a user-friendly decision support system that can be used as a tool for improving their supplier selection process. Specifically, it allows for a more consistent approach to the application of multiple (Traditional, Green and Resilience) criteria. As has been identified in supply chain literature a critical part of the supplier selection process is determining the relative importance of the decision-making factors. This decision support tool addresses some of the challenges associated with the trade-offs that need to be made during supplier selection. Furthermore, through the use of these techniques a manager or buyer is able to express their perception of a supplier and enter it into the tool.

Taking a broader perspective, this collaborative research provides the purchasing manager and their team with an advanced and modern thoughtful regarding their required purchasing strategy. This helps them to contribute towards the development of a resilient business that the company aims to achieve in 2020, in addition to green development that would advance the company’s industry profile. This work had allowed them to appreciate the benefits of a gresilient approach. Furthermore, this collaboration cultured the purchasing department about the crucial necessity for including gresilience criteria as an alternative to the traditional criteria only.

Furthermore, this decision support tool could be used by purchasing or supply chain managers to perform benchmarking of suppliers. This is of particular importance when a company wishes to pursue a multi-sourcing policy where the company would like to have multiple suppliers to enhance their overall resilience for certain component types.

With regards to suppliers, this work may also help them (i.e., suppliers 1 and 2) to enhance their performance according to the highlighted criteria. This is because the presented decision support tool allows the purchasing manager to deliver feedback in an appropriately timed manner to specific suppliers. Therefore, the supplier can evaluate its current performance with its historical performance and make essential adjustments to improve performance.

6 Conclusions

Traditional supplier selection criteria include elements such as cost and product quality but over the last decade companies have been challenged to ‘go green’ and take responsibility for their environmental impact. This is admirable but not necessarily sufficient to guarantee sustainable operations, due to the risk of unexpected supply chain disturbances (Norrman and Jansson 2004; Tang 2006). During or following a disruption, supply chain performance is normally compromised. Thus, companies and supply chains must be resilient in efficiently reacting to unexpected events. It is generally accepted that the overall performance of a supply chain is enhanced through effective supplier selection. Therefore, to cope with the multiple demands on a supply chain business, a supplier selection approach that considers traditional, green and resilience criteria is of paramount importance.

This work presents a development of a unified green and resilient (Gresilient) supplier selection and order allocation approach considering traditional, green and resilience criteria. A supplier selection framework was developed by identifying traditional, green and resilience criteria and sub-criteria. Five steps were followed to evaluate and rank suppliers and allocate the optimal allocation in quantity of orders. Firstly, AHP was applied to evaluate the importance of each criterion and sub-criterion based on the linguistic evaluation of decision makers. The AHP results showed that resilience criteria play a current trend for the company over two the other two criteria (traditional and green criteria). Secondly, TOPSIS was applied to reveal the ranking order of suppliers based on their TGR performance with respect to the importance weight of each criterion and sub-criterion revealed via AHP. Generally, all suppliers revealed low resilience performance, which does not comply with the company’s strategy. Thirdly, a MOPM was developed to obtain the optimal order allocation among suppliers considering their TGR performance as the weights revealed via AHP and TOPSIS were integrated in the MOPM. The ε-constraint method was then used to obtain Pareto solutions and TOPSIS was applied again to select the final Pareto solution as the fourth and fifth steps respectively. The results demonstrate the applicability of the developed approach in helping the purchasing manager at company A to identify a traditional, green and resilient purchasing strategy and evaluate their suppliers. Additionally, it guides the company to order the right quantity of material from the right suppliers according to their performance. The developed evaluation approach was delivered to the purchasing manager as an Excel worksheet to be used for their upcoming supplier assessments, it was a much-appreciated tool to simplify and support their decisions.

Companies that function under similar conditions could use the developed approach for evaluating the healthiness of their suppliers in terms of resilience and greenness. Also, it can be used by suppliers themselves to improve their service through the evaluation of their status with respect to the defined traditional, green and resilience criteria and sub-criteria. This work has established a foundation for future research avenues in highlighting the need for considering resilience pillars in green purchasing strategy.

The study has been focused on chemical manufacturing industry. Similar study conducted in different sector such food industry may need some bit different criteria such as freshness and safety of food products. This would also further prove the applicability of the developed approach in solving similar supplier selection and order allocation problems. Also, this study is limited in considering equal weight for buyers’ opinions. Thus, it was suggested to the purchasing manager to consider different weights considering seniority of buyers into the upcoming evaluation. In the context of the SME case study, the number of decision makers is limited by 3 (the purchasing manager and two buyers) as this was the purchasing team that was available and presented to the research team to validate the developed approach. However, the Excel-based evaluation tool was developed to accommodate 8 decision makers. The purchasing manager was told that all buyers can input their evaluation in the upcoming evaluation of criteria/or suppliers. Thus, it would be interesting to have more decision makers that further illustrate the applicability of the developed approach in aggregating opinions of multiple decision makers. Furthermore, the size of input data (e.g., demand and supply capacity) used in the MOPM reflects the context of case study. Therefore, the capability of the developed MOPM in handling large-sized problem within a reasonable running time has not been explored.

The ongoing work includes the incorporation of social criteria to supplier evaluation. As future research, the developed multi-objective model can be re-developed as a fuzzy multi-objective model to cope with the dynamic nature of some input parameters such as purchasing cost, demands and capacity of suppliers. It would also be interesting to answer the question—how about incorporating the company’s internal resilience criteria (pillars) (e.g., redundancy management, ordering management and operation management) into the evaluation approach and how this could improve their purchasing strategy?