1 Introduction

Throughout history, the human being has struggled with a variety of illnesses and disturbances. Per year, 7% of the population is affected by a rare illness (Hanisch and Rake 2021; Roessler et al. 2021). Since its discovery in mid-2019, the COVID-19 pandemic has become the most heinous outbreak. Before February 2021, the disaster would have claimed over 2 million lives (Kim et al. 2021) and about 108 million people have been infected. Despite many anodyne findings by foreign firms, nations (i.e. emerging economies such as Iran) have been unable to introduce an effective vaccination process for their population due to the impossibility of establishing a supply chain network capable of meeting the vaccine's demand (Duong and Chong 2020). According to the literature, the primary causes of medical supply chain reliability are resource optimization, demand management, and output rate monitoring (Papalexi et al. 2020) which is more catastrophic in countries with underdeveloped infrastructures. In other words, supply chain inefficiency is caused by uncertainty and organizational dysfunctionality (Negi and Anand 2018). On the one hand, health discomfiture is a relatively recent source of supply chain disruption. Furthermore, the globalization of supply chains necessitates flexibility and coordination in supply chain technology (Pettit et al. 2013). In recent years, factors such as coordination, a greater understanding of the medical supply chain system, financial efficiency enhancement, supply and demand forecasts, and product growth duration have been identified as the most significant factors reducing the likelihood of supply chain interruption (Munusamy and Murugesan 2020; Porter and Reay 2016; Wagner and Thakur-Weigold 2018).

Members of the supply chain repurpose their output to reduce total inventory and increase value generation within organizations (Kurt et al. 2019). The repurposing paradigm has highly been examined as a beneficial procedure like information sharing, creativity, or recycling that benefited the supply chain efficiency effectiveness. However, when a rare illness is discovered, manufacturers must find a new use for or reposition their common goods to meet customer demands and resolve supply chain disruptions (Mohanty et al. 2020). This intervention cuts the time required for product production and reportedly lowers the expense and R&D practice in medical industries (De et al. 2021). In the last two years, scholars have conducted extensive research on the concept using artificial intelligence (Zhou et al. 2020), experimental, and data-driven methodologies (Lakizadeh and Hassan Mir-Ashrafi 2021). However, in an emerging economy such as Iran, due to infrastructural, economic, environmental, social and political barriers, implementing new and modern approaches in supply chain management such as supply chain 4.0 or 5.0 is not possible.

In these circumstances, managers develop strategic tactics such as collaboration to deal with disturbances (Mohammaddust et al. 2017). Coordination allows partners to collaborate, schedule, and prioritize their priorities while also saving money and resources (Cao et al. 2010). Managers ensure their organizations’ resilience and visibility by doing so (Cao and Zhang 2011). According to a new report, contract coordination enables companies to outperform their competitors in cost savings and market responsiveness (Jamal et al. 2019). Contracts for supply chain coordination assist businesses in making more coordinated decisions than decentralized activities (Mahdiraji et al. 2014). In the case of the COVID-19 pandemic, these contracts are incredibly advantageous in achieving the joint goal of sellers and buyers, namely overcoming delays in meeting vaccine demand. Supply chain coordination contracts (from now on, SCCCs) often facilitate information exchange and a greater likelihood of sharing experience (Wang et al. 2020a,  b), which increases the possibility of repurposing production. Numerous SCCCs have been studied in the last few years using various experimental, computational, and mathematical modeling approaches (Hu et al. 2018b; Li et al. 2021a; Wang et al., 2020b; ** proactive strategies. For instance, Samani et al. (2020) proposed a two-step process for managing instability in the platelet supply chain, consisting of a proactive and constructive phase to minimize the risk of disruption (Samani et al., 2020). Previously, Pal et al. (2014) investigated a three-tier supply chain to demonstrate the critical nature of stock control during disruptions (Pal et al. 2014). Also, Wang et al. (2020a,  b) proposed a comprehensive supply chain network to promote stability through disruptions (Wang et al. 2020a). The second strategic solution is focused on taking steps in the face of disturbances. The reactive approach enables supply chain members to make quick decisions to adapt to shifts with the least amount of danger (Chowdhury et al. 2021). As an illustration, Zhao et al. (2019) created an agent-based simulation to determine whether a firm's reactive approach prevents disruption (Zhao et al. 2019). Furthermore, Lücker et al. (2019) emphasized the role of inventory and reserve power in stochastic demand as a defensive strategy that minimizes the disturbance (Lücker et al. 2019). Additionally, Jabbarzadeh et al. (2018) suggested a stochastic optimization model for modeling a closed-loop supply chain (CLSC) (Jabbarzadeh et al. 2018). Besides, transshipment was discovered to be a reactive approach that mitigates supply chain disruption (e.g. Elluru et al. 2019; Kaur and Singh 2020). Assuming that coordination contracts serve as a means of proactive policy procurement and repurposing as a reactive strategy, the remainder of this section discusses various types of coordination contracts. Additionally, problems associated with repurposing are studied.

2.2 Coordination contracts

Multiple criteria such as price, size, and quality are described in a buyer–seller partnership by a contract that defines itself as an agreement that ensures all supply chain components function in an integrated rather than decentralized fashion (Tsay et al. 1999). These contracts provide significant benefits in terms of risk mitigation by cooperation (Ghadge et al. 2017), inventory cost savings (Sainathan and Groenevelt 2019), and overall value enhancement by supply chain management (Hu and Feng 2017). Contracts for coordination are mainly focused on game theory, under which each group has the option of cooperating or acting decentralized (Govindan et al. 2013). According to Cachon (2003), supply chain participants cannot profitably deviate arbitrarily from a set of supply chain optimum actions that should be considered coordinated (Cachon 2003). In other terms, they are built following the Nash equilibrium theorem (Biswas and Avittathur 2019). Each contract has several advantages and disadvantages. As a case in point, the wholesale contract approach is risk-free for the manufacturer, and there is no obligation to deliver goods in a certain quantity within a specified time (Adabi and Mashreghi 2019). However, the literature indicates that the primary disadvantage of this contract is the double marginalization effect (Fang 2018). Although the revenue-sharing contract eliminates this impact, it requires retailers to exercise more control over product shortages and sales practices since both the seller and manufacturer share revenue (Vafa Arani et al. 2016). In contrast to these contracts, the two-part tariff (TPT) arrangement provides the wholesaler with the output rate, which is cheaper than the previous methods. This contract has become increasingly popular in recent years as a cost-effective method of minimizing distribution costs within wholesalers (Lv et al. 2019b).

3 Methodology

3.1 Basics and definitions

Zadeh has introduced fuzzy sets in 1965 to deal with uncertainty by assigning a membership degree to each element (Zadeh 1965). Since then, numerous developments of fuzzy numbers are presented e.g. intuitionistic fuzzy, hesitant fuzzy, fuzzy type 2, etc. Intuitionistic fuzzy sets try to consider nonmembership of the elements in addition to membership (Atanassov 1986). Moreover, fuzzy type 2 sets assign a secondary membership to each element (Rickard et al. 2009). Furthermore, hesitant fuzzy sets consider the hesitation of the decisions (Rodríguez et al. 2011). Z-numbers were first proposed by Zadeh to deal with uncertainty (Zadeh 2011; Mokhtarzadeh et al. 2020, 2021). The concept of z-numbers is associated with the issue of the reliability of the information. Due to uncertain conditions alongside high unreliability which was emerged by the Covid-19 pandemic, Z-numbers are a good tool to bring the results closer to reality. Each z-number, \(Z=(A,B)\), has two components in which A is a restriction on the value and B is a reliability of the A. As a huge amount of information is provided by semantic terms, linguistic Z- numbers have been nominated (Wang et al. 2017). Two basic definitions regarding these numbers are described as follows.

Definition 1.

Let X be a universe of discourse, \({S}_{1}=\{{s}_{0}, {s}_{1}, {s}_{2}, \dots , {s}_{2l}\}\) and \({S}_{2}=\{ {s}_{0}^{^{\prime}}, {s}_{1}^{^{\prime}}, {s}_{2}^{^{\prime}}, \dots , {s}_{2k}^{^{\prime}}\}\), be two finite and ordered linguistic terms, l and k are nonnegative integer numbers, \({A}_{\phi (x)}\epsilon {S}_{1}\) and \({B}_{\varphi (x)}\epsilon {S}_{2}\), a linguistic Z-number set Z in X is defined as Eq. (1).

$$Z=\left\{(x, {A}_{\phi \left(x\right)}, {B}_{\varphi \left(x\right)}) |x\epsilon X\right\}$$
(1)

Note that in Eq. (1), \({A}_{\phi \left(x\right)}\) is a restriction on the value and \({B}_{\varphi \left(x\right)}\) is a reliability of the \({A}_{\phi \left(x\right)}\).

Definition 2.

Let \({Z}_{\alpha }=({A}_{\phi \left(\alpha \right)}, {B}_{\varphi \left(\alpha \right)})\) be linguistic Z-number. The score of the \({Z}_{\alpha }\) is computed by Eq. (2).

$$S\left({Z}_{\alpha }\right)={f}^{*}\left({A}_{\phi \left(\alpha \right)}\right)\times {g}^{*}({B}_{\varphi \left(\alpha \right)})$$
(2)

It is noticeable that in Eq. (2), f * and g* are in order the linguistic functions of \({A}_{\phi \left(\alpha \right)}\) and \({B}_{\varphi \left(\alpha \right)}\) which are obtained by Eqs. (3) and (4) (Jiang et al. 2020).

$${f}^{*}\left({A}_{\phi \left(\alpha \right)}\right)=\frac{\phi \left(\alpha \right)}{2l}$$
(3)
$${g}^{*}\left({B}_{\varphi \left(x\right)}\right)=\frac{\varphi \left(\alpha \right)}{2k}$$
(4)

3.2 Methods and tools

DEMATEL-based ANP

DEMATEL-based ANP (DANP) was first proposed by Chiu et al. in 2013 due to the problems of interdependence and feedback among certain criteria (Chiu et al. 2013). This method applies DEMATEL to construct an influential network relations map and, ANP to extract the weights of the criteria. DANP attempts to reduce the gap in each dimension and criterion. This method is described in the following (Hashemi et al. 2021).

Step 1. The influence of each criterion on other criteria is evaluated by experts, normally applying a scale of 0 (no influence) to 4 (highly influence). Matrix G of the Eq. (5) illustrates the result of these assessments.

$$G=\left[{g}_{c}^{ij}\right]=\left[\begin{array}{ccc}{g}_{c}^{11}& \cdots & {g}_{c}^{1n}\\ \vdots & \ddots & \vdots \\ {g}_{c}^{n1}& \dots & {g}_{c}^{nn}\end{array}\right]$$
(5)

It is notable that in Eq. (5), \({g}_{c}^{ij}\) indicates the influence of ith criterion on the jth criterion.

Step 2. The normalized matrix X is computed by Eq. (6), where the value of \(v\) is obtained by Eq. (7).

$$X=vG=v\left[{g}_{c}^{ij}\right]$$
(6)
$$v= \underset{i,j}{\mathrm{min}}\{\frac{1}{\underset{i}{\mathrm{max}}\sum_{j=1}^{n}{g}_{c}^{ij}},\frac{1}{\underset{j}{\mathrm{max}}\sum_{i=1}^{n}{g}_{c}^{ij}}\}$$
(7)

Step 3. The total-influential matrix \({T}_{c}\) is obtained by Eq. (8) where (I) is the identity matrix.

$${T}_{c}=\left[{t}_{c}^{ij}\right]=X+{X}^{2}+\dots +{X}^{l}=X\left(I-X\right);\ when\ \underset{l\to \infty }{\mathrm{lim}}\;{X}^{l}$$
(8)

Step 4. Subsequently, the row sum and the column sum of the matrix are calculated by Eqs. (9) and (10).

$${r}_{i}=[\sum_{j=1}^{n}{t}_{c}^{ij}]$$
(9)
$${s}_{i}=[\sum_{i=1}^{n}{t}_{c}^{ij}]$$
(10)

It should be noted that if \(\left({r}_{i}-{s}_{i}\right)>0\), then criterion i is a member of the casual group which means it affects other criteria. On the other hand, if \(\left({r}_{i}-{s}_{i}\right)<0\), then criterion i is a member of an influenced group. In addition, two different influence matrices are employed. TC is devoted to n criteria and TD pertains to m dimensions of the TC as elaborated in Eq. (11).

$$\begin{array}{c}\\ {T}_{C}=\left[\begin{array}{ccc}{T}_{c}^{11}& \cdots & {T}_{c}^{1m}\\ \vdots & \ddots & \vdots \\ {T}_{c}^{m1}& \cdots & {T}_{c}^{mm}\end{array}\right]\\ \end{array}$$
(11)

Step 5. The total influence matrix TD is normalized by Eq. (12). Hence, normalized total influence matrix TC is built as Eq. (13).

$${T}_{D}^{nor}=\left[\begin{array}{ccc}{t}_{D}^{{nor}_{11}}& \cdots & {t}_{D}^{{nor}_{1m}}\\ \vdots & \ddots & \vdots \\ {t}_{D}^{{nor}_{m1}}& \cdots & {t}_{D}^{{nor}_{mm}}\end{array}\right]=\left[\begin{array}{ccc}\frac{{t}_{D}^{11}}{{t}_{D}^{1}}& \cdots & \frac{{t}_{D}^{1m}}{{t}_{D}^{1}}\\ \vdots & \ddots & \vdots \\ \frac{{t}_{D}^{m1}}{{t}_{D}^{m}}& \cdots & \frac{{t}_{D}^{mm}}{{t}_{D}^{1}}\end{array}\right]$$
(12)
$${T}_{C}^{nor}=\left[\begin{array}{ccc}{T}_{c}^{{nor}_{11}}& \cdots & {T}_{c}^{{nor}_{1m}}\\ \vdots & \ddots & \vdots \\ {T}_{c}^{{nor}_{m1}}& \cdots & {T}_{c}^{{nor}_{mm}}\end{array}\right]$$
(13)

Note that in Eq. (12), \({t}_{D}^{i}\) is the sum row of the ith dimension attained by Eq. (14).

$${t}_{D}^{i}=[\sum_{j=1}^{m}{t}_{D}^{ij}]$$
(14)

Step 6. Unweighted supermatrix WC is constructed by transposing the normalized total influence matrix \({T}_{C}^{nor}\) as shown in Eq. (15).

$${W}_{C}=\left[{T}_{C}^{nor}\right]{^{\prime}}=\left[\begin{array}{ccc}{w}_{c}^{11}& \cdots & {w}_{c}^{1m}\\ \vdots & \ddots & \vdots \\ {w}_{c}^{m1}& \cdots & {w}_{c}^{mm}\end{array}\right]$$
(15)

Step 7. The influential weights of the DANP are attained by Eq. (16).

$${W}_{C}^{*}={T}_{C}^{nor}\times {W}_{C}=\left[\begin{array}{ccc}{T}_{c}^{{nor}_{11}}\times {w}_{c}^{11}& \cdots & {T}_{c}^{{nor}_{1m}}\times {w}_{c}^{1m}\\ \vdots & \ddots & \vdots \\ {T}_{c}^{{nor}_{m1}}\times {w}_{c}^{m1}& \cdots & {T}_{c}^{{nor}_{mm}}\times {w}_{c}^{mm}\end{array}\right]$$
(16)

Step 8. The DANP is obtained by limiting the weighted supermatrix \({W}_{C}^{*}\) by raising it to a sufficiently large power \(\varphi\) as Eq. (17) until it is converged.

$$w=\left({w}_{1}, {w}_{2}, \dots , {w}_{m}\right)=\underset{\varphi \to \infty }{\mathrm{lim}}{({w}_{c}^{*})}^{\varphi }$$
(17)

Comprise Ranking Method (VIKOR)

The VIKOR method has been presented as a multi-criteria decision-making (MCDM) technique to prioritize alternatives found on conflicting criteria (Opricovic and Tzeng 2007). This method proposes its indices base on the closeness to the ideal solution (Sayadi et al. 2009). The Steps of the VIKOR are elaborated below (Fei et al. 2019).

Step 1. The decision matrix is constructed as in Eq. (18).

$$D=\left[{x}_{ij}\right]= \left[\begin{array}{ccc}{x}_{11}& \cdots & {x}_{1m}\\ \vdots & \ddots & \vdots \\ {x}_{n1}& \cdots & {x}_{nm}\end{array}\right]$$
(18)

Note that in Eq. (18), \({x}_{ij}\) is the value of the ith alternative based on the jth criterion.

Step 2. The decision matrix is normalized by Eq. (19).

$$N=\left[{n}_{ij}\right]=\left[\frac{{x}_{ij}}{\sqrt{\sum_{j=1}^{n}{{x}_{ij}}^{2}}}\right]$$
(19)

Step 3. The ideal (f*) and anti-ideal (f−) solution is determined by Eq. (20).

$$\left\{\begin{array}{c}\begin{array}{cc}\begin{array}{c}{{f}_{j}}^{*}=\underset{i}{\mathrm{max}}{c}_{ij}\\ {{{f}_{j}}^{-}=\underset{i}{\mathrm{min}}{c}_{ij}}\end{array}& if {c}_{ij}is\ the\ benefit\ criterion\end{array}\\ \begin{array}{cc}\begin{array}{c}{{f}_{j}}^{*}=\underset{i}{\mathrm{min}}{c}_{ij}\\ {{f}_{j}}^{-}=\underset{i}{\mathrm{max}}{c}_{ij}\end{array}& if {c}_{ij}is\ the\ cost\ criterion\end{array}\end{array}\right.$$
(20)

Step 4. Si and Ri indices are computed by Eqs. (21) and (22).

$${S}_{i}=\sum_{j=1}^{m}{w}_{j}\frac{{f}_{j}^{*}-{f}_{ij}}{{f}_{j}^{*}-{f}_{j}^{-}}$$
(21)
$${R}_{i}=\underset{j}{\mathrm{max}}{w}_{j}\frac{{f}_{j}^{*}-{f}_{ij}}{{f}_{j}^{*}-{f}_{j}^{-}}$$
(22)

It is notable that in Eqs. (21) and (22), \({w}_{j}\) is the weight of criteria j which is extracted by another technique.

Step 5. Eventually, the index Q is computed by Eq. (23).

$${Q}_{i}=v\left(\frac{{S}_{i}-{S}^{*}}{{S}^{-}-{S}^{*}}\right)+(1-v)\left(\frac{{R}_{i}-{R}^{*}}{{R}^{-}-{R}^{*}}\right)$$
(23)

Notice that in Eq. (23), \({S}^{*}\) and \({R}^{*}\) are in order the minimum of \({S}_{i}\) and \({R}_{i}\). In addition, \({S}^{-}\) and \({R}^{-}\) are in order the maximum of \({S}_{i}\) and \({R}_{i}\). Moreover, parameter \(v\) indicates the degree of the agreement of the decision-makers. If the degree of the agreement is high, then \(v>0.5\). If the agreement is reached by the majority of the opinions, then \(v=0.5\). At last, if If the degree of the agreement is low, then \(v<0.5\).

3.3 Research steps

As illustrated in the literature, numerous contradictory criteria (as repurposing challenges) should be considered while selecting the type of SCCCs. Hence, a hybrid DEMATEL-ANP-VIKOR approach is applied to deal with varied criteria and alternatives. In addition, Z-numbers are employed due to the condition with high uncertainty as a result of the COVID-19 pandemic. The research steps are discussed as follows.

Step 1. Identifying Supply chain coordination contracts. Numerous types of SCCCs are gathered by reviewing the literature. These SCCCs are demonstrated in Table 1.

Step 2. Extracting Repurposing Challenges. By studying the literature, different CRCs are detected which are illustrated in Table 2.

Step 3. Data Gathering. A group of experts is invited to discuss the questionnaires of the research. This group included fifteen experts with high experience and expertise in the field of study from the health, drug and pharmaceutical sectors of the emerging economy of Iran (see the expert profiles in Fig. 2). These experts were selected by snowball sampling found on researchers’ judgment on their expertise and experience. This means that each expert introduced several other experts to complete the group. Two face-to-face sessions (considering social distancing) have been organized which lasted approximately 12 h in total. In the first session, researchers introduced the concept of collected core repurposing challenges in Table 2. In the following, the experts have discussed the impact of each challenge on others to reach a consensus. This group applied the linguistic Z-number scale of Table 3 to express their opinion.

Fig. 2
figure 2

Experts’ Profile Infographic

Full size image
Table 3 Linguistic Terms to Evaluate Criteria (core repurposing challenges)
Full size table

In the second session, the SCCCs were elaborated by researchers for experts according to Table 1. Then the experts argued to assess the influence of each SCCC facing the challenges of repurposing. Likewise, they have applied the linguistic z-number scale of Table 4.

Table 4 Linguistic Terms to Evaluate Alternatives (SCCCs)
Full size table

The demographic information of the experts is shown in Fig. 2.

Step 4. Extracting the weights of CRCs via linguistic Z-DANP. To consider the uncertainty and to obtain more reliable results, the DANP method is applied under the condition of linguistic Z-numbers. The steps of Z-DANP are described below.

  1. 1.

    The effect of each criterion on other criteria and the certainty of each evaluation are determined by pairwise applying the Z-number scale of Table 3. The evaluation matrix of Eq. (24) is constructed.

$${G}_{Z}=\left[{Z}_{ij}\right]=[{\left({s}_{k}, {s}_{l}^{^{\prime}}\right)}_{ij}]$$
(24)

Note that in Eq. (24), \({s}_{k}\) is the influence of criterion i on criterion j and \({s}_{l}^{^{\prime}}\) is the reliability of the evaluation.

  1. 2.

    The score of each evaluation is computed by Eq. (2) to (4) and the crisp matrix of Eq. (25) is shaped.

$${G}_{c}=\left[{g}_{c}^{ij}\right]=[{\left({f}^{*}({s}_{k}\right)\times {g}^{*}({s}_{l}^{^{\prime}}))}_{ij}$$
(25)
  1. 3.

    The weights of the criteria are extracted by the DANP method, applying Eq. (5) to (17).

Step 5. Prioritizing the SCCCs via linguistic Z-VIKOR. Alongside DANP, to achieve more reliable prioritization of the contracts, linguistic z-numbered evaluations of the experts are analyzed by the VIKOR method. The steps of the linguistic Z-VIKOR are elaborated below.

  1. 1.

    The decision matrix of Eq. (26) is composed of applying linguistic terms in Table 4.

$${D}_{Z}=\left[{z}_{ij}^{^{\prime}}\right]=[{\left({s}_{k}^{^{\prime\prime} }, {s}_{l}^{^{\prime}}\right)}_{ij}]$$
(26)

It is noticeable that in Eq. (26), \({s}_{k}^{^{\prime\prime} }\) is the influence of the alternative i on the criterion j and \({s}_{l}^{^{\prime}}\) is the certainty of the assessment.

  1. 2.

    The scores of the z-numbered evaluations are calculated by Eq. (2) to (4) and the crisp decision matrix is shaped as demonstrated in Eq. (27).

$${D}_{c}=\left[{x}_{ij}\right]=[{\left({f}^{*}({s}_{k}^{^{\prime\prime} }\right)\times {g}^{*}({s}_{l}^{^{\prime}}))}_{ij}]$$
(27)
  1. 3.

    The alternatives are prioritized by the VIKOR method employing Eq. (18) to (23).

Step 6. Classifying The SCCCs. The prioritized SCCCs are clustered into four groups (according to the score quartiles emanated from linguistic Z-VIKOR) including diamond, gold, star and question mark. After that, each group is discussed. The research steps are presented in Fig. 3.

Fig. 3
figure 3

Research Framework

Full size image

4 Findings and results

The current study considers 17 coordination contracts with an integrated approach and evaluates their effects on mitigating repurposing challenges. By using an uncertain multi-criteria decision-making multi-layer approach including DEMATEL, ANP and VIKOR with linguistic Z-numbers, an accurate ranking of contracts based on their effectiveness in the face of challenges is provided. Hence, companies can implement the most appropriate possible strategies based on them. At first, by reviewing the literature the various types of SCCCs and the CRCs are gathered which have been illustrated in Tables 1 and 2, respectively. Next, the evaluations of experts on the effect of each CRCs on others have been collected to extract the weights of CRCs. The results are illustrated in Table 5.

Table 5 The Z-numbered matrix of the influences of criteria on each other
Full size table

After evaluating the effects, the score of each linguistic z-assessment is computed and the crisp matrix is constructed (Eqs. (2) to (4)). Next, the matrix is normalized (Eqs. (6) and (7)). Afterwards, the total influence matrix is computed (Eq. (8)) which is shown in Table 6.

Table 6 Total influence matrix of DEMATEL
Full size table

The CRSs are analyzed by obtaining the row sum and the column sum (Eqs. (9) and (10)) of the total influence matrix (Table 6). The results are presented as follows (Table 7). The green cells in the last column present the causes and the red ones the effects.

Table 7 z-DEMATEL results
Full size table

As illustrated in Figure, C1 is the most influential criterion on others. Moreover, C7 and C8 are the most influenced criteria. In addition, C2 is the most related within the system. Succeeding, the total influence matrix is normalized (Eq. 11) as shown in Table 8 and the cause and effect diagram of CRCs is shaped in Fig. 4.

Table 8 Normalized total influence matrix for DANP
Full size table
Fig. 4
figure 4

Cause and Effect Diagram of CRCs

Full size image

By transposing the normalized total influence matrix (Eqs. (12) and (13)), an unweighted supermatrix is constructed. Consequently, the weighted supermatrix is constructed by the multiplication of the total influence matrix and unweighted supermatrix via Eqs. (14) to (16). Finally, the weights of the criteria are extracted employing limiting the weighted supermatrix by raising it to a sufficiently large value by Eq. (17). The weights of the core repurposing challenges are mentioned in Table 9.

Table 9 Weights of CRCs (core repurposing challenges) emanated from z-DANP
Full size table

As elaborated in Table 9, collaboration is the most significant CRC. Besides, data availability is also crucial. In the following, the experts evaluated the effect of each SCCC facing with each of CRCs. The evaluations have been conducted applying the Z-numbered scale and the Z-numbered decision matrix of Table 10 has been constructed.

Table 10 The linguistic Z-numbered decision matrix for VIKOR
Full size table

The score of the evaluations of the decision matrix is computed (Eqs. (2) to (4)) and the crisp decision matrix is shaped (Eq. (18)). After attaining the crisp matrix, the decision matrix is normalized to apply the VIKOR method by Eq. (19). The results are illustrated in Table 11. As all the criteria are benefit criteria, the ideal value is the maximum value and the anti-ideal value is the minimum value of each column as shown in the last two rows (Eq. (20)).

Table 11 Normalized decision matrix
Full size table

Consequently, Si, Ri, and Qi are computed via Eqs. (21) to (23). Accordingly, the final score and rank of SCCCs are obtained and presented in Table 12. It is notable that due to the major agreement of the experts, (v) was considered 0.5.

Table 12 Prioritization of SCCCs
Full size table

As illustrated in Table 12, effort-sharing contracts can reduce the challenges of repurposing more effectively than other types of contracts. In contrast, risk-sharing contracts cannot face the challenges, efficiently. Following, the contracts are divided into four groups according to the score quartiles emanated from linguistic z-VIKOR including diamond, gold, star and question mark as illustrated in Table 13.

Table 13 SCCCs Clusters
Full size table

Table 13 demonstrates the four groups of contracts. As shown in the mentioned table, effort sharing, cost-sharing, credit option and buyback contracts are the best contracts that companies can select to reduce CRCs. These findings are discussed further in Sect. 5.

5 Discussion and implications

With the spread of Covid-19, the future of numerous industrial infrastructures and planning in all countries was seriously questioned. This ignorance and inability to predict the future had serious effects on various industries. Under these circumstances, the activities of the pharmaceutical industry not only did not stop like many other industries but also increased rapidly (Fox et al. 2020). In this situation, pharmaceutical companies were forced to try to achieve drug treatment and vaccines for this disease, as well as develop the production volume of their current effective drugs. In addition to investing in scientific studies and manufacturing infrastructure, focusing on distribution systems also became crucial for these companies (Lucero-Prisno et al. 2020). There were two main reasons for this. First, that corporate distribution systems could not cope with the high volume of production. Second, quarantine in countries has severely disrupted transportation and imposed significant costs on companies. This situation was even more intensive for underdeveloped countries and emerging economies such as Iran as the studied case. Hence, the way pharmaceutical companies collaborate with other companies inside and outside the industry (Vedel 2021), governments and international institutions, including the World Health Organization (WHO), faced serious changes (Chakraborty et al. 2020). In this regard, according to the weights extracted in Table 9, collaboration got the most critical challenge for these companies. Moreover, escalating the speed of companies' comprehensive activities increased their need for data (Bolislis et al. 2020). This need took on a more serious form as data collection and analysis faced meaningful difficulties in the new context. On the other hand, in addition to the ignorance of the new situation, the competition for the highest benefit also became another major reason for companies not having access to data (Meyer 2020). Therefore, as shown in Table 9, data availability is a significant challenge for companies. Furthermore, The Covid-19 pandemic disrupted all the rules, regulations, and orders governing corporate interactions that had been created and developed over the years (Ueda et al. 2021). As a result, according to Table 9, the regulation framework plays a highlighted role as a CRC. In contrast, the new conditions predicted that pharmaceutical companies would become the most profitable enterprises. As a consequence, the willingness to invest in these companies increased and the shares of these companies jumped significantly. In addition, governments and international organizations have invested heavily in the development of pharmaceutical companies. For this reason, financial support for companies according to Table 9 is not a significant challenge in the merging economy of Iran as the majority of the economy and enterprises in the drug and pharmaceutical sectors are managed by the officials.

On the other hand, according to Table 13, four types of diamond contracts (the highest-ranked cluster of coordination contracts) are effort sharing, cost-sharing, credit option and buyback. This means that the four contracts are more effective in reducing the severity of the repurposing challenges. As in the new context, achieving the desired result and goals is not very reliable, contracts that focus on the efforts of companies instead of focusing on the results can help them solve the challenges (Mahdiraji et al. 2020). For this reason, the effort-sharing contract was ranked first in the diamond category. In addition, as explained earlier, with a sudden mutation incorporate costs, sharing these costs can go a long way toward solving their challenges, and as a result, cost-sharing contracts have a high priority. Moreover, due to the high increase in demand and limitations in responding to the needs of all applicants, it is especially important to pay attention to their past performance and historical orders to prioritize them and pricing appropriately. That's why credit option contracts are in the diamond category. Finally, since the required capital and production, distribution, and sales costs, as well as the existing demand, are not predictable, the buyback contract can provide sufficient confidence for the members of the supply chain. This prioritization seems to be reasonably valid for the develo** country of Iran as well. However, given the financial sanctions, financial support seems to be more important, and in addition, contracts that pay more attention to this issue, such as cost-sharing contracts, received a higher rank. As collaboration and data availability are the most significant challenges, the contracts that can reduce the effects of the mentioned challenges are also efficient. Hence, four contracts including two-part tariff, a quantity discount, quantity flexibility and bonus contracts are classified as the gold cluster. A two-part tariff contract obligates retailers to pay a fixed franchise fee to suppliers. Hence, it makes a relation between retailer and supplier directly and strengthens supply chain relationships and, on the other hand, provides suppliers with more information from retailers, which can be very helpful. Moreover, the quantity flexibility and quantity discount contracts, which are found on the number of orders, are very effective against the challenge of lack of demand information. Flexibility reduces potential losses in erroneous demand forecasting, and discount-based contracts generally reduce the cost of large quantity orders. Additionally, these contracts can increase the level of collaboration by encouraging buyers, which in turn ensures the supplier's profit. Furthermore, bonus contracts can consolidate the relationships in the supply chain by increasing collaboration through more supplier involvement in all aspects of the supply chain. Contrarily, star clusters containing revenue sharing, option, profit sharing, and backup supplier contracts can sometimes be brilliant in reducing challenges; however, they can not have a favorable effect on other challenges for all members of the supply chain. Revenue and profit-sharing contracts can lead to more supplier collaboration with lower levels of the supply chain. Nonetheless, due to the lack of information about the certainty of sufficient income and profit, the collaboration would not be stable. The other two contracts in this cluster can also affect the challenge of data availability by empowering and supporting lower levels of the supply chain; nevertheless, it does not necessarily mean that they will satisfy the supplier and thus building up the collaboration. Eventually, the effect of the last cluster contracts on resolving or reducing the challenges is not clear and these contracts are not recommended for repurposing strategies.

To check the validity of the results, the ranking of the proposed approach with other popular methods including Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), COmplex PRoportional ASsessment (COPRAS), and Evaluation Based on Distance from Average Solution (EDAS) has been considered (Mahdiraji et al. 2021). The results are presented as a radar chart illustrated in Fig. 5 As the figure presents, there is no marked difference amongst the methods, indicating the robustness of the proposed multi-layer approach.

Fig. 5
figure 5

Comparison of rankings and robustness of results

Full size image

In the present study, an attempt has been made to present a new framework to view coordination contracts with a unique perspective. These efforts have been made in the past, but the condition of the Covid 19 pandemic needs to be reconsidered. Combining DEMATEL-ANP and VIKOR methods with linguistic Z-number was one of the new achievements of this research. Shen and Wang (2018) and Das et al. (2020) have integrated the Z-numbers with VIKOR but linguistic Z-numbers have not been employed before ( Shen and Wang 2018; Das et al. 2020). Moreover, Kumar and Anbanandam (2020) and Li et al. (2021a,  b) have in order applied to grey and interval-valued intuitionistic fuzzy DANP, but also no research has combined linguistic Z-number with the DANP method (Kumar and Anbanandam 2020; Li et al. 2021b) It is important to pay attention to this combination to ensure sufficient validity of the calculations and the results obtained because the degree of uncertainty in these conditions is very high.

As explained above, Covid 19 disease created new conditions for companies, and supply chain managers were forced to look at partnership contracts from a different perspective. Until now, looking at contracts has generally been aimed at increasing capabilities and gaining more advantage from them. However, in the new context, paying attention to the challenges and reducing the effect of their potential harms on the performance of companies became especially important, and as a result of the present study, it tried to look at the issue of coordination contracts from this perspective and their impact in mitigating repurposing challenges. Iran as an emerging economy has faced serious obstacles in the development of its pharmaceutical industry due to mismanagement, corruption, and financial sanctions. Even after the outbreak of this disease, Iran needs to establish communication and cooperative interactions more than developed countries. However, even many underdeveloped or emerging countries have managed the vaccination procedure more efficient than Iran (e.g. Cuba, Turkey, UAE, etc.), This happened at a time when, first, international financial transfers were not as easy as in other countries, and second, Irans financial and economic structure was more vulnerable than in developed countries. In this regard, Iran tried to meet its needs by relying on its domestic capabilities. To achieve this, it became important to establish a broader horizontal and vertical relationship in the supply chain of pharmaceutical companies, which are also the governmental public sector. As a result, this country has entered the fifth peak of the COVID-19 death rate in July 2021. Although the Iranian pharmaceutical industry faced this pandemic differently from the rest of the world, diamond-type contracts, and in particular cost-sharing contracts, can help address key repurposing challenges, including financial support.

6 Conclusion and future recommendations

With the spread of the covid-19 pandemic, serious global developments took place in various industries. The pharmaceutical industry is one of the main industries that had to adapt quickly to the new conditions. In this regard, the industry needs to review various aspects of its operations, including supply chain management. Choosing the right coordination contract, which until now was mainly aimed at increasing the advantage, now needs to be done to reduce the impact of the repurposing challenges. In this research, a DEMATEL-ANP-VIKOR framework under the condition of linguistic Z-numbers has been proposed to evaluate the effect of each supply chain coordination contract on the decrease of the core repurposing challenges. The results demonstrated that collaboration, data availability, and regulatory framework are the most significant repurposing challenges and effort sharing, cost-sharing, credit option and buyback contracts can affect them more influentially.

This research also faces some limitations. First of all, only the experts of the Iranian pharmaceutical sector have participated in this research. Furthermore, a questionnaire was attained by the focus group. The results would be changed if each expert complete the questionnaire independently. Moreover, this research was implemented in the emerging economy of Iran. It is recommended to run similar research for developed countries for benchmarking the results. Additionally, this study is achieved during Covid-19. Complementary research is suggested to perform for post-Covid-19. Sooner or later, other scholars can conduct the scheduled approach in their sector, industry, supply chain, or territory and benchmark the results with this research. From the perspective of theory, although, this article has benefited from linguistic Z-numbers in the multi-layer decision-making approach; however, it is recommended to apply novel techniques such as the Markov chain to consider the dynamism of the data during the time in future studies. Moreover, besides linguistic Z-numbers, other conditions of uncertainty e.g., hesitant fuzzy, interval-valued intuitionistic fuzzy, and Neutrosophic numbers can also be integrated with MCDM techniques to check whether the results are robust or not. Furthermore, the results emanated in this research are based on selective methods including DEMATEL, ANP, and VIKOR. The authors recommend that in the future, other scholars benefit from the combination of interpretive structural modeling (ISM) (Jafari-Sadeghi et al. 2021) and principal component analysis (PCA) with the DEMATEL method for more reliability of the results and a clear conceptual model demonstrating the relationship amongst the repurposing challenges.