Fostering the Reuse of Manufacturing Resources for Resilient and Sustainable Supply Chains

In the current context characterized by turbulent market conditions and the increasing relevance of sustainability requirements, reconfigurable manufacturing systems (RMSs) offer great potentialities for supply chains and networks. While plenty of contributions have addressed RMSs from a technological and system-specific perspective since the mid-1990s, the research interest for the strategic potentialities of RMSs at the supply chain level is recent and mainly related to building supply chains’ resilience and sustainability. Despite the interest, methods to support supply chains to strategically exploit RMSs are still missing, while being highly needed. In this paper, a method—consisting of an index to assess machines reusability and a mixed integer programming (MIP) algorithm—is provided to support the identification of reusable and reconfigurable machine candidates at the early stage of the strategic network design. The overall method allows machines to be compared based on their reusability and geographical locations. The application of the method, as well as an example referring to the production of emergency devices during the COVID-19 pandemic are reported. The theoretical and practical implications of the study are also discussed, and, among others, strategic parameters related to machines have been identified and elaborated as enablers of supply chain reconfigurability; the proposed method supports practitioners in improving supply chain resilience and sustainability. The method also encourages practitioners towards the development and adoption of reconfigurable machines. Finally, this study also has social impacts for local communities and stimulates customer-centric collaboration among companies belonging to similar industries and sectors.


Introduction
Nowadays, specific contextual factors such as the turbulent market conditions and the growing consciousness towards sustainable development are pressuring manufacturers and supply chains. Disruptions arising from many sources including natural disasters, pandemics, exhaustion of resources or geopolitical factors happen rapidly and without warning [1]. Supply chains need resilience, i.e., the adaptive capability to prepare for unexpected events, respond to disruptions and recover from them [1]. For example, during the COVID-19 pandemic, the closing of most of the European borders forced supply chains to reconfigure their networks and manage the emergency by reusing locally available manufacturing resources [2]. Supply chains also aim to enhance network sustainability while ensuring adequate profitability. Historically, encouraged by severe price competition between logistics and transportation companies [3], manufacturers have seized the opportunity to source materials and products internationally in order to reduce their bottom-line cost [4]. Today, supply chains have an increasing interest in reducing their carbon footprint

Background and Literature Review
Supply chain resilience and sustainability are impacted by the strategic network design phase [20]. Indeed, the configuration or design of the supply chain is a strategic task [21]. Since resilience and sustainability are both extremely relevant to supply chains [20], many studies have addressed the impact of manufacturing resources on these performances; however, these were not in the reconfigurability research domain; in particular, published studies did not investigate the potentialities of reconfigurable resources supporting network reconfigurations. For example, Jabbarzadeh et al. [20] presented a methodology for the design of a sustainable supply network that performs resiliently in the face of random disruptions based on the sustainability performance of the suppliers. Li et al. [22] outlined a mechanism for the impact of manufacturing resources on sustainable development.
In the conducted literature review, two main research domains were investigated through the following search string: "reconfigurable manufacturing" and "supply chain". The search was conducted on Scopus and Web of Science (WoS), as relevant databases to identify scientific contributions. To ensure the identification of the most pertinent articles, The proposed method consists of a new index to assess the reusability of technical resources, which is used in a mixed integer programming (MIP) algorithm to compare different network configurations and support the identification of reusable and reconfigurable resource candidates at the early stage of the strategic network design. The application of the overall method to improve supply chain resilience or sustainability is discussed in Section 4. As illustrated in Section 3.1, for a needed operation type, the reusability index of a candidate resource is a number within the interval [0, 1]; its quantification is based on the assessment of both: (i) the similarity of the candidate with a selected benchmark resource and (ii) the reconfigurability of the candidate. As illustrated in Section 3.2, for each of the needed operation types, the reusability index is one of the inputs of the MIP algorithm; the algorithm also considers the geographical locations of candidate resources and their distances from areas of interest in order to identify and select, for each needed operation type, those candidates having the highest reusability index within the areas of interest.

Reusability Index
To support the strategic network design phase, the reusability assessment should be based on a few essential parameters describing the technical resources, i.e., the machines at the workstation level. For the remainder of this paper, "machine" is generically used to refer to either a machine or a robot changing (including joining and mechanical fastening) one or more physical and/or chemical characteristics of the input product or part according to the operation sheets. Machines usually entail high investment costs and greatly affect the reconfigurability potentialities at network level.
Based on the classification code proposed by Sorensen et al. [29], four features, describing a machine at workstation level, its relationship with the operations (process domain), and with a few selected properties of the output, are chosen in this study: • the general description of the machine functionality (GMF), i.e., the operations that can be executed by the machine. Depending on the specific machine, GMF can either be: (i) transformations which modify the geometry, mechanical and/or physical properties of products or parts; (ii) assembly operations, in which two or more separate parts are joined to form subassemblies or products [39]; • the interval representing the range of sizes of the output products or parts (RS); • the list of different materials of the output products or parts (RM); • the production capacity of the machine (PC), representing the relationship between the machine functionality and the overall output volumes.
GMF could be described through the classification code related to workstations, and specifically machines, provided by Sorensen et al.; regardless, the way GMF, RS, RM and PC should be coded in a consistent and universal way is considered outside the scope of the present study, while the reason for their inclusion in the essential parameters supporting the early stage of the strategic network design phase is hereafter justified, specifically: GMF allows the comparison between machines (in the resource domain) based on the needed operations (thus the process domain); RS and PC are also included because product or part size and production volumes are the main drivers for the design of manufacturing systems and greatly impact the physical characteristics of technical resources [6,29]. The features RS and PC also permit implicit consideration of other technical resources such as material handling system (e.g., the RS property drives size and type of handling systems). Finally, the RM feature is included due to the increasing relevance of sustainability requirements, which are leading companies, for example, to replace pollutive materials with sustainable or recycled ones.
Considering the operation i, implemented by the machine X i , the assessment of the reusability of another machine Z i requires the evaluation of the similarity between its functionality and the functionality provided by X i . X i could also be a selected benchmark machine for executing the operation i. The reusability of Z i also depends on its reconfigurability, thus on its modularity [12,16].
In this study, the reusability index at the workstation level. For the remainder of this paper, "machine" is generically used to refer to either a machine or a robot changing (including joining and mechanical fastening) one or more physical and/or chemical characteristics of the input product or part according to the operation sheets. Machines usually entail high investment costs and greatly affect the reconfigurability potentialities at network level. Based on the classification code proposed by Sorensen et al. [29], four features, describing a machine at workstation level, its relationship with the operations (process domain), and with a few selected properties of the output, are chosen in this study: • the general description of the machine functionality (GMF), i.e., the operations that can be executed by the machine. Depending on the specific machine, GMF can either be: (i) transformations which modify the geometry, mechanical and/or physical properties of products or parts; (ii) assembly operations, in which two or more separate parts are joined to form subassemblies or products [39]; • the interval representing the range of sizes of the output products or parts (RS); • the list of different materials of the output products or parts (RM); • the production capacity of the machine (PC), representing the relationship between the machine functionality and the overall output volumes.
GMF could be described through the classification code related to workstations, and specifically machines, provided by Sorensen et al.; regardless, the way GMF, RS, RM and PC should be coded in a consistent and universal way is considered outside the scope of the present study, while the reason for their inclusion in the essential parameters supporting the early stage of the strategic network design phase is hereafter justified, specifically: GMF allows the comparison between machines (in the resource domain) based on the needed operations (thus the process domain); RS and PC are also included because product or part size and production volumes are the main drivers for the design of manufacturing systems and greatly impact the physical characteristics of technical resources [6,29]. The features RS and PC also permit implicit consideration of other technical resources such as material handling system (e.g., the RS property drives size and type of handling systems). Finally, the RM feature is included due to the increasing relevance of sustainability requirements, which are leading companies, for example, to replace pollutive materials with sustainable or recycled ones.
Considering the operation i, implemented by the machine Xi, the assessment of the reusability of another machine Zi requires the evaluation of the similarity between its functionality and the functionality provided by Xi. Xi could also be a selected benchmark machine for executing the operation i. The reusability of Zi also depends on its reconfigurability, thus on its modularity [12,16].
In this study, the reusability index ɣi (Xi, Zi) of a candidate machine Zi is calculated through the similarity Si(Xi, Zi) and reconfigurability Ri(Zi) vectors, where: (X i , Z i ) of a candidate machine Z i is calculated through the similarity S i (X i , Z i ) and reconfigurability R i (Z i ) vectors, where: The four components s ij and r ij of the two vectors can assume binary values that are set considering, respectively, GMF, RS, RM and PC. Specifically, the components of S i (X i , Z i ) are defined by comparing the machine X i with the candidate Z i : Moreover, σ i (X i , Z i ) ∈ [0, 1], the similarity index of Z i with X i in the current configuration, is introduced and calculated as follows: To assess machine reusability considering jointly similarity and modularity, in this study, machine reconfigurability is evaluated according to the possibility to add, remove or replace modules in order to implement the required operation.
The components of R i (Z i ) do not require a comparison between X i and Z i , but their definition depends on the operation i and on the modularity of Z i , specifically: • r i1 = 1 if GMF of Z i can be changed by replacing one or more modules of Z i , otherwise, r i1 = 0; • r i2 = 1 if RS of Z i can be changed by replacing one or more modules of Z i , otherwise, r i2 = 0; • r i3 = 1 if RM of Z i can be changed by replacing one or more modules of Z i , otherwise, r i3 = 0; • r i4 = 1 if PC of Z i can be changed by adding/removing one or more modules of Z i , otherwise, r i4 = 0.
In the mathematical formulation, the reusability index is a function of the machine similarity and reconfigurability • the production capacity of the machine (PC), representing the relationship between the machine functionality and the overall output volumes.
GMF could be described through the classification code related to workstations, and specifically machines, provided by Sorensen et al.; regardless, the way GMF, RS, RM and PC should be coded in a consistent and universal way is considered outside the scope of the present study, while the reason for their inclusion in the essential parameters supporting the early stage of the strategic network design phase is hereafter justified, specifically: GMF allows the comparison between machines (in the resource domain) based on the needed operations (thus the process domain); RS and PC are also included because product or part size and production volumes are the main drivers for the design of manufacturing systems and greatly impact the physical characteristics of technical resources [6,29]. The features RS and PC also permit implicit consideration of other technical resources such as material handling system (e.g., the RS property drives size and type of handling systems). Finally, the RM feature is included due to the increasing relevance of sustainability requirements, which are leading companies, for example, to replace pollutive materials with sustainable or recycled ones.
Considering the operation i, implemented by the machine Xi, the assessment of the reusability of another machine Zi requires the evaluation of the similarity between its functionality and the functionality provided by Xi. Xi could also be a selected benchmark machine for executing the operation i. The reusability of Zi also depends on its reconfigurability, thus on its modularity [12,16].
In this study, the reusability index ɣ i (Xi, Zi) of a candidate machine Zi is calculated through the similarity Si(Xi, Zi) and reconfigurability Ri(Zi) vectors, where: The four components sij and rij of the two vectors can assume binary values that are set considering, respectively, GMF, RS, RM and PC. Specifically, the components of Si(Xi,Zi) are defined by comparing the machine Xi with the candidate Zi: Moreover, σi(Xi,Zi) ∈ [0, 1], the similarity index of Zi with Xi in the current configuration, is introduced and calculated as follows: • σi(Xi,Zi) = ∑j = 1,…4(ωjsij) where • [ω1;…;ω4]: ∑j = 1,…4(ωj) = 1 are context-specific weights given to GMF, RS, RM and PC. : • the production capacity of the machine (PC), representing the relationship between the machine functionality and the overall output volumes.
GMF could be described through the classification code related to workstations, and specifically machines, provided by Sorensen et al.; regardless, the way GMF, RS, RM and PC should be coded in a consistent and universal way is considered outside the scope of the present study, while the reason for their inclusion in the essential parameters supporting the early stage of the strategic network design phase is hereafter justified, specifically: GMF allows the comparison between machines (in the resource domain) based on the needed operations (thus the process domain); RS and PC are also included because product or part size and production volumes are the main drivers for the design of manufacturing systems and greatly impact the physical characteristics of technical resources [6,29]. The features RS and PC also permit implicit consideration of other technical resources such as material handling system (e.g., the RS property drives size and type of handling systems). Finally, the RM feature is included due to the increasing relevance of sustainability requirements, which are leading companies, for example, to replace pollutive materials with sustainable or recycled ones.
Considering the operation i, implemented by the machine Xi, the assessment of the reusability of another machine Zi requires the evaluation of the similarity between its functionality and the functionality provided by Xi. Xi could also be a selected benchmark machine for executing the operation i. The reusability of Zi also depends on its reconfigurability, thus on its modularity [12,16].
In this study, the reusability index ɣ i (Xi, Zi) of a candidate machine Zi is calculated through the similarity Si(Xi, Zi) and reconfigurability Ri(Zi) vectors, where: The four components sij and rij of the two vectors can assume binary values that are set considering, respectively, GMF, RS, RM and PC. Specifically, the components of Si (Xi,Zi) are defined by comparing the machine Xi with the candidate Zi: Moreover, σi(Xi,Zi) ∈ [0, 1], the similarity index of Zi with Xi in the current configuration, is introduced and calculated as follows: • σi(Xi,Zi) = ∑j = 1,…4(ωjsij) where • [ω1;…;ω4]: ∑j = 1,…4(ωj) = 1 are context-specific weights given to GMF, RS, RM and PC.
the interval representing the range of sizes of the output products or parts (RS); • the list of different materials of the output products or parts (RM); • the production capacity of the machine (PC), representing the relationship between the machine functionality and the overall output volumes.
GMF could be described through the classification code related to workstations, and specifically machines, provided by Sorensen et al.; regardless, the way GMF, RS, RM and PC should be coded in a consistent and universal way is considered outside the scope of the present study, while the reason for their inclusion in the essential parameters supporting the early stage of the strategic network design phase is hereafter justified, specifically: GMF allows the comparison between machines (in the resource domain) based on the needed operations (thus the process domain); RS and PC are also included because product or part size and production volumes are the main drivers for the design of manufacturing systems and greatly impact the physical characteristics of technical resources [6,29]. The features RS and PC also permit implicit consideration of other technical resources such as material handling system (e.g., the RS property drives size and type of handling systems). Finally, the RM feature is included due to the increasing relevance of sustainability requirements, which are leading companies, for example, to replace pollutive materials with sustainable or recycled ones.
Considering the operation i, implemented by the machine Xi, the assessment of the reusability of another machine Zi requires the evaluation of the similarity between its functionality and the functionality provided by Xi. Xi could also be a selected benchmark machine for executing the operation i. The reusability of Zi also depends on its reconfigurability, thus on its modularity [12,16].
In this study, the reusability index ɣ i (Xi, parts are joined to form subassemblies or products [39]; • the interval representing the range of sizes of the output products or parts (RS); • the list of different materials of the output products or parts (RM); • the production capacity of the machine (PC), representing the relationship between the machine functionality and the overall output volumes.
GMF could be described through the classification code related to workstations, and specifically machines, provided by Sorensen et al.; regardless, the way GMF, RS, RM and PC should be coded in a consistent and universal way is considered outside the scope of the present study, while the reason for their inclusion in the essential parameters supporting the early stage of the strategic network design phase is hereafter justified, specifically: GMF allows the comparison between machines (in the resource domain) based on the needed operations (thus the process domain); RS and PC are also included because product or part size and production volumes are the main drivers for the design of manufacturing systems and greatly impact the physical characteristics of technical resources [6,29]. The features RS and PC also permit implicit consideration of other technical resources such as material handling system (e.g., the RS property drives size and type of handling systems). Finally, the RM feature is included due to the increasing relevance of sustainability requirements, which are leading companies, for example, to replace pollutive materials with sustainable or recycled ones.
Considering the operation i, implemented by the machine Xi, the assessment of the reusability of another machine Zi requires the evaluation of the similarity between its functionality and the functionality provided by Xi. Xi could also be a selected benchmark machine for executing the operation i. The reusability of Zi also depends on its reconfigurability, thus on its modularity [12,16].
In this study, the reusability index ɣ i (Xi, To assess machine reusability considering jointly similarity and modularity, in this study, machine reconfigurability is evaluated according to the possibility to add, remove or replace modules in order to implement the required operation. The components of Ri(Zi) do not require a comparison between Xi and Zi, but their definition depends on the operation i and on the modularity of Zi, specifically: In the mathematical formulation, the reusability index is a function of the machine similarity and reconfigurability ɣ: SxR → [0, 1]; ɣi,k(i) (Xi, Zi) is calculated as follows: Concluding, the four essential features (GMF, RS, RM and PC) have been specifically selected since the proposed reusability index is intended for strategic use by networks of companies. Moreover, the attribution of binary values to the components of the similarity Si(Xi, Zi) and reusability Ri(Zi) vectors is aligned with the aim to provide an assessment tool in the indispensable early stage of network configuration: the identification of suitable (reusable, thus profitable) candidate machines. The use of binary values not only makes the use of the tool easier, but it also supports fast identification of the most promising reusable machines. A subsequent phase of analysis of the candidates may be required, where additional detailing information could be added (see for example [29,40]). The presented assessment can be easily adjusted to address other manufacturing resources and/or include different features in order to support detailed and operational decisions (rather than comprehensive and strategic ones as aimed in this study).

Mixed Integer Programming (MIP) Algorithm
The proposed MIP algorithm (Algorithm 1) allows the comparison of different network configurations. The problem's data, parameters, decision variables and MIP formulation are defined below. To assess machine reusability considering jointly similarity and modularity, in this study, machine reconfigurability is evaluated according to the possibility to add, remove or replace modules in order to implement the required operation.
The components of Ri(Zi) do not require a comparison between Xi and Zi, but their definition depends on the operation i and on the modularity of Zi, specifically: In the mathematical formulation, the reusability index is a function of the machine similarity and reconfigurability ɣ: SxR → [0, 1]; ɣi,k(i) (Xi, Zi) is calculated as follows: is a four-component vector, representing the Boolean negation of the similarity vector Si(Xi, Zi); thus, in the formula, the term [(˺Si) • Ri]/4 is the scalar product of two vectors, divided by 4 which is the cardinality of the vectors.
Concluding, the four essential features (GMF, RS, RM and PC) have been specifically selected since the proposed reusability index is intended for strategic use by networks of companies. Moreover, the attribution of binary values to the components of the similarity Si(Xi, Zi) and reusability Ri(Zi) vectors is aligned with the aim to provide an assessment tool in the indispensable early stage of network configuration: the identification of suitable (reusable, thus profitable) candidate machines. The use of binary values not only makes the use of the tool easier, but it also supports fast identification of the most promising reusable machines. A subsequent phase of analysis of the candidates may be required, where additional detailing information could be added (see for example [29,40]). The presented assessment can be easily adjusted to address other manufacturing resources and/or include different features in order to support detailed and operational decisions (rather than comprehensive and strategic ones as aimed in this study).

Mixed Integer Programming (MIP) Algorithm
The proposed MIP algorithm (Algorithm 1) allows the comparison of different network configurations. The problem's data, parameters, decision variables and MIP formulation are defined below. To assess machine reusability considering jointly similarity a study, machine reconfigurability is evaluated according to the poss or replace modules in order to implement the required operation.
The components of Ri(Zi) do not require a comparison betwe definition depends on the operation i and on the modularity of Zi, In the mathematical formulation, the reusability index is a fu similarity and reconfigurability ɣ: Concluding, the four essential features (GMF, RS, RM and PC) selected since the proposed reusability index is intended for strateg companies. Moreover, the attribution of binary values to the compo Si(Xi, Zi) and reusability Ri(Zi) vectors is aligned with the aim to p tool in the indispensable early stage of network configuration: the ble (reusable, thus profitable) candidate machines. The use of b makes the use of the tool easier, but it also supports fast identificat ising reusable machines. A subsequent phase of analysis of the c quired, where additional detailing information could be added (se The presented assessment can be easily adjusted to address oth sources and/or include different features in order to support detaile cisions (rather than comprehensive and strategic ones as aimed in t

Mixed Integer Programming (MIP) Algorithm
The proposed MIP algorithm (Algorithm 1) allows the compa work configurations. The problem's data, parameters, decision var lation are defined below.
Zl,k(l)), i ≠ l ∈ O, distance within candidates pertaining operation types · R i ]/4 is the scalar product of two vectors, divided by 4 which is the cardinality of the vectors.
Concluding, the four essential features (GMF, RS, RM and PC) have been specifically selected since the proposed reusability index is intended for strategic use by networks of companies. Moreover, the attribution of binary values to the components of the similarity S i (X i , Z i ) and reusability R i (Z i ) vectors is aligned with the aim to provide an assessment tool in the indispensable early stage of network configuration: the identification of suitable (reusable, thus profitable) candidate machines. The use of binary values not only makes the use of the tool easier, but it also supports fast identification of the most promising reusable machines. A subsequent phase of analysis of the candidates may be required, where additional detailing information could be added (see for example [29,40]). The presented assessment can be easily adjusted to address other manufacturing resources and/or include different features in order to support detailed and operational decisions (rather than comprehensive and strategic ones as aimed in this study).

Mixed Integer Programming (MIP) Algorithm
The proposed MIP algorithm (Algorithm 1) allows the comparison of different network configurations. The problem's data, parameters, decision variables and MIP formulation are defined below.

Data
• O = (o1,…,on), set of the n needed operation types given by the route and operation sheets • M, set of machines • Xi ∈ M, i = oi ∈ O, benchmark machine or machine currently implementing oi • Zi,k(i) ∈ M, k(i) = (1,…, mi), set of the mi candidates that could execute oi • C, centroid representing an area of interest (e.g., location of the customer) • LM, set of locations of machines M including C • D(a, b) = distance between a and b, a, b ∈ LM • D(C, Zi,k(i)), Ɐ i ∈ O, distance between candidates and C • D(Zi,k(i), Zl,k(l)), i ≠ l ∈ O, distance within candidates pertaining to different operation types i ∈ O, distance between candidates and C • D(Z i,k(i) , Z l,k(l) ), i = l ∈ O, distance within candidates pertaining to different operation types • 0 ≤ uct or part size and production volumes are the main drivers for the design of manufacturing systems and greatly impact the physical characteristics of technical resources [6,29]. The features RS and PC also permit implicit consideration of other technical resources such as material handling system (e.g., the RS property drives size and type of handling systems). Finally, the RM feature is included due to the increasing relevance of sustainability requirements, which are leading companies, for example, to replace pollutive materials with sustainable or recycled ones. Considering the operation i, implemented by the machine Xi, the assessment of the reusability of another machine Zi requires the evaluation of the similarity between its functionality and the functionality provided by Xi. Xi could also be a selected benchmark machine for executing the operation i. The reusability of Zi also depends on its reconfigurability, thus on its modularity [12,16].
In this study, the reusability index ɣ i (Xi, Zi) of a candidate machine Zi is calculated through the similarity Si(Xi, Zi) and reconfigurability Ri(Zi) vectors, where: The four components sij and rij of the two vectors can assume binary values that are set considering, respectively, GMF, RS, RM and PC. Specifically, the components of Si(Xi,Zi) are defined by comparing the machine Xi with the candidate Zi: Moreover, σi(Xi,Zi) ∈ [0, 1], the similarity index of Zi with Xi in the current configuration, is introduced and calculated as follows: : ∑j = 1,…4(ωj) = 1 are context-specific weights given to GMF, RS, RM and PC.
i,k(i) ≤ 1 reusability index of Z i,k(i) (calculated based on X i and Z i,k(i) as illustrated in Section 3.1)

Parameters
• v, maximum admissible distance between a candidate and C • w, maximum admissible distance within candidates (optional).
Decision variables • 0 ≤ ɣi,k(i) ≤ 1 reusability index of Zi,k(i) (calculated based on Xi and Zi,k(i) as illustrated in Section 3.1) Parameters • v, maximum admissible distance between a candidate and C • w, maximum admissible distance within candidates (optional).  In the first phase of the algorithm, for the first operation i ∈ O, the objective (1) is to identify the candidate Zi,k(i) having minimum distance from the centroid C representing the area of interest. The objective (2) aims to identify the candidate Zi,k(i) with maximum reusability, considering similarity and reconfigurability to replace machine Xi. Since the two objectives might be conflicting, the objective (1) can be replaced with the constraint (3), which, depending on the parameter v, defines the maximum admissible distance between the candidate Zi,k(i) and the centroid C. Indeed, when distance D(C, Zi,k(i)) > v, then zi,k(i) = 0, while when distance D(C, Zi,k(i)) ≤ v, then zi,k(i) = 1; thus it represents an admissible solution.
When the identification of the zi,k(i), which maximizes the objective (2), is completed for the first operation i, a subsequent operation i + 1 is considered, and this is reiterated until candidate machines are investigated for all n required operations i ∈ O. The constraint (4) verifies that a candidate machine is selected for all n operations. If the constraint (4) is not satisfied, it has not been possible to identify reusable candidates for one or more operations. In that case, the decision maker should modify the parameter v, thus enlarging the space of admissible solutions.
Phase 2 of the algorithm can be optionally implemented; by introducing the constraint (5), the set of admissible solutions is potentially reduced and a new optimal solution might be identified. Indeed, (5) ensures that the internal distance between candidate machines pertaining to the required operation types is lower than the parameter w.

Decision Logic of the Method
The decision logic of the overall method, including reusability assessment and MIP algorithm (only phase 1 is represented), is reported in Figure 3.
erties of products or parts; (ii) assembly operations, in which two or more separate parts are joined to form subassemblies or products [39]; • the interval representing the range of sizes of the output products or parts (RS); • the list of different materials of the output products or parts (RM); • the production capacity of the machine (PC), representing the relationship between the machine functionality and the overall output volumes.
GMF could be described through the classification code related to workstations, and specifically machines, provided by Sorensen et al.; regardless, the way GMF, RS, RM and PC should be coded in a consistent and universal way is considered outside the scope of the present study, while the reason for their inclusion in the essential parameters supporting the early stage of the strategic network design phase is hereafter justified, specifically: GMF allows the comparison between machines (in the resource domain) based on the needed operations (thus the process domain); RS and PC are also included because product or part size and production volumes are the main drivers for the design of manufacturing systems and greatly impact the physical characteristics of technical resources [6,29]. The features RS and PC also permit implicit consideration of other technical resources such as material handling system (e.g., the RS property drives size and type of handling systems). Finally, the RM feature is included due to the increasing relevance of sustainability requirements, which are leading companies, for example, to replace pollutive materials with sustainable or recycled ones.
Considering the operation i, implemented by the machine Xi, the assessment of the reusability of another machine Zi requires the evaluation of the similarity between its functionality and the functionality provided by Xi. Xi could also be a selected benchmark machine for executing the operation i. The reusability of Zi also depends on its reconfigurability, thus on its modularity [12,16].
In this study, the reusability index ɣ i (Xi, Zi) of a candidate machine Zi is calculated through the similarity Si(Xi, Zi) and reconfigurability Ri(Zi) vectors, where: The four components sij and rij of the two vectors can assume binary values that are set considering, respectively, GMF, RS, RM and PC. Specifically, the components of are defined by comparing the machine Xi with the candidate Zi: Moreover, σi(Xi,Zi) ∈ [0, 1], the similarity index of Zi with Xi in the current configuration, is introduced and calculated as follows: • [ω1;…;ω4]: ∑j = 1,…4(ωj) = 1 are context-specific weights given to GMF, RS, RM and PC. Figure 2 represents the relationship between O, set of the n needed operation types and M, set of machines, including current machine X i and the set of the replacing candidates Z i,k(i) . In the first phase of the algorithm, for the first operation i ∈ O, the objective (1) is to identify the candidate Z i,k(i) having minimum distance from the centroid C representing the area of interest. The objective (2) aims to identify the candidate Z i,k(i) with maximum reusability, considering similarity and reconfigurability to replace machine X i . Since the two objectives might be conflicting, the objective (1) can be replaced with the constraint (3), which, depending on the parameter v, defines the maximum admissible distance between the candidate Z i,k(i) and the centroid C. Indeed, when distance D(C, Z i,k(i) ) > v, then z i,k(i) = 0, while when distance D(C, Z i,k(i) ) ≤ v, then z i,k(i) = 1; thus it represents an admissible solution.
When the identification of the z i,k(i) , which maximizes the objective (2), is completed for the first operation i, a subsequent operation i + 1 is considered, and this is reiterated until candidate machines are investigated for all n required operations i ∈ O. The constraint (4) verifies that a candidate machine is selected for all n operations. If the constraint (4) is not satisfied, it has not been possible to identify reusable candidates for one or more operations. In that case, the decision maker should modify the parameter v, thus enlarging the space of admissible solutions.
Phase 2 of the algorithm can be optionally implemented; by introducing the constraint (5), the set of admissible solutions is potentially reduced and a new optimal solution might be identified. Indeed, (5) ensures that the internal distance between candidate machines pertaining to the required operation types is lower than the parameter w.

Decision Logic of the Method
The decision logic of the overall method, including reusability assessment and MIP algorithm (only phase 1 is represented), is reported in Figure 3.  Figure 3 shows that, for an individual operation i ∈ O, information about the GMF, RS, RM and PC, in the form of coded items, are used to compare each candidate machine Z ik(i) , k(i) = (1, . . . ,m i ) and X i and calculate S ik(i) ; the reconfigurability of Z ik(i) is calculated whenever σ ik(i) = 1, based on the coded information about the reconfigurability of Z ik(i) . The candidate Z ik(i) with maximum reusability at the workstation level. For the remainder of this paper, "machine" is generically used to refer to either a machine or a robot changing (including joining and mechanical fastening) one or more physical and/or chemical characteristics of the input product or part according to the operation sheets. Machines usually entail high investment costs and greatly affect the reconfigurability potentialities at network level. Based on the classification code proposed by Sorensen et al. [29], four features, describing a machine at workstation level, its relationship with the operations (process domain), and with a few selected properties of the output, are chosen in this study: • the general description of the machine functionality (GMF), i.e., the operations that can be executed by the machine. Depending on the specific machine, GMF can either be: (i) transformations which modify the geometry, mechanical and/or physical properties of products or parts; (ii) assembly operations, in which two or more separate parts are joined to form subassemblies or products [39]; • the interval representing the range of sizes of the output products or parts (RS); • the list of different materials of the output products or parts (RM); • the production capacity of the machine (PC), representing the relationship between the machine functionality and the overall output volumes.
GMF could be described through the classification code related to workstations, and specifically machines, provided by Sorensen et al.; regardless, the way GMF, RS, RM and PC should be coded in a consistent and universal way is considered outside the scope of the present study, while the reason for their inclusion in the essential parameters supporting the early stage of the strategic network design phase is hereafter justified, specifically: GMF allows the comparison between machines (in the resource domain) based on the needed operations (thus the process domain); RS and PC are also included because product or part size and production volumes are the main drivers for the design of manufacturing systems and greatly impact the physical characteristics of technical resources [6,29]. The features RS and PC also permit implicit consideration of other technical resources such as material handling system (e.g., the RS property drives size and type of handling systems). Finally, the RM feature is included due to the increasing relevance of sustainability requirements, which are leading companies, for example, to replace pollutive materials with sustainable or recycled ones.
Considering the operation i, implemented by the machine Xi, the assessment of the reusability of another machine Zi requires the evaluation of the similarity between its functionality and the functionality provided by Xi. Xi could also be a selected benchmark machine for executing the operation i. The reusability of Zi also depends on its reconfigurability, thus on its modularity [12,16].
In this study, the reusability index ɣ i (Xi, Zi) of a candidate machine Zi is calculated through the similarity Si(Xi, Zi) and reconfigurability Ri(Zi) vectors, where: i,k(i) is selected, and the same procedure is reiterated for each operation i ∈ O. The procedure is initialized with the first needed operation i = 1 and related candidate machines and ends with the last needed operation i = n and related candidate machines.

Application of the Method
The application of the method, including the interpretation of the parameters, as well as the illustrative example, are described in this section. The method allows machines to be compared based on their reusability and geographical locations and can therefore be used to improve supply chain resilience and sustainability. Indeed, the preliminary identification of the areas of interest might depend on the supply chain's need to: (i) resiliently reconfigure a network after a major disruption or (ii) move manufacturing processes within areas of interest (e.g., closer to local customers) to reduce the network carbon footprint.

Interpretation of the Parameters of the Method
In the proposed method, parameters at the workstation level. For the remainder of this paper, "machine" is generically used to refer to either a machine or a robot changing (including joining and mechanical fastening) one or more physical and/or chemical characteristics of the input product or part according to the operation sheets. Machines usually entail high investment costs and greatly affect the reconfigurability potentialities at network level. Based on the classification code proposed by Sorensen et al. [29], four features, describing a machine at workstation level, its relationship with the operations (process domain), and with a few selected properties of the output, are chosen in this study: • the general description of the machine functionality (GMF), i.e., the operations that can be executed by the machine. Depending on the specific machine, GMF can either be: (i) transformations which modify the geometry, mechanical and/or physical properties of products or parts; (ii) assembly operations, in which two or more separate parts are joined to form subassemblies or products [39]; • the interval representing the range of sizes of the output products or parts (RS); • the list of different materials of the output products or parts (RM); • the production capacity of the machine (PC), representing the relationship between the machine functionality and the overall output volumes.
GMF could be described through the classification code related to workstations, and specifically machines, provided by Sorensen et al.; regardless, the way GMF, RS, RM and PC should be coded in a consistent and universal way is considered outside the scope of the present study, while the reason for their inclusion in the essential parameters supporting the early stage of the strategic network design phase is hereafter justified, specifically: GMF allows the comparison between machines (in the resource domain) based on the needed operations (thus the process domain); RS and PC are also included because product or part size and production volumes are the main drivers for the design of manufacturing systems and greatly impact the physical characteristics of technical resources [6,29]. The features RS and PC also permit implicit consideration of other technical resources such as material handling system (e.g., the RS property drives size and type of handling systems). Finally, the RM feature is included due to the increasing relevance of sustainability requirements, which are leading companies, for example, to replace pollutive materials with sustainable or recycled ones.
Considering the operation i, implemented by the machine Xi, the assessment of the reusability of another machine Zi requires the evaluation of the similarity between its functionality and the functionality provided by Xi. Xi could also be a selected benchmark machine for executing the operation i. The reusability of Zi also depends on its reconfigurability, thus on its modularity [12,16].
In this study, the reusability index ɣ i (Xi, Zi)  at the workstation level. For the remainder of this paper, "machine" is generically used to refer to either a machine or a robot changing (including joining and mechanical fastening) one or more physical and/or chemical characteristics of the input product or part according to the operation sheets. Machines usually entail high investment costs and greatly affect the reconfigurability potentialities at network level. Based on the classification code proposed by Sorensen et al. [29], four features, describing a machine at workstation level, its relationship with the operations (process domain), and with a few selected properties of the output, are chosen in this study: • the general description of the machine functionality (GMF), i.e., the operations that can be executed by the machine. Depending on the specific machine, GMF can either be: (i) transformations which modify the geometry, mechanical and/or physical properties of products or parts; (ii) assembly operations, in which two or more separate parts are joined to form subassemblies or products [39]; • the interval representing the range of sizes of the output products or parts (RS); • the list of different materials of the output products or parts (RM); • the production capacity of the machine (PC), representing the relationship between the machine functionality and the overall output volumes.
GMF could be described through the classification code related to workstations, and specifically machines, provided by Sorensen et al.; regardless, the way GMF, RS, RM and PC should be coded in a consistent and universal way is considered outside the scope of the present study, while the reason for their inclusion in the essential parameters supporting the early stage of the strategic network design phase is hereafter justified, specifically: GMF allows the comparison between machines (in the resource domain) based on the needed operations (thus the process domain); RS and PC are also included because product or part size and production volumes are the main drivers for the design of manufacturing systems and greatly impact the physical characteristics of technical resources [6,29]. The features RS and PC also permit implicit consideration of other technical resources such as material handling system (e.g., the RS property drives size and type of handling systems). Finally, the RM feature is included due to the increasing relevance of sustainability requirements, which are leading companies, for example, to replace pollutive materials with sustainable or recycled ones.
Considering the operation i, implemented by the machine Xi, the assessment of the reusability of another machine Zi requires the evaluation of the similarity between its functionality and the functionality provided by Xi. Xi could also be a selected benchmark machine for executing the operation i. The reusability of Zi also depends on its reconfigurability, thus on its modularity [12,16].
In this study, the reusability index ɣ i (Xi, Zi)  at the workstation level. For the remainder of this paper, "machine" is generically used to refer to either a machine or a robot changing (including joining and mechanical fastening) one or more physical and/or chemical characteristics of the input product or part according to the operation sheets. Machines usually entail high investment costs and greatly affect the reconfigurability potentialities at network level. Based on the classification code proposed by Sorensen et al. [29], four features, describing a machine at workstation level, its relationship with the operations (process domain), and with a few selected properties of the output, are chosen in this study: • the general description of the machine functionality (GMF), i.e., the operations that can be executed by the machine. Depending on the specific machine, GMF can either be: (i) transformations which modify the geometry, mechanical and/or physical properties of products or parts; (ii) assembly operations, in which two or more separate parts are joined to form subassemblies or products [39]; • the interval representing the range of sizes of the output products or parts (RS); • the list of different materials of the output products or parts (RM); • the production capacity of the machine (PC), representing the relationship between the machine functionality and the overall output volumes.
GMF could be described through the classification code related to workstations, and specifically machines, provided by Sorensen et al.; regardless, the way GMF, RS, RM and PC should be coded in a consistent and universal way is considered outside the scope of the present study, while the reason for their inclusion in the essential parameters supporting the early stage of the strategic network design phase is hereafter justified, specifically: GMF allows the comparison between machines (in the resource domain) based on the needed operations (thus the process domain); RS and PC are also included because product or part size and production volumes are the main drivers for the design of manufacturing systems and greatly impact the physical characteristics of technical resources [6,29]. The features RS and PC also permit implicit consideration of other technical resources such as material handling system (e.g., the RS property drives size and type of handling systems). Finally, the RM feature is included due to the increasing relevance of sustainability requirements, which are leading companies, for example, to replace pollutive materials with sustainable or recycled ones.
Considering the operation i, implemented by the machine Xi, the assessment of the reusability of another machine Zi requires the evaluation of the similarity between its functionality and the functionality provided by Xi. Xi could also be a selected benchmark machine for executing the operation i. The reusability of Zi also depends on its reconfigurability, thus on its modularity [12,16].
In this study, the reusability index ɣ i (Xi, Zi) of a candidate machine Zi is calculated through the similarity Si(Xi, Zi) and reconfigurability Ri(Zi) vectors, where: The four components sij and rij of the two vectors can assume binary values that are set considering, respectively, GMF, RS, RM and PC. Specifically, the components of i,k(i) tends towards 1, the cost of replacing the X i with Z i,k(i) decreases due to the possibility to reuse existing modules;  ); thus, in the formula, the vectors, divided by 4 which is the cardinal Concluding, the four essential feature selected since the proposed reusability ind companies. Moreover, the attribution of bi Si(Xi, Zi) and reusability Ri(Zi) vectors is a tool in the indispensable early stage of net ble (reusable, thus profitable) candidate makes the use of the tool easier, but it also ising reusable machines. A subsequent p quired, where additional detailing inform The presented assessment can be easily sources and/or include different features in cisions (rather than comprehensive and str

Mixed Integer Programming (MIP) Algor
The proposed MIP algorithm (Algori work configurations. The problem's data, p lation are defined below. , but it is usually lower than investing in a purpose-built system.
The parameter v, the maximum admissible distance between a candidate and C, can be a pure or weighted geographical distance, estimating the maximum admissible cost associated with the transportation. More importantly, the definition of v might be driven by the supply chain's requirements in terms of resilience or sustainability.
The economic interpretation of the parameter w, the maximum admissible distance within candidates, is coherent with the impact of v.
The decision maker can repeat several times the MIP algorithm by progressively reducing the parameter v from a starting value to a minimum value. The starting value v may be the distance between the machines currently implementing the needed operations and the area of interest. The minimum value of v is constrained by the identification of admissible solutions. By setting an adequately low value of v, the identified machines determine a reduced transportation cost due to the lower distance from areas of interest.
Furthermore, defining the space of admissible solutions, the parameter v indirectly impacts on the reconfiguration costs, which are captured by the reusability index main), and with a few selected properties of the output, are chosen • the general description of the machine functionality (GMF), i can be executed by the machine. Depending on the specific ma be: (i) transformations which modify the geometry, mechanical erties of products or parts; (ii) assembly operations, in which parts are joined to form subassemblies or products [39]; • the interval representing the range of sizes of the output prod • the list of different materials of the output products or parts (R • the production capacity of the machine (PC), representing the the machine functionality and the overall output volumes.
GMF could be described through the classification code relate specifically machines, provided by Sorensen et al.; regardless, the w PC should be coded in a consistent and universal way is considere the present study, while the reason for their inclusion in the essentia ing the early stage of the strategic network design phase is hereafte GMF allows the comparison between machines (in the resource needed operations (thus the process domain); RS and PC are also in uct or part size and production volumes are the main drivers for t turing systems and greatly impact the physical characteristics of tec The features RS and PC also permit implicit consideration of oth such as material handling system (e.g., the RS property drives size systems). Finally, the RM feature is included due to the increasing bility requirements, which are leading companies, for example, to r rials with sustainable or recycled ones.
Considering the operation i, implemented by the machine Xi, reusability of another machine Zi requires the evaluation of the functionality and the functionality provided by Xi. Xi could also be machine for executing the operation i. The reusability of Zi also dep rability, thus on its modularity [12,16].
In this study, the reusability index ɣ i (Xi, Zi) of a candidate m calculated through the similarity Si(Xi, Zi) and reconfigurability Ri( When the second phase of the algorithm is implemented, the decision maker can repeat the algorithm by progressively reducing the parameter w. The parameter w impacts on the transportation cost by considering the distance within the machines of the identified solution. Therefore, w ensures the identification of an adequately low number of companies providing the required machines. Additionally, the parameter w, together with the reusability index Based on the classification code proposed by Sorensen et al. [29], four features, describing a machine at workstation level, its relationship with the operations (process domain), and with a few selected properties of the output, are chosen in this study: • the general description of the machine functionality (GMF), i.e., the operations that can be executed by the machine. Depending on the specific machine, GMF can either be: (i) transformations which modify the geometry, mechanical and/or physical properties of products or parts; (ii) assembly operations, in which two or more separate parts are joined to form subassemblies or products [39]; • the interval representing the range of sizes of the output products or parts (RS); • the list of different materials of the output products or parts (RM); • the production capacity of the machine (PC), representing the relationship between the machine functionality and the overall output volumes.
GMF could be described through the classification code related to workstations, and specifically machines, provided by Sorensen et al.; regardless, the way GMF, RS, RM and PC should be coded in a consistent and universal way is considered outside the scope of the present study, while the reason for their inclusion in the essential parameters supporting the early stage of the strategic network design phase is hereafter justified, specifically: GMF allows the comparison between machines (in the resource domain) based on the needed operations (thus the process domain); RS and PC are also included because product or part size and production volumes are the main drivers for the design of manufacturing systems and greatly impact the physical characteristics of technical resources [6,29]. The features RS and PC also permit implicit consideration of other technical resources such as material handling system (e.g., the RS property drives size and type of handling systems). Finally, the RM feature is included due to the increasing relevance of sustainability requirements, which are leading companies, for example, to replace pollutive materials with sustainable or recycled ones.
Considering the operation i, implemented by the machine Xi, the assessment of the reusability of another machine Zi requires the evaluation of the similarity between its functionality and the functionality provided by Xi. Xi could also be a selected benchmark machine for executing the operation i. The reusability of Zi also depends on its reconfigurability, thus on its modularity [12,16].
In this study, the reusability index ɣ i (Xi, Zi)  i,k(i) , supports an economic comparison of the admissible solutions.

Illustrative Example
The illustrative example is contextualized in the COVID-19 pandemic that forced communities to identify local resources to face the emergency. The exhaustion of relevant resources that drives the green transition determines a situation analogous to the COVID-19 and other health emergencies, as these situations revolve around the need to rapidly identify and exploit replacement resources. Similarly, geopolitical turbulences, such as wars and embargos, require the identification of alternative network configurations.
Due to the closing of borders, local companies need to cluster into a local supply chain in a country F to produce mechanical ventilators, which are highly needed in the great majority of national hospitals [10]. National hospitals have centroid C. Specifically, bi-level positive airway pressure masks are needed; in this scenario, a global company GC provides the masks' moulding process, i.e., machine X, at manufacturing sites located outside country F, while all other machines are already provided by local companies. In the MIP formulation, the objective (1) is replaced with the constraint (3) and the parameter v is introduced in order to ensure that the replacement machines will be located in the country F. Thus, the functionality of X, provided by GC, is described in Table 1, reporting the general machine functionality (GMF), the range of sizes and shapes of the output parts (RS), the range of materials of the output parts (RM) and the relationship between the machine functionality and the overall output volumes (PC). Table 1 also shows the distance between the machine provider and the centroid C as a function of the parameter v = 300 km. The local companies Alpha, Beta and Gamma, provide the same information for their candidate moulding processes, respectively, Z alpha , Z beta and Z gamma , as reported in Table 1. Table 1 also shows the admissibility of the binary variables z alpha , z beta and z gamma , as they satisfy the constraint (3). The three companies also provide information about machine reconfigurability with reference to machine functionality GMF, RS, RM and PC, as summarised in Table 2. The data in Tables 1 and 2  at the workstation level. For the remainder of this paper, "machine" is generically used to refer to either a machine or a robot changing (including joining and mechanical fastening) one or more physical and/or chemical characteristics of the input product or part according to the operation sheets. Machines usually entail high investment costs and greatly affect the reconfigurability potentialities at network level. Based on the classification code proposed by Sorensen et al. [29], four features, describing a machine at workstation level, its relationship with the operations (process domain), and with a few selected properties of the output, are chosen in this study: • the general description of the machine functionality (GMF), i.e., the operations that can be executed by the machine. Depending on the specific machine, GMF can either be: (i) transformations which modify the geometry, mechanical and/or physical properties of products or parts; (ii) assembly operations, in which two or more separate parts are joined to form subassemblies or products [39]; • the interval representing the range of sizes of the output products or parts (RS); • the list of different materials of the output products or parts (RM); • the production capacity of the machine (PC), representing the relationship between the machine functionality and the overall output volumes.
GMF could be described through the classification code related to workstations, and specifically machines, provided by Sorensen et al.; regardless, the way GMF, RS, RM and PC should be coded in a consistent and universal way is considered outside the scope of the present study, while the reason for their inclusion in the essential parameters supporting the early stage of the strategic network design phase is hereafter justified, specifically: GMF allows the comparison between machines (in the resource domain) based on the needed operations (thus the process domain); RS and PC are also included because product or part size and production volumes are the main drivers for the design of manufacturing systems and greatly impact the physical characteristics of technical resources [6,29]. The features RS and PC also permit implicit consideration of other technical resources such as material handling system (e.g., the RS property drives size and type of handling systems). Finally, the RM feature is included due to the increasing relevance of sustainability requirements, which are leading companies, for example, to replace pollutive materials with sustainable or recycled ones.
Considering the operation i, implemented by the machine Xi, the assessment of the reusability of another machine Zi requires the evaluation of the similarity between its functionality and the functionality provided by Xi. Xi could also be a selected benchmark machine for executing the operation i. The reusability of Zi also depends on its reconfigurability, thus on its modularity [12,16].
In this study, the reusability index ɣ i (Xi, Zi) of a candidate machine Zi is calculated through the similarity Si(Xi, Zi) and reconfigurability Ri(Zi) vectors, where: The four components sij and rij of the two vectors can assume binary values that are set considering, respectively, GMF, RS, RM and PC. Specifically, the components of at the workstation level. For the remainder of this paper, "machine" is generically used to refer to either a machine or a robot changing (including joining and mechanical fastening) one or more physical and/or chemical characteristics of the input product or part according to the operation sheets. Machines usually entail high investment costs and greatly affect the reconfigurability potentialities at network level. Based on the classification code proposed by Sorensen et al. [29], four features, describing a machine at workstation level, its relationship with the operations (process domain), and with a few selected properties of the output, are chosen in this study: • the general description of the machine functionality (GMF), i.e., the operations that can be executed by the machine. Depending on the specific machine, GMF can either be: (i) transformations which modify the geometry, mechanical and/or physical properties of products or parts; (ii) assembly operations, in which two or more separate parts are joined to form subassemblies or products [39]; • the interval representing the range of sizes of the output products or parts (RS); • the list of different materials of the output products or parts (RM); • the production capacity of the machine (PC), representing the relationship between the machine functionality and the overall output volumes.
GMF could be described through the classification code related to workstations, and specifically machines, provided by Sorensen et al.; regardless, the way GMF, RS, RM and PC should be coded in a consistent and universal way is considered outside the scope of the present study, while the reason for their inclusion in the essential parameters supporting the early stage of the strategic network design phase is hereafter justified, specifically: GMF allows the comparison between machines (in the resource domain) based on the needed operations (thus the process domain); RS and PC are also included because product or part size and production volumes are the main drivers for the design of manufacturing systems and greatly impact the physical characteristics of technical resources [6,29]. The features RS and PC also permit implicit consideration of other technical resources such as material handling system (e.g., the RS property drives size and type of handling systems). Finally, the RM feature is included due to the increasing relevance of sustainability requirements, which are leading companies, for example, to replace pollutive materials with sustainable or recycled ones.
Considering the operation i, implemented by the machine Xi, the assessment of the reusability of another machine Zi requires the evaluation of the similarity between its functionality and the functionality provided by Xi. Xi could also be a selected benchmark machine for executing the operation i. The reusability of Zi also depends on its reconfigurability, thus on its modularity [12,16].
In this study, the reusability index ɣ i (Xi, Zi) of a candidate machine Zi is calculated through the similarity Si(Xi, Zi) and reconfigurability Ri(Zi) vectors, where: The four components sij and rij of the two vectors can assume binary values that are set considering, respectively, GMF, RS, RM and PC. Specifically, the components of at the workstation level. For the remainder of this paper, "machine" is generically used to refer to either a machine or a robot changing (including joining and mechanical fastening) one or more physical and/or chemical characteristics of the input product or part according to the operation sheets. Machines usually entail high investment costs and greatly affect the reconfigurability potentialities at network level. Based on the classification code proposed by Sorensen et al. [29], four features, describing a machine at workstation level, its relationship with the operations (process domain), and with a few selected properties of the output, are chosen in this study: • the general description of the machine functionality (GMF), i.e., the operations that can be executed by the machine. Depending on the specific machine, GMF can either be: (i) transformations which modify the geometry, mechanical and/or physical properties of products or parts; (ii) assembly operations, in which two or more separate parts are joined to form subassemblies or products [39]; • the interval representing the range of sizes of the output products or parts (RS); • the list of different materials of the output products or parts (RM); • the production capacity of the machine (PC), representing the relationship between the machine functionality and the overall output volumes.
GMF could be described through the classification code related to workstations, and specifically machines, provided by Sorensen et al.; regardless, the way GMF, RS, RM and PC should be coded in a consistent and universal way is considered outside the scope of the present study, while the reason for their inclusion in the essential parameters supporting the early stage of the strategic network design phase is hereafter justified, specifically: GMF allows the comparison between machines (in the resource domain) based on the needed operations (thus the process domain); RS and PC are also included because product or part size and production volumes are the main drivers for the design of manufacturing systems and greatly impact the physical characteristics of technical resources [6,29]. The features RS and PC also permit implicit consideration of other technical resources such as material handling system (e.g., the RS property drives size and type of handling systems). Finally, the RM feature is included due to the increasing relevance of sustainability requirements, which are leading companies, for example, to replace pollutive materials with sustainable or recycled ones.
Considering the operation i, implemented by the machine Xi, the assessment of the reusability of another machine Zi requires the evaluation of the similarity between its functionality and the functionality provided by Xi. Xi could also be a selected benchmark machine for executing the operation i. The reusability of Zi also depends on its reconfigurability, thus on its modularity [12,16].
In this study, the reusability index ɣ i (Xi, Zi) of a candidate machine Zi is calculated through the similarity Si(Xi, Zi) and reconfigurability Ri(Zi) vectors, where: The four components sij and rij of the two vectors can assume binary values that are set considering, respectively, GMF, RS, RM and PC. Specifically, the components of gamma shown in Table 3. In this example, the context-specific weights are assumed equal (ω j = 0.25). The MIP algorithm selects the company Gamma, as it maximizes the objective (2), and minimizes the reconfiguration cost.   No; to change it, the whole machine should be replaced Not outside the range specified in Table 1 Not outside the range specified in Table 1 No; to change it, the whole machine should be replicated/removed Z beta No; to change it, the whole machine should be replaced Not outside the range specified in Table 1 Not outside the range specified in Table 1 No; to change it, the whole machine should be replicated/removed Z gamma No; to change it, the whole machine should be replaced Yes; a 3D printer is used to construct new moulds, extending the range of sizes of parts Not outside the range specified in Table 1 No; to change it, the whole machine should be replicated/removed Table 3. Calculation of at the workstation level. For the remainder of this paper, "machine" is generically used to refer to either a machine or a robot changing (including joining and mechanical fastening) one or more physical and/or chemical characteristics of the input product or part according to the operation sheets. Machines usually entail high investment costs and greatly affect the reconfigurability potentialities at network level.
Based on the classification code proposed by Sorensen et al. [29], four features, describing a machine at workstation level, its relationship with the operations (process domain), and with a few selected properties of the output, are chosen in this study: • the general description of the machine functionality (GMF), i.e., the operations that can be executed by the machine. Depending on the specific machine, GMF can either be: (i) transformations which modify the geometry, mechanical and/or physical properties of products or parts; (ii) assembly operations, in which two or more separate parts are joined to form subassemblies or products [39]; • the interval representing the range of sizes of the output products or parts (RS); • the list of different materials of the output products or parts (RM); • the production capacity of the machine (PC), representing the relationship between the machine functionality and the overall output volumes.
GMF could be described through the classification code related to workstations, and specifically machines, provided by Sorensen et al.; regardless, the way GMF, RS, RM and PC should be coded in a consistent and universal way is considered outside the scope of the present study, while the reason for their inclusion in the essential parameters supporting the early stage of the strategic network design phase is hereafter justified, specifically: GMF allows the comparison between machines (in the resource domain) based on the needed operations (thus the process domain); RS and PC are also included because product or part size and production volumes are the main drivers for the design of manufacturing systems and greatly impact the physical characteristics of technical resources [6,29]. The features RS and PC also permit implicit consideration of other technical resources such as material handling system (e.g., the RS property drives size and type of handling systems). Finally, the RM feature is included due to the increasing relevance of sustainability requirements, which are leading companies, for example, to replace pollutive materials with sustainable or recycled ones.
Considering the operation i, implemented by the machine Xi, the assessment of the reusability of another machine Zi requires the evaluation of the similarity between its functionality and the functionality provided by Xi. Xi could also be a selected benchmark machine for executing the operation i. The reusability of Zi also depends on its reconfigurability, thus on its modularity [12,16].
In this study, the reusability index ɣ i (Xi, Zi) of a candidate machine Zi is calculated through the similarity Si(Xi, Zi) and reconfigurability Ri(Zi) vectors, where: at the workstation level. For the remainder of this paper, "machine" is generically used to refer to either a machine or a robot changing (including joining and mechanical fastening) one or more physical and/or chemical characteristics of the input product or part according to the operation sheets. Machines usually entail high investment costs and greatly affect the reconfigurability potentialities at network level. Based on the classification code proposed by Sorensen et al. [29], four features, describing a machine at workstation level, its relationship with the operations (process domain), and with a few selected properties of the output, are chosen in this study: • the general description of the machine functionality (GMF), i.e., the operations that can be executed by the machine. Depending on the specific machine, GMF can either be: (i) transformations which modify the geometry, mechanical and/or physical properties of products or parts; (ii) assembly operations, in which two or more separate parts are joined to form subassemblies or products [39]; • the interval representing the range of sizes of the output products or parts (RS); • the list of different materials of the output products or parts (RM); • the production capacity of the machine (PC), representing the relationship between the machine functionality and the overall output volumes.
GMF could be described through the classification code related to workstations, and specifically machines, provided by Sorensen et al.; regardless, the way GMF, RS, RM and PC should be coded in a consistent and universal way is considered outside the scope of the present study, while the reason for their inclusion in the essential parameters supporting the early stage of the strategic network design phase is hereafter justified, specifically: GMF allows the comparison between machines (in the resource domain) based on the needed operations (thus the process domain); RS and PC are also included because product or part size and production volumes are the main drivers for the design of manufacturing systems and greatly impact the physical characteristics of technical resources [6,29]. The features RS and PC also permit implicit consideration of other technical resources such as material handling system (e.g., the RS property drives size and type of handling systems). Finally, the RM feature is included due to the increasing relevance of sustainability requirements, which are leading companies, for example, to replace pollutive materials with sustainable or recycled ones.
Considering the operation i, implemented by the machine Xi, the assessment of the reusability of another machine Zi requires the evaluation of the similarity between its functionality and the functionality provided by Xi. Xi could also be a selected benchmark machine for executing the operation i. The reusability of Zi also depends on its reconfigurability, thus on its modularity [12,16].
In this study, the reusability index ɣ i (Xi, Zi) of a candidate machine Zi is calculated through the similarity Si(Xi, Zi) and reconfigurability Ri(Zi) vectors, where: at the workstation level. For the remainder of this paper, "machine" is generically used to refer to either a machine or a robot changing (including joining and mechanical fastening) one or more physical and/or chemical characteristics of the input product or part according to the operation sheets. Machines usually entail high investment costs and greatly affect the reconfigurability potentialities at network level. Based on the classification code proposed by Sorensen et al. [29], four features, describing a machine at workstation level, its relationship with the operations (process domain), and with a few selected properties of the output, are chosen in this study: • the general description of the machine functionality (GMF), i.e., the operations that can be executed by the machine. Depending on the specific machine, GMF can either be: (i) transformations which modify the geometry, mechanical and/or physical properties of products or parts; (ii) assembly operations, in which two or more separate parts are joined to form subassemblies or products [39]; • the interval representing the range of sizes of the output products or parts (RS); • the list of different materials of the output products or parts (RM); • the production capacity of the machine (PC), representing the relationship between the machine functionality and the overall output volumes.
GMF could be described through the classification code related to workstations, and specifically machines, provided by Sorensen et al.; regardless, the way GMF, RS, RM and PC should be coded in a consistent and universal way is considered outside the scope of the present study, while the reason for their inclusion in the essential parameters supporting the early stage of the strategic network design phase is hereafter justified, specifically: GMF allows the comparison between machines (in the resource domain) based on the needed operations (thus the process domain); RS and PC are also included because product or part size and production volumes are the main drivers for the design of manufacturing systems and greatly impact the physical characteristics of technical resources [6,29]. The features RS and PC also permit implicit consideration of other technical resources such as material handling system (e.g., the RS property drives size and type of handling systems). Finally, the RM feature is included due to the increasing relevance of sustainability requirements, which are leading companies, for example, to replace pollutive materials with sustainable or recycled ones.
Considering the operation i, implemented by the machine Xi, the assessment of the reusability of another machine Zi requires the evaluation of the similarity between its functionality and the functionality provided by Xi. Xi could also be a selected benchmark machine for executing the operation i. The reusability of Zi also depends on its reconfigurability, thus on its modularity [12,16].
In this study, the reusability index ɣ i (Xi, Zi) of a candidate machine Zi is calculated through the similarity Si(Xi, Zi) and reconfigurability Ri(Zi) vectors, where:    Table 1 Not outside the range specified in Table 1 No; to change it, the whole machine should be replicated/removed

Zbeta
No; to change it, the whole machine should be replaced Not outside the range specified in Table 1 Not outside the range specified in Table 1 No; to change it, the whole machine should be replicated/removed  Table 1 No; to change it, the whole machine should be replicated/removed Table 3. Calculation of ɣalpha, ɣbeta and ɣgamma.

Zalpha Z beta Z gamma
Si (s1 = 0, s2 = 1, s3 = 0, s4 = 1) (s1 = 1, s2 = 0, s3 = 1, s4 = 1) (s1 = 1, s2 = 0, s3 = 1, s4 = 1) In the second phase of the algorithm, the constraint (5) is added; since all other companies involved in manufacturing the masks are already located in country F, the centroid LN representing the location of the local network is introduced. Constraint (5) is set as D(LN, Zk) ≤ 75 km. Table 1 reports these distances. The algorithm excludes company Beta. Figure 4 represents the solution in the Euclidean space considering the constraint (5), with respect to the distance D (LN, Zk), and the complement to 1 of the reusability index ɣ. It shows that company Alpha has the lowest distance from LN; it also shows that company Gamma has the highest reusability index. After the addition of (5), company Gamma is still in the admissible domain, and it is selected by the algorithm as it maximizes (2). Then, a more detailed analysis of the needed reconfiguration effort should follow; this might eventually lead to the modification of the parameters of the algorithm and/or the removal of specific candidates in order to re-run the algorithm so as to explore new solutions. at the workstation level. For the remainder of this paper, "machine" is generically used to refer to either a machine or a robot changing (including joining and mechanical fastening) one or more physical and/or chemical characteristics of the input product or part according to the operation sheets. Machines usually entail high investment costs and greatly affect the reconfigurability potentialities at network level. Based on the classification code proposed by Sorensen et al. [29], four features, describing a machine at workstation level, its relationship with the operations (process domain), and with a few selected properties of the output, are chosen in this study: • the general description of the machine functionality (GMF), i.e., the operations that can be executed by the machine. Depending on the specific machine, GMF can either be: (i) transformations which modify the geometry, mechanical and/or physical properties of products or parts; (ii) assembly operations, in which two or more separate parts are joined to form subassemblies or products [39]; • the interval representing the range of sizes of the output products or parts (RS); • the list of different materials of the output products or parts (RM); • the production capacity of the machine (PC), representing the relationship between the machine functionality and the overall output volumes.
GMF could be described through the classification code related to workstations, and specifically machines, provided by Sorensen et al.; regardless, the way GMF, RS, RM and PC should be coded in a consistent and universal way is considered outside the scope of the present study, while the reason for their inclusion in the essential parameters supporting the early stage of the strategic network design phase is hereafter justified, specifically: GMF allows the comparison between machines (in the resource domain) based on the needed operations (thus the process domain); RS and PC are also included because product or part size and production volumes are the main drivers for the design of manufacturing systems and greatly impact the physical characteristics of technical resources [6,29]. The features RS and PC also permit implicit consideration of other technical resources such as material handling system (e.g., the RS property drives size and type of handling systems). Finally, the RM feature is included due to the increasing relevance of sustainability requirements, which are leading companies, for example, to replace pollutive materials with sustainable or recycled ones.
Considering the operation i, implemented by the machine Xi, the assessment of the reusability of another machine Zi requires the evaluation of the similarity between its functionality and the functionality provided by Xi. Xi could also be a selected benchmark machine for executing the operation i. The reusability of Zi also depends on its reconfigurability, thus on its modularity [12,16].
In this study, the reusability index ɣ i (Xi,  In the second phase of the algorithm, the constraint (5) is added; since all other companies involved in manufacturing the masks are already located in country F, the centroid LN representing the location of the local network is introduced. Constraint (5) is set as D(LN, Z k ) ≤ 75 km. Table 1 reports these distances. The algorithm excludes company Beta. Figure 4 represents the solution in the Euclidean space considering the constraint (5), with respect to the distance D(LN, Z k ), and the complement to 1 of the reusability index Sustainability 2022, 14, x FOR PEER REVIEW at the workstation level. For the remainder of this p refer to either a machine or a robot changing (inclu one or more physical and/or chemical characterist ing to the operation sheets. Machines usually enta fect the reconfigurability potentialities at network Based on the classification code proposed by scribing a machine at workstation level, its relatio main), and with a few selected properties of the ou • the production capacity of the machine (PC), the machine functionality and the overall out GMF could be described through the classific specifically machines, provided by Sorensen et al.; PC should be coded in a consistent and universal the present study, while the reason for their inclusi ing the early stage of the strategic network design GMF allows the comparison between machines ( needed operations (thus the process domain); RS a uct or part size and production volumes are the m turing systems and greatly impact the physical cha The features RS and PC also permit implicit con such as material handling system (e.g., the RS pro systems). Finally, the RM feature is included due bility requirements, which are leading companies, rials with sustainable or recycled ones.
Considering the operation i, implemented by reusability of another machine Zi requires the ev functionality and the functionality provided by Xi machine for executing the operation i. The reusabi rability, thus on its modularity [12,16].
In this study, the reusability index ɣ i (Xi, Zi) calculated through the similarity Si(Xi, Zi) and reco Moreover, σi(Xi,Zi) ∈ [0, 1], the similarity inde . It shows that company Alpha has the lowest distance from LN; it also shows that company Gamma has the highest reusability index. After the addition of (5), company Gamma is still in the admissible domain, and it is selected by the algorithm as it maximizes (2). Then, a more detailed analysis of the needed reconfiguration effort should follow; this might eventually lead to the modification of the parameters of the algorithm and/or the removal of specific candidates in order to re-run the algorithm so as to explore new solutions.

Discussion
From a theoretical perspective, this study contributes to the recent stream of research addressing the benefits of RMSs for supply chains' responsiveness and sustainability. This study also contributes by showing how RMSs enable strategic supply chain reconfigurability based on their reusability. Indeed, relevant parameters related to machines, i.e., the general functionality, the range of sizes and materials and the production capacity have been used to assess machines' reusability based on similarity and reconfigurability.
Moreover, the mixed integer programming (MIP) algorithm supports the identification of reusable and reconfigurable candidates at the early stage of the strategic network design. Thus, it contributes to filling the existing research gap identified in Section 1. Finally, this study implicitly remarks on the relevance of IT systems and information sharing in the Industry 4.0 era, and encourages the development of ontologies and standard classifications aimed at supporting companies with resilient and sustainable collaboration.
From a practical perspective, the proposed method supports practitioners in identifying reusable and reconfigurable machines when aiming to improve supply chain resilience and sustainability. Indeed, due to either an unexpected disruption or aiming to reduce the carbon footprint of a supply chain, companies might need to move a number of manufacturing processes in specific areas of interest, and they would be interested in identifying reusable machines to ensure responsive and cost-effective network reconfigurations. The method can be used in a versatile way by: • an individual company that aims to modify the configuration of its production sites, in order to compare machines when establishing new sites or designing a new network of sites. It permits candidate solutions to be compared with respect to the associated reconfiguration and transportation costs; • a network of companies.
Therefore, the method supports the dynamic clustering of manufacturing sites or companies into industrial networks, thus ensuring higher resilience towards sudden changes.
The method also supports supply chains and networks to adopt more environmentally sustainable configurations because it provides a procedure to move manufacturing processes in specific areas of interest (e.g., closer to local customers), consequently reducing the carbon footprint of the supply chain due to the transportation of products or parts. Moreover, as supply chains aim to enhance network sustainability while also ensuring adequate profitability, the fact that the algorithm aims at identifying the candidates with maximum reusability supports the identification of cost-effective network configuration options.
Finally, the method aims to encourage practitioners towards the development and adoption of modular and reconfigurable machines, as these can be reused along the system's life cycle, opening them up to new business opportunities.

Conclusions and Outlook
The turbulent and unpredictable geopolitical context has recently had a relevant impact on the manufacturing industry and demands for resilient and sustainable supply chains. This study provides a method for manufacturing companies to assess machine reusability and an MIP algorithm supporting the identification of reusable and reconfigurable machine candidates at the early stage of the strategic network design. The overall method allows machines to be compared based on their reusability and geographical locations and can therefore be used to improve supply chain resilience and/or sustainability.
Collaboration among different manufacturers is a key aspect in the proposed method. To this regard, manufacturers' profitability lies in both the reuse of local machines rather than investing in local systems purpose-built, and the reduction in logistics and transportation costs. The reliance on the availability and sharing of structured information is another critical aspect of this study. In the Industry 4.0 era, companies should be able to share standard information about manufacturing resources; however, the digitalization level of many manufacturing companies is still under development. To this end, governments and organizations should encourage the diffusion of databases, where each company could share standardized information to collaborate resiliently and sustainably. This would also require new managerial approaches. Moreover, governments and organizations should foster the diffusion of methods to assess the appropriateness of currently adopted IT systems, as well as the availability/establishment of the data to allow resilient and sustainable collaborations.
Concerning the impact of this study, the proposed method leads to the following consequences: • the promotion of social sustainability thanks to the creation of value for local communities, also ensured by the collaboration with local companies, which have more insights on local customers and local economies. • the fostering of new business models where capacity sharing permits not only a reduction in the total capital assets of the involved companies, but also network resilience and sustainability to be enhanced.
Regarding the limitations of the study, the proposed reusability assessment relies on a limited number of essential parameters referred to the machines and on the attribution of binary values, which implies fast exclusion of several candidates. However, the selected choices and simplified assumptions were carefully made given the aim to support strategic network reconfigurability. Moreover, as discussed in Section 3, the proposed method can be easily adjusted to include different features and specific analyses. A limitation of the overall method is the specific focus on machines as the main source of investment costs during the strategic network design; other sources of investments might need consideration, also depending on sectors and industries, and this is certainly an aspect that could be investigated in future research.
Other directions for future research are: to apply the proposed method in industrial contexts; mature the reusability index to enable accurate evaluations of reconfiguration costs and efforts; directly connect the method to the quantification of the impact of supply chain resilience and sustainability.

Data Availability Statement:
The data that support the findings of this study are available from the corresponding author, [A.N.], upon reasonable request.

Conflicts of Interest:
The authors declare no conflict of interest.