Supply Chain Resilience: A Common Weights Efficiency Analysis with Non-discretionary and Non-controllable Inputs

As the backbone of the global economy, contemporary SCs encounter substantial risks and vulnerabilities due to the instability of the operational environment and major disruptions that make it increasingly complicated to plan for the future effectively (Juan et al., 2022a, 2022b; Klibi et al., 2018). The COVID-19 pandemic fundamentally changed the SC landscape, resulting in a “new normal” of constant flux. This new state has been shaped by a series of disruptions caused by this pandemic (Rahman et al., 2022). Given the persistent nature of the challenges posed by this state, it is critical to consider the application of dynamic resilience measurement in the new phase of the SC during the post-pandemic and companies should immunise their SC by taking behavioural biases and social effects into account and re-evaluating their contractual responsibilities (Asian et al., 2020). Moreover, in the post-pandemic, companies make every attempt to restore their profitability (Wided, 2023). With its adaptability capacity, SCRes can prove highly effective in dealing with ongoing challenges (Settembre-Blundo et al., 2021). By incorporating elements of avoidance, absorption, and elasticity, a SC can be designed to be dynamically resilient and better equipped to cope with the new normal (Mithani, 2020). If the industry and its SCs cannot adapt to new situations after disruption, making strategic decisions to improve resiliency is necessary to prevent resulting shortages (Singh et al., 2021a, 2021b; Tucker et al., 2020). Hence, SCNs should be sufficiently robust and resilient to ensure ongoing operations even in the event of disruptions. (Dixit et al., 2020b).

SCRes is described as “the adaptive capability of the SC to prepare for unexpected events, respond to disruptions, and recover from them by maintaining continuity of operations at the desired level of connectedness and control over structure and function” (Ponomarov & Holcomb, 2009, p. 131). Market volatility and supply interruptions resulted in significant decrease in the short-term and long-term revenues of many organisations with worldwide supply networks (Asian & Nie, 2014; S. Singh et al., 2021a, 2021b). A SC's design and structure substantially affect its resilience, which determines the impact of the disruption (Ojha et al., 2018; Rezaei Somarin et al., 2018). For example, the undesirable effects of disruptions on SCNs with many locally located nodes are much higher than those on networks with nodes that are scattered across a larger distance. In addition, when a specific node aggregates supplies and feeds the demand of several other nodes, then any disruption of this central node makes the whole SC defected and non-operational (Dixit et al., 2020b). Longer and larger SCs with more tiers and depth make the partnering companies more vulnerable to disruptions (Alfarsi et al., 2019; Paul et al., 2019).

Many historical disruptions have exposed SCs to risks. For instance, when the Tohoku earthquake hit Japan in 2011, it not only disrupted the Japanese and Asian SCs but also resulted in shortages in the SC of associated industries in Europe (Scholten et al., 2014). So, SCRes is viewed as a risk mitigation strategy in response to disruptions and to deal with an unstable operational environment (Alfarsi et al., 2019). SCNs become more resilient through proactive strategies such as efficient collaborations among firms, higher visibility, more flexibility (Chowdhury & Quaddus, 2016; Klibi et al., 2018), multiple sourcing to increase redundancy and back-up suppliers, holding extra safety stocks, and growing capacity of facilities (e.g. manufacturing, warehousing, logistics and transportation) (Klibi et al., 2018; Salehi Sadghiani et al., 2015). However, responsiveness and recovery are the reactive strategies to improve the resiliency of the SCs (Kamalahmadi & Mellat-Parast, 2015). After defining flexibility, visibility, and resilience, it is important to understand their effects within a SC (Dolgui & Ivanov, 2022; Singh et al., 2019a, 2019b). These three attributes enhance the chain's resilience and robustness (Mackay et al., 2020). Flexibility facilitates swift adaptation to unexpected circumstances, while visibility provides real-time insights into operations, enabling better decision-making (Dubey et al., 2021). Resilience embodies the ability of the SC to recover from disruptions quickly, a trait bolstered by flexibility and visibility (Juan et al., 2022a, 2022b).

Enhancing SCRes through over-increasing capacity and boundless redundancy becomes a very expensive decision (Sokolov et al., 2015). Therefore, measuring SCRes using data analytics is crucial to analysing the efficacy of different strategies for improving resilience (Kaur & Singh, 2022; Klibi et al., 2018). Analysing the resilience of the entire SCN enables practising SC managers to clearly understand the weaknesses of the network and address those shortcomings by implementing suitable strategies and warning every firm in the network about the risks and vulnerabilities that they encounter in their business environment (Li & Zobel, 2020). The improved knowledge of the business environment in which the firms function enables them to devise more effective responses to disruptions through informed investment decisions (Juan et al., 2022a, 2022b).

Along with the increase in the current global use of natural gas, which composes 25% of the energy mix (International Energy Agency, 2016), the intensity and frequency of disruptive risks to the energy sector and natural gas in particular are increasing (Ding et al., 2020) which can be the result of natural disasters, economic risks, geopolitical risks, maritime transportation risk and so on (Geng et al., 2017). Studies on energy security most often concentrate on the vulnerability of a nation to supply shortages. To some extent, they have recommended solutions to mitigate the impacts of disruptions and crises by focusing on solutions to decrease the frequency and intensity of disruptions (pre-disruption mitigation). However, they have not elaborated on the role of efficient use of resources in lowering the vulnerability of SCs through post-disruption resilience (Rose et al., 2018).

Thus, the efficiency of SCNs in terms of resilience and capacity to recover after disruptions necessitates more research. This study adopts data envelopment analysis (DEA) to bridge this gap and examine the resiliency of SCNs. DEA is a mathematical approach based on linear programming that uses multiple inputs and outputs to evaluate the efficiency of homogeneous decision-making units (DMUs) (Kiani Mavi et al., 2021). DEA shines in its versatility and adaptability. Unlike simulation and optimisation models that require a predefined objective function and assumptions about the distribution of data, DEA does not demand such preconditions, granting it more flexibility. It uses empirical data to construct a piecewise linear surface to envelop the data points, creating an efficiency frontier to evaluate other units against (Jradi & Ruggiero, 2023). The ability of DEA to work with multiple inputs and outputs simultaneously without any need to specify weights in advance is its key advantage over most statistical methods (Goker & Karsak, 2021). Therefore, DEA is exceptionally well suited for assessing complex systems like SCs where numerous elements interact and influence one another.

Since the traditional models of DEA are flexible in attributing weights to input and output variables to measure efficiency (Jahanshahloo et al., 2011; Tavana et al., 2015), they produce a different weighting scheme for each DMU to maximise its efficiency score. This weighting scheme results in several DMUs becoming efficient. The common set of weights (CSW) analysis overcomes this shortcoming by evaluating the efficiency of all DMUs consistently (Kiani Mavi et al., 2019a, 2019b). This study performs a common weights analysis using the ideal point method. The advantage of the ideal point method is in determining the amount of improvement for inefficient DMUs (Kiani Mavi et al., 2019a, 2019b). This research significantly contributes to advancing resilience strategies in the Pacific region, particularly in the SCNs domain. The proposed model contributes to the exploration of a strategic approach towards resilience by analysing the distinct obstacles and potential advantages of SCRes in the Pacific region. The incorporation of non-discretionary and non-controllable inputs within the CSW model demonstrates the interplay between economic, social, environmental, and political elements that influence resilience in the Pacific region.

Complexity theories, particularly complex adaptive systems (CAS) and complexity thinking (CT), have assisted supply chains practitioners to better analyse their intricate dynamics (Rebs et al., 2019; Tsolakis et al., 2021; Wieland et al., 2023; Wilden et al., 2022). Nilsson and Gammelgaard (2012) provided a paradigmatic reflection on these approaches, contrasting them with the traditional systems approach which has long dominated SCM and logistics research. They argue that current challenges of organisational complexity in supply chain management, such as those related to innovation, learning, and sense-making, can be effectively investigated through the fundamental assumptions of CAS and CT which are centred around adaptation, emergent behaviour, and nonlinear interactions. This perspective is echoed by Elias et al. (2021), who apply systems thinking to analyse sustainable wood supply chains in Amazon, showcasing the applicability of these approaches in diverse and complex contexts. The inclusion of complexity approaches in the broader discourse of SCM provides valuable alternative perspectives that complement and enrich the understanding of the supply chain dynamics. Acknowledging these theories not only aligns with the current trajectory of the field but also opens up avenues for future research to analyse the multifaceted nature of supply chains through various theoretical lenses (Naim et al., 2019; Waller et al., 2015).

This paper is structured as follows: Sect. "Literature Review" reviews the literature on SCN resilience, approaches to analyse it, and common weight analysis in DEA. In Sect. "Proposed ideal Point Common Weights Model with Non-discretionary and Non-controllable Inputs", the developed common set of weights model is presented. Sect. "Case Study: LPG Supply Chain" illustrates a case study in the LPG sector and discusses the results. Finally, Sect. "Conclusion" provides the concluding remarks.

The extant literature on SCRes has provided valuable insights. However, a significant research gap exists in effectively measuring and enhancing resilience in SCNs, particularly in the Pacific region. It is imperative for companies to have an optimal balance between operational efficiency and organisational flexibility to hedge uncertainty and mitigate disruptions arising from unpredictability. From a methodological perspective, existing approaches to assess the resilience of SCs frequently exhibit limitations in their ability to consider non-discretionary and non-controllable variables and their capacity to offer a comprehensive ranking of SCNs based on the metrics that define the notion of resilience. On the other hand, the existing body of literature on SCRes in the Pacific region is limited, particularly in strategies that consider distinctive regional characteristics such as population density and the geographical distances between supply and demand nodes. There is an apparent necessity for developing an evaluation framework that specifically targets the deficiencies in assessing SCRes. This framework provides valuable insights to SC managers in the Pacific region.

Charnes et al. (1978) crafted the CCR model to measure the relative efficiency of similar DMUs. Under constant returns to scale (CRS), the relative efficiency of DMU_p is obtained by Program (1).

If \({E}_{p}^{*}=1\), then \({{\text{DMU}}}_{p}\) is called efficient; otherwise, when \({E}_{p}^{*}<1,\) it is referred to as an inefficient DMU.

In real-world settings, managers are not able to control non-discretionary and non-controllable inputs that are exogenously fixed (Lotfi et al., 2007). By extending the CCR model, therefore, we propose Program (2) to evaluate the efficiency of DMUs when they are operating with discretionary (D), non-discretionary (ND), and non-controllable (NC) inputs under CRS conditions. We distinguish between the non-controllable and non-discretionary inputs, assuming that no slack is allowed for non-controllable inputs (Cooper et al., 2007).where \({x}_{ij},i=1,\dots ,m\) are the discretionary inputs of \({DMU}_{j}\), \({z}_{kj}, k=1,\dots ,l\) are the non-discretionary inputs of \({DMU}_{j}\), and \({d}_{cj}, c=1,\dots ,b\) are the non-controllable inputs of \({DMU}_{j}\).

The principal advantage of producing a common weights vector is restricting the weight flexibility of original DEA models to provide a consistent and identical basis to evaluate all DMUs (Shabani et al., 2019). Conducting CSW analysis, all DMUs do not get the full efficiency score (Hosseinzadeh Lotfi et al., 2013). Regardless of the approach to generating CSW, the common set of weights models enable managers and policymakers to evaluate the performance of all DMUs on a consistent basis to enunciate strategies to enhance the performance of inefficient ones. The rationale of the deal point method is minimising the distance between every DMU and the ideal or the best DMU with the lowest amount of inputs and the highest amount of outputs (Sun et al., 2013). Thus, \({DMU}_{I}\), the ideal DMU, is defined as Eq. 3:where \({{\text{x}}}_{i ({\text{min}})}={\text{min}}\left\{\left.{x}_{ij}\right|j=1,\dots ,n\right\}, \left(i=1,\dots ,m\right)\mathrm{ and }{{\text{y}}}_{r ({\text{max}})}={\text{max}}\left\{\left.{y}_{rj}\right|j=1,\dots ,n\right\}, \left(r=1,\dots ,s\right)\). In Eq. 3, \({X}_{{\text{min}}}\) denotes the vector of inputs and \({Y}_{{\text{max}}}\) denotes the vector of outputs of the ideal DMU.

Since the ideal point model tries to minimise the distance between each DMU and the ideal DMU, then Model (4) meets this objective and gives a CSW (Sun et al., 2013).

The objective function in Model (4) minimises the total distance between each DMU and the ideal DMU. The first set of constraints guarantee that the relative efficiency of DMUs do not exceed unity. The second and third constraints determine weights of inputs and outputs to ensure that the ideal DMU lie on the efficiency frontier.

Implementing the ideal point method to generate a common set of weights for Model (2) results in the common weights Model (5):

Model (5) determines the common set of weights for inputs (including non-discretionary and non-controllable) and outputs to minimise the overall distance between all DMUs and the idel DMU. Model (5) distinguishes from Model (4) by modelling the non-discretionary and non-controllbale inputs. Because managers do not have control over these variables, they negatively contribute to the outputs \(\left[\sum_{r=1}^{s}{u}_{r}{y}_{rj}-\sum_{k=1}^{l}{f}_{k}{z}_{kj}-\sum_{c=1}^{b}{h}_{c}{d}_{cj}\right]\) of DMUs. The first set of constraints in Model (5) ensures that the relative efficiency of each DMU remains in the range (0,1] given that \({h}_{c}\) is a non-constrained-in-sign variable. The second and third constraints position the ideal DMU on the efficiency frontier.

The optimal solution of Model (5), \(\left({u}_{r}^{*},{v}_{i}^{*},{f}_{k}^{*},{h}_{c}^{*}\right),\) will be the common set of weights to evaluate the relative efficiency of DMUs which is obtained by Eq. 6, where \({E}_{p}^{*}\) is the efficiency of \({DMU}_{p}\) calculated by the common set of weights.

There has been a notable shift towards using LPG in the energy domain, notably in Pacific region, motivated mainly by its limited or absence of subsidies. LPG has emerged as a viable option that is not only economically accessible and environmentally friendly but also demonstrates superior distribution capabilities. This practical energy source is both cost-effective and easily transportable. Additionally, it establishes a sustainable trajectory for attaining environmental goals by significantly reducing home and industrial pollutants. This is especially evident when it replaces more carbon-intensive fuels like firewood or kerosene in various applications (Abhimanyu Bhuchar, 2020). LPG is progressively emerging as a cost-effective and environmentally friendly intermediate alternative during the shift from conventional liquid petroleum fuels to renewable energy sources. LPG is now used by Pacific Island governments and territories, mainly for domestic culinary activities. If the use of LPG were to be extended to replace all cooking kerosene and biomass throughout the Pacific area, it is plausible that the existing demand may see a twofold increase. The rationale for advocating for this modification is grounded on health considerations, environmental sustainability, and potential cost reductions for individual homes. Nevertheless, it is reasonable to anticipate that the rise in demand will lead to varying degrees of improved economies of scale across Pacific Island Countries and Territories. The potential escalation in volume may prompt some Pacific Island Countries and Territories to transition towards bulk distribution methods, hence potentially exerting a substantial influence on the price at which goods are transported. The use of LPG in transportation or the implementation of local piped gas networks might potentially lead to an additional rise in volumes and perhaps result in improved economic benefits associated with bulk imports. The ongoing experimentation in Fiji involves the use of LPG in heavy-duty vehicles and the amalgamation of LPG with other fuel sources for power production, drawing upon existing commercial technologies present in Australia. In 2050, although LPG continues to have a restricted use in cooking within some rising markets and developing nations, the predominant sources catering to 95% of cooking energy requirements are electricity and contemporary bioenergy (Morgan & Atkinson, 2016). Therefore, all the processes that are related to LPG have emerged as key elements of their economic framework. Due to the intricate and expensive nature of installing infrastructure for LPG, it is essential to consider numerous factors. Additionally, given the potential disruptions and risks across every stage of the process, effective management is crucial to enhance the resilience of the system. Energy SCs are of huge significance for societies. Any disruption in the energy sector and its associated SCs might have devastating economic impacts on companies dealing with producing and distributing energy products (Urciuoli et al., 2014).

Many factors, such as supply and demand nodes and their available capacity, are important for assessing the resilience of SCNs, as any disruption in those variables results in the uncertainty and vulnerability of the SCN (Alikhani et al., 2021; Lu et al., 2018). The inputs and outputs for measuring supply chain resilience using common weight DEA model are explained below:

Node degree and clustering coefficient: These are topographical measurements emphasising the SCN's structural design and connectivity. High connectivity typically suggests enhanced resilience as suppliers with extensive connections have various alternatives to supply goods, thereby reducing disruption risks (Pourhejazy et al., 2017; Zhao et al., 2011). These parameters comprise the average node degree (the mean number of connections per node) and the average clustering coefficient (a measure of the degree of mutual connectivity among nodes).

Both node degree (Chen & Lin, 2012; Hearnshaw & Wilson, 2013; Kim et al., 2015; Sahlmueller & Hellingrath, 2022; Xia, 2020; Xu et al., 2016) and clustering coefficient (Geng et al., 2014; Hearnshaw & Wilson, 2013; Li et al., 2020; Mari et al., 2015; Xia, 2020) have positive impacts on supply chain resilience by showing how SC nodes are interconnected.

The average node degree (AND) shows the average number of connections for every node and is obtained by Eq. 7;where N is the total number of nodes in the network and \({k}_{i}\) represents the number of connections between node i and the reset of the network.

In addition, the average clustering coefficient (ACC) evaluates the degree of mutual exchange connections between the nodes in the network. ACC is calculated by Eq. 8;where \({N}_{i}\) is the number of immediately connected neighbours of node i.

Number of supply nodes: This parameter, another topographical measure, indicates the quantity of supply points in the SCN. A lower figure implies a more centralised network, which might result in slower recovery post-disturbances. The number of supply nodes also impacts the scale of potential disruptions, with a decentralised system typically yielding less severe impacts due to the distributed nature of the supply nodes. The number of supply nodes can enhance the capacity of the SCN, better accommodating demand than before. This can be equated with supplier diversity; a greater number of nodes may bolster flexibility (Etemadnia et al., 2015; Khan et al., 2021; Lam, 2021; Wang et al., 2015; Zhao et al., 2022). The density of a supply network means that a higher number of nodes are located at short distances. In case of local disruptions such as natural disasters, a higher density increases the vulnerability of the SCN and, as a result, decreases the SCRes (Dixit et al., 2020b).

Available capacity: This operational metric reveals the presence of spare supply capacity within the network. It is deduced through the complete potential supply ability across the network and an availability ratio. This measure provides a lucid indication of the network's robustness in handling disruptions. Available capacity serves as a resilient strategy for networks. While increasing capacity may escalate costs, particularly holding and warehousing expenses, it can strengthen the network against disruptions (Hosseini et al., 2019; Mohammed et al., 2023; Shashi et al., 2020; Tan et al., 2020).

Total distance: As an operational parameter, total distance signifies the cumulative distance between demand and supply nodes. The distance between nodes has implications for lead times, transportation expenditures, and vulnerability to disruptions. Minimising this distance can shield the SCN from potential disruptions and uncertainties (Chen & Lin, 2012; Djomo et al., 2023; Hearnshaw & Wilson, 2013; Xu et al., 2016; Zahraee et al., 2022). Lesser total distance generally contributes to increased resilience as it reduces logistical complexities and facilitates more efficient demand–supply balancing.

Population density: This societal factor assesses the populace concentration around supply facilities. Higher densities indicate heightened societal risk if a supply facility hazard occurs. This measure provides an insight into potential societal impact and can influence risk management strategies. This metric is paramount in evaluating network resilience, with denser areas indicating heightened potential societal impacts (Cooper et al., 2007; Gružauskas, 2020; Gružauskas & Burinskienė, 2022; Haeri et al., 2020; Liu & Zhao, 2015). This study considers population density a non-controllable input (Cooper et al., 2007), as SC managers and decision-makers do not control it.

Data for the SCNs are shown in Table 1, which are adopted from Pourhejazy et al. (2017).

Running MATLAB R2016b to solve Models (2) and (5) gives the efficiency score of SCNs. This study assumes that outputs change at the same ratio that inputs change and vice versa, so it employs the CCR model for efficiency analysis. As mentioned, Model (2) provides different sets of weights for each SCN. For example, Table 2 shows the weights of inputs and outputs for SCN-1 and SCN-2 with the highest and lowest ranks, respectively.

As the number of nodes in a network grows, the network's vulnerability becomes magnified, thereby exacerbating the potential for susceptibility (Alikhani et al., 2023). This is because disruptions at any one node may create delays and disruptions in manufacturing, distribution, and customer service across the whole SC (Sawik, 2022). A SC's resilience can be enhanced by fortifying its nodes to totally or partially shield facilities against threats (Sawik, 2022).

Organisations seeking to increase their resilience to the impact of disruptions might consider investing in the available capacity and diversifying their supply sources to swiftly adjust to unanticipated shifts in demand or supply (Goldbeck et al., 2020). When dealing with disruptions, a SC with excess capacity is stronger than one without (Riccardo et al., 2021). This is because a "buffer" created by the excess capacity can accommodate swings in demand or supply. Therefore, the availability of backup capacity is also crucial since it helps mitigate the impact of disruptions (Hosseini et al., 2019). Back-up capacity helps speed up the SC's recovery after disruptions (Ivanov, 2019).

Distance, in this context, refers to the physical separation between the SC's various nodes, such as suppliers, manufacturers, distributors, and warehouses (Birkie & Trucco, 2020).

Transportation costs, lead times, and vulnerability to disruptions all rise in direct proportion to the distance and separation of these nodes (Li et al., 2017; Musazzi et al., 2020).

SC management faces difficulties in communication and coordination due to the inherent complexity that distance adds to the process (Li et al., 2017). There are a number of ways in which physical separation weakens SCs. For instance, as lead times are extended, SCs may be more susceptible to disruptions since delays at any point in the chain might have a ripple effect on the other parts (Sawik, 2023). In addition, transportation costs may rise with increasing distance, cutting into SC profits (Mohammed et al., 2019). Finally, as SCs get more complicated, it might be more difficult to effectively coordinate and communicate with other levels (Pimenta et al., 2022). However, geographical diversification of suppliers is one method through which businesses can mitigate the detrimental effects of distance on SCRes (Li et al., 2017). By doing so, businesses continue to provide a consistent supply of products and services despite disruptions at a single site. They could become more resilient and competitive as a result.

Population density may have a substantial effect on SCRes since it can alter the availability and efficacy of resources and transportation networks (Salama & McGarvey, 2021). Population density can have a significant impact on distribution strategies, as it can influence the availability and efficiency of transportation systems, the cost of resources, and the complexity of the SCN. The allocation of resources in low-density areas may be more challenging and require different distribution strategies than those in high-density areas (Gružauskas & Burinskienė, 2022). Population density can impact the efficiency of transportation networks since excessive traffic volume and congestion can cause delays and interruptions in the transfer of products. This may affect the speed and dependability of delivery, which in turn can affect SCRes (Gružauskas, 2020).

Node degree, when discussing SCNs, measures how many connections an individual node has to other nodes (Xia, 2020). The degree of a node is a topological indicator that provides insight into the interconnectedness and complexity of a SCN, both of which are vital in determining the network's resilience (Zhao et al., 2011). Most SC partners choose the company with the highest capacity, and this is reflected in the node degree. Manufacturers and distributors with a higher degree indicate stronger buying power and a wider reach to potential clients, while suppliers with a higher degree indicate a more robust supply capacity. Hence, the new node is added to the network according to the current nodes and a probability that is proportionate to the degree of the existing nodes. Therefore, in addition to indicating the node's relative relevance in the network, a node's degree may provide insight into its practical capabilities (Geng et al., 2013).

A node's tendency to cluster with others is quantified by its clustering coefficient. Each node's clustering may be thought of as the percentage of all potential triangles (3 loops) that pass through that node (Li et al., 2020). A high clustering coefficient enhances the SC's susceptibility (Brandon-Jones et al., 2015). The development of SCNs is intricately linked to the manner in which levels engage with each other through interconnections and interactions. In this regard, the clustering coefficient serves as an invaluable metric for measuring the level of connectivity within such networks. By capturing the extent to which nodes are interconnected within the network, the clustering coefficient offers a powerful tool for evaluating the evolution of SC systems (Geng et al., 2014).

The flexibility of weights and choosing different weighting schemes by the conventional CCR model results in having 13 efficient SCNs with an efficiency score of 1. When 59% of SCNs are identified as efficient, discriminating them for complete ranking is almost impossible. The proposed CSW model resolves this issue by generating a common set of weights to analyse the resilience of SCNs as follows:

Using Eq. 6, the efficiency score of SCNs in terms of resiliency is obtained, as shown in Table 3. The projection of discretionary inputs on the CCR efficiency frontier (4th and 5th columns) shows that SCNs can reduce their inputs to the projected values to produce the same outputs in order to become efficient (resilient). On the other hand, the projection of outputs on the CCR efficiency frontier (6th and 7th columns) show that SCNs can become efficient/resilient by expanding their clustering coefficient and node degree while using the same amount of inputs. Findings show that the CCR model identifies 13 efficient SCNs with an average efficiency score of 0.9468, while the proposed CSW model identifies one SCN with the highest efficiency score with the average of 0.7335. Therefore, the proposed CSW model ensures complete ranking of DMUs with a higher discrimination power.

Findings show the resilience score of 22 SCNs, indicating that SCN-1 has the highest resilience score (0.9459) and SCN-10 has the lowest resilience score (0.5813). Comparing the configuration of SCN-1 and SCN-3, the two top SCNs show that SCN-1 has yielded fewer outputs using fewer discretionary inputs. While their first outputs are close to each other, the clustering coefficient of SCN-1 is ten times smaller than that of SCN-3. The higher resilience score of SCN-1 can be attributed to inputs, both discretionary inputs (number of supply nodes and available capacity) and non-discretionary inputs (total distance) and non-controllable inputs (population density). SCN-1 has technically operated very well as it has used fewer resources compared to SCN-3. While SCN-1 has a better status than SCN-3 in terms of population density (less population density increases SCRes), it suffers from a long geographical distance to demand nodes which reduces its capability to respond to disruptions and be resilient. The optimal solution shows that the average node degree is the most important output variable (\({u}_{1}^{*}=0.4742\)) in determining the resilience of SCNs. This variable measures the connectivity of elements of the SCN, and higher connectivity means that knowledge sharing among the nodes is higher, so they have a common understanding of the disruptive situations and are better prepared to respond to them.

Comparing SCN-1 as the highly resilient and SCN-10 as the least resilient SCN shows that SCN-10 has produced much higher outputs with significantly higher amounts of discretionary inputs. While SCN-10 enjoys a shorter distance (over 34% shorter), its population density is over 200% more than that of SCN-1, which reduces its capacity to respond to disruptions and recover from them after any disruption occurs. As the technical efficiency of SCN-10 is 0.5813, so, 0.4187 parts of the discretionary inputs are not efficiently used to contribute to its resilience. In order to improve its resilience and operate as a fully resilient SCN, while it is operating under a 106,870 km distance and 13,895 population density, SCN-10 can reduce its discretionary inputs from (5, 87,422.7) to \(\left(2.9065\approx 3, 50818.82\right)\) to yield the same outputs (2.022, 1.6). To improve the market share and SC surplus, SCNs tend to expand their outputs instead of reducing the inputs. Focusing on SCN-10 from the output perspective reveals that if this SCN makes more connections with other networks and increases the outputs from (2.022, 1.600) to (3.4784, 2.7525), can position itself on the efficiency frontier and become a resilient network. These benchmarking practices help SCNs to focus on their capabilities to enhance their resilience.

Results show that various configurations of SCNs can impact the resilience level. For the Pacific region, this could imply that optimal planning and management of the number of supply nodes, their capacities, and their geographical locations could enhance the resilience of their LPG SCs. Managers can easily control discretionary inputs such as the number of supply bases and the network's available capacity in supplying the items during recovery. While increasing the capacity and adding to the supply nodes are costly for the SCN, these practices increase the resilience of SCNs, and if required, managers implement strategies to accomplish them.

The LPG SCs in the Pacific region are recommended to increase capacity and diversify supply sources to improve SCRes. Table 3 implies that LPG SCs should invest in infrastructures to increase capacity and diversify sources of LPG to react expeditiously to changing demand and supply. On the other hand, we found that non-discretionary inputs such as total distance among the supply and demand nodes and population density greatly impact the resilience of SCNs. Since manipulating non-controllable inputs such as population density is impossible and changing some non-discretionary inputs such as total distance among the supply and demand nodes is extremely costly (and even in many cases, the losses of the SCN because of longer distances are less than the cost of moving supply nodes to geographically closer locations), managers must formulate strategies to minimise the negative impacts of disruptions. Provided the above-mentioned non-discretionary inputs, holding extra inventories in the supply bases and securing multiple supply sources improves the resilience of SCNs. Given the unique geographical dispersion of the Pacific Islands, the distance between SC nodes could impact SCRes. Therefore, determining the supply node's optimal and strategic location and focusing on efficient transportation is important in helping managers make optimal decisions. Besides, key nodes, i.e. major distribution centres or suppliers, should have strong connections to other nodes to react to disruptions appropriately. The Pacific Island nations can enhance the resilience of their SCs by increasing the clustering coefficient and node degree of their SCNs by building more connections with other SCs, thus ensuring smoother operations during disruptions.

Given the flow of materials, cash, and information between the SC partners, it is expected that the information flow experiences a higher clustering coefficient compared to the other flows in the efficient SCs. The drawback of having a low clustering coefficient is that it might result in more inefficiencies due to the higher difficulty of coordination and collaboration throughout the network (Hearnshaw & Wilson, 2013). Thus, to improve the efficiency and therefore the resilience of supply networks, SC managers can build more social connections with other members of the network to increase the mutual flow of materials and information. Furthermore, in the post-pandemic era, good resilient strategies involve proactive strategies that anticipate changes and reactive strategies that respond to new challenges.

SCs are constantly exposed to disruptions, including natural disasters and man-made disruptive events. SCs need to improve their capabilities to proactively and reactively respond to disruptions through risk mitigation and devising business continuity plans. In the post-pandemic period, the issue of SCRes is to adapt to new and unanticipated disruptions while maintaining a balance between efficiency and adaptability. The pandemic has shown the weaknesses and interdependencies of global SCs, requiring companies to engage in resilience-building strategies such as supplier diversity, enhanced visibility and transparency, and the use of new technology. Nonetheless, these solutions may need substantial expenditures and may have an effect on the cost and pace of operations, resulting in a trade-off between resilience and profitability. In this context, SC finance emerges as a critical lever to balance this trade-off. By providing more efficient financing options, it enhances SC cost optimisation, thereby reducing the cost burden of resilience strategies. Additionally, it can mitigate SCRes risks by ensuring more robust financial flows, contributing to SCRes through enhanced financial stability, which is vital in periods of disruption. Moreover, the strategic use of SC finance is instrumental in enhancing SC performance by aligning financial flows with operational needs, ensuring that SCs are not only resilient but also financially optimised. The SCRes of 22 LPG SCs has been measured and analysed in this study. Given the presence of several non-discretionary and non-controllable factors and their impacts (which are more likely negative) on the resilience of SCs, we developed a common set of weights model with non-discretionary and non-controllable inputs to evaluate the resilience of SCNs. The proposed model has the capability to provide SC managers with the complete ranking of the SCNs and highlight the best practices by solving only one linear program. SCNs are able to determine their excess inputs and try to minimise them to increase resilience. Looking at the population density and total distance among supply and demand nodes, holding extra inventories and extending the supplier base are two suitable strategies that speed up the recovery from disruptions. Despite the provided strengths of the proposed model, it does not look at the outputs and how much they should increase to make the network efficient. Future studies can extend the proposed methodology to non-oriented DEA models to assess the resilience of SCNs to offer a wider view of SCRes and the needed output upswing for peak operations. Secondly, investigating the changing nature of SCs can delve deeper into resilient responses to evolving situations. Lastly, studying the effects of technologies like artificial intelligence and blockchain on SCRes can shed light on the influence of digital evolution on SC efficiency and adaptability.