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Simulation-optimization methods for designing and assessing resilient supply chain networks under uncertainty scenarios: A review

The design of supply chain networks (SCNs) aims at determining the number, location, and capacity of production facilities, as well as the allocation of markets (customers) and suppliers to one or more of these facilities. This paper reviews the existing literature on the use of simulation-optimization methods in the design of resilient SCNs. From this review, we classify some of the many works in the topic according to factors such as their methodology, the approach they use to deal with uncertainty and risk, etc. The paper also identifies several research opportunities, such as the inclusion of multiple criteria (e.g., monetary, environmental, and social dimensions) during the design-optimization process and the convenience of considering hybrid approaches combining metaheuristic algorithms, simulation, and machine learning methods to account for uncertainty and dynamic conditions, respectively.


Introduction
A supply chain network (SCN) is a typical example of a complex and large-scale system [11] define it as a network of suppliers, manufacturing plants, warehouses, and distribution channels organized to acquire raw materials, convert these raw materials into finished products, and distribute these products among customers. Many decisions must be made in such a complex system in order to guarantee a good performance. However, the more complex a system is, the more imprecise or inexact is the information available to characterize it and, therefore, the greater the uncertainty level [15].
Supply chain network design (SCND) is a concept broadly studied during the last decades, both from a qualitative and a quantitative perspective. Authors have referred to it by using the terms supply chain design and supply chain network design [23] state that a SCND problem "comprises the decisions regarding the number and location of production facilities, the amount of capacity at each facility, the assignment of each market region to one or more locations, and supplier selection for sub-assemblies, components and materials". These decisions are related to a strategic level, and must be optimized considering a long-term (usually several years) efficient operation of the supply chain as a whole [6]. One of the more challenging responsibilities in SCND is addressing uncertainty.
The remaining of this document is organized as follows: Section 2 extends the motivation of this paper by explaining the extent of previous literature reviews addressing SCND resilience and sim-opt methods in this field. Section 3 explains the research methodology employed to carry out this review. The findings of this paper are presented in Section 4, where discussions on relevant works are also presented in Sections 4.1 and 4.2, respectively. Section 5 provides insights and future research directions by analyzing how emerging hybrid methods can be useful for designing resilient SCNs under uncertainty or dynamic conditions, as well as the concept of 'agile' SCND. The paper ends in Section 6 by outlining some concluding remarks.

Previous literature reviews and positioning of our work
To the best of our knowledge, there are no published literature reviews that combine sim-opt methods with SCN resilience. A review by [123] highlights the use of sim-opt frameworks as a growing research area. Integrated problems such as location-routing, inventory-routing, and location-inventory are analyzed, and sim-opt applications are studied. Finally, the authors analyze papers addressing sustainability issues, concluding that this is a relevant trend along with resilience. Therefore, they state that sim-opt frameworks are the main tool to design and manage SCNs. However, despite the relevance these authors give to resilience, they do not analyze papers considering this dimension.
A total of 19 review papers discussing the concept of "supply chain resilience" were found since 2015. Only one review previous to 2015 was found [122]. Here, the authors relate the SCN resilience concept to traditional resilience concepts from the ecological, social, psychological, and economic fields. Most of these works are conceptual, i.e., they discuss about resilience and some related concepts. These conceptual papers help to clarify terms in order to have a better understanding on the topic. For instance, [167] carry out a systematic review in which risk sources and resilience factors in agri-food supply chains are identified. In addition, particular parameters that can affect this type of SCNs are presented. A systematic review by Stone and Rahimifard [146] includes 137 articles from different fields such as engineering, operations management, ecology, and social sciences in order to identify definitions, elements, and strategies that can be relevant for resilience in agri-food SCNs. More recently, [52] perform also a review from a multidisciplinary point of view (including supply chain management, information systems, psychology, among others) to establish differences and similarities between agility and resilience concepts. [153] reviewed 91 papers related to SCN resilience, showing that most studies (43%) are conceptual or theoretical, and 36% of them adopt modeling approaches. Several definitions of "resilience" are provided, as well as proactive and reactive strategies for building resilient SCNs. Associated concepts like flexibility, redundancy, collaboration, and agility are identified. Little attention is paid by these authors to modeling articles. Such concepts and others related to SCN resilience are also identified by Sawyerr and Harrison [139], who call them "formative elements". These are compared with characteristics of high reliability organizations. Alternatively, Radhakrishnan et al. [126] call these concepts as "key capabilities". They identify 4 of them: flexibility, velocity, visibility and collaboration, as well as 13 attributes related to SCN resilience [140] expand such concepts by identifying resiliencerelated barriers, metrics and strategies. These are presented into a unified framework after analyzing 125 papers. Additional topics are analyzed by Ali and Gölgeci [5], who combine SLR with VOSviewer Co-occurrence Analysis to identify a set of drivers, barriers, theories, moderators, mediators and research methods in SCN resilience.
A systematic review of 67 papers is carried out by Hohenstein et al. [66]. Here, many SCN resilience definitions are presented. The quantitative approach is only addressed by analyzing some papers regarding how to measure resilient designs [91] establish a typological framework by performing a review of the SCN resilience concept. Few definitions are shown, and the core of the review is to expose such typology. Terms like supply chain disruptions, risk, vulnerabilities, or capabilities form the conceptual taxonomy to classify reviewed papers. This paper highlights that the SCN resilience concept is far from being mature. An SLR methodology is also used in a review by [33] to synthesize conceptual and empirical studies related to resilience in supply networks. A total of 9 key constructs of SCN resilience are identified and defined: risk, general vulnerability, operational vulnerability, complexity, uncertainty, risk management, agility, supply chain understanding, and collaboration [83] review 100 papers, proceedings, and book chapters related to enterprise and supply chain resilience concepts. Only 6 articles that use operations research and management science tools were found. Unlike other review papers, these authors include some resilience-enterprise definitions. Several principles and strategies are also identified.
[42] provide a review focusing on both vulnerability and resilience terms. A total of 40 articles were reviewed, 28 regarding resilience and 12 regarding vulnerability. A few definitions related to these terms are provided. Finally, papers relating resilience, vulnerability, and some performance measures are shown [4] also carry out a literature review to analyze the SCN resilience concept based on 103 articles. Many definitions are provided and 5 capabilities are analyzed (ability to anticipate, to adapt, to respond, to recover, and to learn). Nevertheless, its most important contribution is the conceptual synthesis, which is performed via a holistic model [156] state the importance of analyzing SCN definitions besides the usual resilience-related ones. Then, a review of studies that apply resilience to supply chain management is provided. The authors conclude that the SCN resilience concept becomes more relevant when considering holistic SCNs, i.e., when a set of SCNs are interdependent. So far, the 16 shown papers address SCN resilience from a qualitative point of view, i.e., they analyze a set of concepts related to this topic. Common drivers characterizing resilience are identified, such as agility, collaboration or flexibility. Nevertheless, given the relative novelty of the topic, there is not still a unified general framework, and each author shows a different set of concepts. Alternatively, 4 papers addressing quantitative approaches in SCN resilience were found: [74], [39], [132] and [67]. These authors' remarks establish that most of their reviewed papers are conceptual and, therefore, there is a lack regarding the use of quantitative models for addressing SCN resilience. For instance, [74] provide a review about both disruptions and recovery in supply chain design and planning. Their perspective is to show papers that use quantitative tools regarding disruptions risks (natural or human-induced disasters, strikes, etc.), by differentiating these from operational risks (produced by uncertainty in demand, lead-time, or any other business-related variables). The authors dedicate a few paragraphs to papers that address sustainability. [39] review papers addressing the ripple effect in the supply chain through a quantitative approach. Quantitative tools such as mathematical optimization, simulation, control theory, complexity analysis, and reliability research are identified, although particularities about these models are not analyzed [132] offers a review focusing on the use of quantitative methods to support decisions related to SCND resilience. Strategic, tactical, and operational decisions are identified in 39 papers, as well as the modeling approach, definitions, and 48 resilience factors. [67] identify both qualitative and quantitative drivers of SCN resilience. Their work is based on the concept of "resilience capacity", which comprises three lines of defense: absorptive capacity, adaptive capacity and restorative capacity.
Notice that both conceptual and quantitative reviews are quite recent. This shows a growing interest in the SCN resilience topic. Moreover, although the papers by [39,67,74] address the resilience concept along them, the focus is different than the one employed in our review. For instance, the main topic of the review by Dolgui et al. [39] is not resilience but the ripple effect. Furthermore, we define a taxonomy more exhaustive and explicit than that used by Hosseini et al. [67] and Ivanov et al. [74]. For example, the latter shows a clear focus in disruption risks, which we extend by including operational risks in our analysis. Finally, we address some aspects that these authors do not consider explicitly, such as the uncertain parameters analysis or our exposition of papers tackling real-world cases. Regarding the article by Ribeiro and Barbosa-Povoa [132], they analyze all decisions levels (strategic, tactical, and operational) from only 39 papers, which shows the need of studying more thoroughly each of these levels. This is an additional contribution of our work.
An important branch of resilience studies is the metrics used to assess the supply chain performance. Measuring resilience becomes relevant not only to design new supply chains, but also to evaluate an already operational SCN. In this case, resilience metrics are useful for decision-makers to implement strategies that increase resilience at minimal cost. Both quantitative and qualitative indicators can be found. For instance, Cardoso et al. [22] propose a mixed-integer linear programming model to design a resilient supply chain. The network performance is assessed through 11 quantitative indicators, which are classified into three types: network design, network centralization and operational indicators. A real-world European supply chain is considered as a case study [147] perform a review about resilience metrics from the transportation infrastructure point of view. The functionality of these networks is taken as a core to define two types of resilience metrics: functionality-related and socioeconomic metrics.
From a qualitative point of view, Soni et al. [143] present a study in which 10 resilience enablers are identified to design a unique supply chain resilience index through a graph theory model. Data from both a literature review and surveys answered by Indian firms are used to identify the enablers. Agility, collaboration, supply chain structure, among others, are identified as enablers [142] perform an SLR where 17 performance indicators are identified. The supply chain network design is presented as one of these indicators, as well as agility, collaboration and others. Authors divide the SCN resilience into 3 phases: anticipation, resistance, and response and recovery. Notice in all these cited papers that authors highlight the supply chain network design as an important factor to assess resilience, i.e., resilience can not be studied properly without considering design and long-term decisions. This fact shows the relevance of our review.

A systematic literature review methodology
A key requirement in a literature review is that each stage of the process has to be defined in a protocol "intended to guide the whole review, thereby reducing the possible sources of bias which arise from authors making idiosyncratic decisions at different stages of the review process" [9]. Our review methodology is based on the systematic literature review (SLR) approach introduced by [36], which is characterized by "its distinct and exacting principles", its replicability, transparency, and robustness to produce solid and reliable evidence. In addition, reviews related to resilience in SCNs (see Section 2) have been carried out mostly using an SLR methodology.
The SLR steps are: (i) question formulation; (ii) location of studies; (iii) study selection and evaluation; (iv) analysis and synthesis; and (v) reporting and use of results. Firstly, it is important to formulate suitable questions to delimit the research and avoid to search topics that do not fit into the reviews' objectives. Therefore, a general question was formulated as: How sim-opt methods have been used to design resilient SCNs? To answer this general question, the following specific queries were formulated: 1. Which mathematical approaches have been used to design resilient SCNs? 2. Which solving approaches and objective criteria have been used to find solutions to these problems? 3. How uncertainty is addressed when designing resilient SCNs? 4. Which special and real-world cases are addressed by resilient SCND papers? 5. Which challenges remain open when designing resilient SCNs under uncertainty?
Next, papers published in journals and proceedings indexed in Scopus and Web of Science, as well as papers found in the ScienceDirect database, and in the Google Scholar search engine were collected. The search was conducted from a more general combination of terms to a more specific one, namely: • resilien* AND supply AND chain • resilien* AND supply AND chain AND network AND design • resilien* AND supply AND chain AND network AND design AND mathematical AND model • resilien* AND supply AND chain AND network AND design AND optimi?ation • resilien* AND supply AND chain AND network AND design AND simulation • resilien* AND supply AND chain AND network AND design AND optimi?ation AND simulation Notice that the search term "optimi?ation" was employed in order to capture both "optimisation" in British English and "optimization" in American English. The search was carried out in the fields title, abstract, and keywords. The term network was then suppressed to make additional search, since some papers do not use such a word. Mainly qualitative studies were found, even after using the terms mathematical model, optimi?ation, and simulation. These key terms were mainly used to search for review papers already analyzed in Section 2. In this regard, an additional search was conducted by limiting the document types to reviews. In addition, papers previous to the year 2000 were excluded, as well as those studies that do not tackle strategic decisions, according to the definition by [49]. However, when using the last combination of terms just a few papers were found. Some of them had already been collected, and others were not coherent with our research questions. For this reason, a sixth research question without including the term resilien* was formulated, namely: How sim-opt methods have been used to design SCNs? Then, a new search was conducted by using the next additional terms: • supply AND chain AND design AND simulation AND optimi?ation • supply AND chain AND network AND design AND simulation AND optimi?ation As a result of this last search, papers not including the combination of optimization and simulation techniques were excluded. In this way, we increased our scope and it was possible to establish a more complete framework. A total of 163 articles were short-listed by considering the aforementioned criteria. From these, 93 papers are related to SCND resilience, 49 to sim-opt methods in SCND, and 21 articles are reviews (all of them already analyzed in Section 2). The short-listed papers were organized in a spreadsheet, where basic information about the papers was registered: title, authors, year, and journal. Also, after an initial review, a taxonomy was built to analyze and synthesize SCND resilience and sim-opt papers, namely: • Mathematical approach: this refers to the method used to model the problem, e.g., robust optimization, stochastic programming, etc.
• Solving approach: this refers to the method employed by the authors to solve the proposed model, e.g., exact methods, metaheuristics, etc.
• Uncertain parameters: in a model, it is usual to consider some parameters as uncertain and others as known. Common uncertain parameters are: demand, cost, capacity, etc.
• Uncertainty approach: this refers to the way the authors model the uncertain parameters, e.g., by means of probability distributions, fuzzy sets, etc.
• Objective criterion: variables like cost, income, or profit are usually minimized or maximized in mathematical models when designing SCNs. In addition, it is possible that several conflicting objectives are considered, which leads to adapt the model and its solving approach.
• Supply chain design special case: some special cases regarding SCND can be found in the literature. These are conceptual models based on real-world characteristics that influence the design of a supply chain considering criteria that are specific of that model. These criteria can be: objectives, constraints, variables, or parameters. For instance, the sustainable SCND is a special case that not only considers the traditional economic goal but also environmental and social objectives. Other special cases found in the literature are: green SCND, closed-loop SCND, etc.
• Application to a real-world case: this refers to the fact that the problem and its solution have been applied to a real-life case; otherwise the paper is classified as a theoretical contribution.
Besides, when analyzing SCND resilience papers, the additional criterion type of risk is considered to build the taxonomy, which refers to operational risks, disruption risks, or both [149]. Then, a deeper review of the full text of papers was carried out, after which 42 papers (25 related to SCND resilience and 17 to sim-opt methods) were rejected because they do not match our research questions. Hence, 68 SCND papers and 32 sim-opt papers are analyzed in this work. Such analysis consists in: (i) identifying basic elements, such as authors, year and journal; (ii) identifying how each element of our taxonomy is addressed by every analyzed paper; and (iii) classifying extracted information in spreadsheets. Then, the main findings are synthesized in tables and figures for better presentation, and to identify better the characteristics of each paper according to our taxonomy.

Main findings from the SLR process
A detailed analysis of the short-listed papers is presented in Sections 4.1 and 4.2. An overview of published works is firstly given here. Notice that the number of papers published in the topic has increased exponentially over time, with about 77% having appeared in the last five years (between 2015 and April 2020). Hence, this research field is under expansion, as shown in Fig. 1. Observe that 87% of publications about resilience in SCND appeared during this period. Besides, 66% of the short-listed papers are based on reallife situations, in both SCND resilience and sim-opt SCND topics. The rest of the papers carry out experiments using theoretical data.
Regarding the journals where the publications about resilient SCND have appeared (Fig. 2), about 60% of works were published

Resilient SCND
The taxonomy previously defined has been used to analyze and synthesize 68 short-listed papers. Table 1 shows that most papers use stochastic programming as a modeling tool for the supply chain, followed by mixed-integer linear programming (MILP). Some authors propose hybrid optimization models, such as Fahimnia and Jabbarzadeh [44] -who propose a model that integrates stochastic, fuzzy, and goal programming-, or [87] -who mix stochastic with possibilistic programming. Six papers use both simulation and optimization methods in some way. Four of them use Monte-Carlo simulation to generate test scenarios [77,89,96,109]. The other two papers hybridize more deeply simulation with optimization methods in a resilience framework. One of them is the paper by Aqlan and Lam [7], who mix simulation with goal programming to manage supply chain risks in a real-world hybrid sim-opt model. A strategic-tactical multi-objective deterministic linear model that uses goal programming is used in the optimization part. Outputs of this model feed the stochastic simulation part and vice-versa. The other paper that makes use of sim-opt methods is authored by Li and Zhang [97], who solve the uncapacitated facility location problem with facility disruptions. A two-stage stochastic programming model is presented, as well as a scenario-based model. This problem is solved via the sample average approximation method, which is based on Monte Carlo simulation. Disruptions are modeled in a binary fashion, i.e., a facility may fail completely or not.
In general, the use of simulation methods is not as widespread as optimization. Thus, about 75% of the analyzed papers propose a pure optimization model. Pure simulation methods are used by 16% of the analyzed papers, with discrete-event simulation (DES) as the preferred tool. Finally, only 9% of the papers use a hybrid approach in designing resilient SCNs.
Heuristic and metaheuristic methods are used very scarcely in SCND resilience (Table 2). For instance, only [115] and [168] propose heuristics to enhance computational efficiency. Regarding metaheuristics, Bottani et al. [16] employ an Ant Colony Optimization algorithm (ACO), and [64] and [165] propose hybrid metaheuristics as a solution approach: a Taguchi-based memetic algorithm (TMA) for the first case, and a combination among differential evolution algorithm, variable neighborhood search algorithm and game theory (DVG) for the second case. This fact shows the high potential of designing heuristic-based approaches, given that strategic real-world problems might be both NP-hard and contain large-sized instances [2,34,125].
Most authors solve their proposed model by using exact methods, although some of them employ a relaxation procedure. For instance, [77] make use of Lagrangian relaxation. These authors propose a hybrid robust-stochastic optimization model to design an Iranian engine oil SCN. Both supply and demand are uncertain, as well as the occurrence of a fire in any facility. After solving the proposed model, Monte Carlo simulation is used to generate random instances for uncertain parameters and evaluate the solutions yielded by the model. Regardless a hybrid model is used or not, all authors that use any kind of simulation model in Table 1 are referred as they use simulation as solving approach in Table 2. For instance, Carvalho et al. [23] design a resilient SCN for an automotive sector company in Portugal via a DES model. Redundancy and flexibility strategies are assessed to mitigate the effects of "supply delay" disturbance.
The use of scenarios is the most frequent uncertainty approach (Table 3), either with assigned probabilities or not. Only 7 out of 68 papers do not consider any probability. Thus, for example, Fattahi et al. [45] propose a stochastic program in which the occurrence probability of each scenario is explicitly defined and introduced in the model.
Employing explicit probability distributions to address uncertainty is not as widespread as employing scenarios with assigned probabilities, although some authors hybridize them [16,35,89,130]. Therefore, the use of probabilities is very frequent in works regarding SCND resilience, due to its easiness of tractability. A total of 21 out of 68 articles include probability distributions in the model, in which 9 papers propose an optimization model, 8 papers propose a simulation model, and 4 papers hybridize both methods. Although only 12 out of 68 papers employ fuzzy numbers, such use shows a recent trend among the recently published papers. Thus, in general 36 out of 68 (53%) papers have been published since 2018, while 9 out of 12 (75%) papers using fuzzy numbers were published in the same period. Only a paper employing fuzzy numbers was published before 2017. This is the paper by Sadghiani et al. [134], who propose a fuzzy robust optimization model to design a robust and resilient Iranian retail SCN. A multi-step solving methodology is used to reduce the number of scenarios and both operational and disruption risks are considered. They also assign some probabilities to such scenarios. Table 3 also shows papers classified by type of risk. According to Tang [149], risks can be classified into two types: operational  risks and disruption risks. Operational risks are inherent to the supply chain normal operation, such as: uncertain demand, capacity, or costs. Disruption risks are related to serious incidents, such as natural and human-induced disasters (e.g., earthquakes, floods, terrorist attacks, etc.). The fact that 91% of the papers address disruptions indicates that this is a core topic when designing and assessing a resilient SCN, due to the importance of returning to its original state after facing any major incident. Nevertheless, 30 out of 68 papers not only consider disruptions risks but also operational risks. For instance, Klibi and Martel [89] tackle both by proposing various modeling approaches, which are based in stochastic programming. Scenarios are generated through Monte Carlo simulation and demand and network disruptions are addressed by using a multi-hazards approach. Fig. 3 shows the number of papers differentiated by type of risk and mathematical approach. Optimization methods are highly employed whenever disruption risks are considered. The proportion decreases when only operational risks are modeled. This fact shows that using hybrid sim-opt methods is an open challenge when designing and assessing resilient SCNs, especially if both types of risks are considered. Furthermore, the use of hybrid methods becomes relevant to model uncertain scenarios, since it offers a good balance between realism and cost-efficiency. Table 4 shows the taxonomy regarding the uncertain parameters. Demand and capacity are the most frequent parameters when considering operational risks. In regard to disruption risks, node disruption is modeled by 49% of the papers, which shows the relevance of considering disrupted facilities when designing and assessing resilient SCNs. In our taxonomy, a node disruption occurs when a supplier location or a facility breaks down completely and demand must be met by other facilities. If capacity or supply are only reduced partially, this was not considered in the node disruption parameter, but in the capacity and supply ones, respectively.
Link disruption is also a modeled parameter regarding disruption risk, although not as frequent as node disruption. The former one refers to the interruption in the flow, e.g., because an arc in the network is broken or because the means of transport fail. Notice that only [48,141,164] (out of 14 papers) consider link disruptions but not node disruptions. The other 11 articles consider both.
A total of 19 out of 68 papers model only one uncertain parameter, and the rest considers at least two of them. For instance, [111] consider that demand, capacity, costs, and CO 2 emissions are uncertain. They show a fuzzy multi-objective programming model to design and assess a green and resilient SCN. Four resilience pillars are proposed to be maximized: robustness, agility, leanness, and flexibility. Also, they consider minimization of cost and environmental impact.
Some authors use particular uncertain parameters that are not considered in other papers. For example, Namdar et al. [113] consider that spot market price, lost sale penalty, capacity, and node disruption (in the supplier) are uncertain. They propose a scenariobased two-stage stochastic programming model to design a resilient supply chain considering risk aversion and both operational and disruption risks. Both proactive and reactive strategies are analyzed to achieve resilience. Visibility and collaboration are among the proactive strategies, while spot purchasing and multiple sourcing are among the reactive strategies. Finally, some numerical examples are used to test the approach. Table 5 shows the model objective criterion. Both optimization (minimization and maximization) and non-optimization criteria are considered. The latter one refers especially to simulation models in which the objectives are the model output variables. In this case, measuring resilience is the most used objective. In general, the most utilized criterion is cost minimization (53% of papers), either in a single-objective model or a multi-objective model. For instance, Dehghani et al. [35] propose only a cost minimization objective, considering both business-as-usual and disruption uncertainties to design a resilient solar photo-voltaic cells manufacturing SCN. Robust optimization is used to model this strategic-tactical problem in which 30 parameters are uncertain. Most of them are different types of fixed and variable costs. Profit and net present value maximization are also relevant objectives considered in some papers. For instance, Behzadi et al. [10] propose a strategic-tactical stochastic programming model to help agri-food supply chain decisionmakers to choose robust and resilient strategies versus disruption risk. The model is applied to a kiwifruit global SCN. Nevertheless, profit, net present value and the other objective variables considered by a few authors are not as used as cost minimization. Resilience, the core concept of interest in our work, is maximized only in 5 out of 68 papers, although alternatively 3 works minimize deresiliency or non-resiliency. Some researchers also address environmental aspects, such as CO 2 emissions or environmental impact, as well as social impact.
Also, 25 out of 68 references optimize multiple objectives, which are identified with an asterisk in Table 5. Notice that neither resilience nor de-resiliency are never a unique objective, i.e., they are always optimized along with cost. This shows that, despite resilience may have a relative relevance in an explicit objective, it should not be considered alone due to the high cost that a resilient design may lead to. Papers that employ multiple objectives must use some procedure in order to address such multiplicity [87] are the only authors who employ the Reservation Level-driven Tchebycheff Procedure (RLTP), and explain why both the weighted sum method and the ϵ-constraint method are not appropriate. However, evidence shows that these methods are preferred when considering multiple objectives, as well as the use of the LP-metric method or Compromise programming (Table 6). For example, Jabbarzadeh et al. [76] propose a bi-objective model that seeks to minimize expected total cost and to maximize expected sustainability  performance. A set of scenarios with a probability of occurrence is defined and the model is applied to a plastic pipe industry. In addition, authors never consider more than 4 objectives. Besides, there is not a clear relation between the number of objectives and the solving method, which shows that apparently such number does not have any influence in the chosen method. Anyway, since 2018 there is a clear trend in employing either the ϵ-constraint or the LP-metric method instead of weighted sums. Deeper research is  necessary to establish pros and cons of using one or another method to solve multi-objective models oriented to design and assess resilient SCNs. SCND special cases are also studied. They imply to consider particular variables, objectives or constraints, which are additional to traditional parameters such as costs, demand, or capacity. Green SCND is the special case that addresses environmental aspects. The closed-loop SCND special case also usually considers green aspects [78]. Likewise, the sustainable SCND must include them by definition [165], as well as social topics. Some authors have mixed these special cases with SCND resilience ( Table 7). Notice that sustainability and green practices may impact negatively on the supply chain resilience [70]. For instance, a paper by Fahimnia and Jabbarzadeh [44] couples the sustainability concept with the resilience concept. This is achieved by designing a SCN through stochastic fuzzy goal programming. The sustainability approach implies that the model is multi-objective. These authors define SCND Table 5 SCND resilience references according to objective criterion.
Competitive supply chain is another identified special case in SCND. In this context, "competitive" means that competition among rivals is explicitly considered when designing a SCN. Rivals' competitive actions may lead to lose market-share because, for example, clients buy the product to other suppliers [48,129]. Therefore, quantities supplied by rivals are variables in the proposed model. Finally, [50] do not only design a competitive supply chain, but they take into account green and closed-loop characteristics in a biobjective fuzzy model that considers both operational and disruption risks. Table 7 also shows that most papers (45 out of 68) apply their model to a real-world case. This fact shows the high importance of considering resilience to solve problems of real-life SCNs, and demonstrates the relevance that companies give to the negative consequences of operational and disruption risks, such as loss of customers and money, or even loss of lives due to the occurrence of natural or human-induced disasters. Besides, most papers that address some supply chain special case apply the model in a real-world Table 7 SCND resilience references according to the supply chain special case and real-world case.

Authors
Supply chain special case Real-world case [7] --A high-end server manufacturing company [10] Agricultural A kiwifruit supply chain in New Zealand [16] --A supply chain for ready-made UHT tomato sauce [20] Closed-loop A European supply chain [21] Closed-loop A European supply chain [23] --A Portuguese automotive supply chain [35] --A Photovoltaic (solar) cells supply chain [44] Sustainable An Australian sportswear production and distribution company [45] --An Iranian glass supply chain [48] Competitive An Iranian automotive parts and services supplier [50] Closed-loop, Competitive, Green A filter manufacturing company [51] Closed-loop An Iranian glass company [60] --An Iranian blood supply chain [61] --A Jordanian blood supply chain [62] --An Iranian supply chain for fertilizers [64] --A global electro-medical device manufacturer [67] Agricultural An Iranian wheat supply chain [69] --A European supply chain [70] Sustainable A global supply chain in electronics [77] --An Iranian engine oil company [76] Sustainable A plastic pipe industry [78] Closed-loop An Iranian glass supply chain [75] Green An electricity supply chain in Iran [80] --A beef supply chain in China [94] --A supply chain from automotive industry [96] --A Chinese mobile phone supply chain [99] --Three Australian resource industries: fisheries, agriculture, and mining [101] Agricultural Procurement of corn stover, switchgrass, and Miscanthus in US [103] Sustainable A garment manufacturing firm based in Pakistan [102] --A food processing company [108] Closed-loop, Sustainable An automobile assembly company [110] Green A meat supply chain in the UK [111] Green A meat supply chain [112] Agricultural An Iranian bioethanol supply chain [124] Closed-loop -- [129] Competitive An automotive supply chain [131] Closed-loop A European chemical process supply chain [133] --An Iranian pharmaceutical company [134] --An Iranian retail chain [144] Agricultural -- [148] Competitive -- [152] --A drug supply chain in US [159] --A supply chain from automotive industry [160] Closed-loop, Green An Iranian dairy company [161] Closed-loop, Green An Iranian dairy company [165] Sustainable A pharmaceutical supply chain network [164] --An Iranian hazardous-materials supply chain [168] --A biofuel supply chain in US case, which shows that theoretical models usually address generic SCNs. Finally, notice that some papers considering real-world cases from the agricultural sector are not classified as belonging to agricultural special case. This is because these papers do not address any uncertain parameter specific of an agricultural supply chain.

Simulation-optimization methods in SCND
Hybrid sim-opt methods refer to the interaction between optimization and simulation "to find near-optimal solutions to complex or stochastic optimization problems" [81]. In particular, this section analyzes the use of such methods for designing and assessing supply chains. Table 8 shows both the optimization and the simulation approaches used by each analyzed paper. Regarding optimization, MILP is the most used approach (53%). Regarding simulation, DES is the preferred one (59%). The mix between these particular approaches is the most used hybridization (31% of the papers).
All papers combine two methods, with the exception of Costa et al. [29], who hybridize three methods. They propose a sim-opt Table 8 Sim-opt references according to the mathematical approach.

Authors
Exact method Heuristic Metaheuristic [26] X [28] TS [29] X [30] GA, EP [32] X [34] ILS [85] X [107] X [37] GA [40] X [41] X [55] X [58] X [59] X [79] GA [84] X [86] OptQuest [88] X [90] GA [92] NSGA-II [93] X [95] X [106] X [135] X [136] X [137] PSO [151] GA [154] X [158] GA [162] OAA [163] NP, OCBA [166] X Tabu search Genetic Algorithm Evolutionary Programming Iterated local search Non-dominated Sorting Genetic Algorithm II Particle swarm optimization Outer-approximation algorithm Nested Partitioning Optimal Computing Budget Allocation model to design a Colombian supply chain for bio-diesel production and distribution from palm oil feed-stock. Firstly, a deterministic simulation model is used to design the production process and obtain the production cost. This feeds a MILP model for locating production plants. Finally, a goal programming model is proposed to perform a micro-location considering social aspects. Exact methods are used by 59% of papers ( Table 9). The other half uses heuristic or metaheuristic methods. These are preferred in those cases in which fast solutions are required and near-optimal solutions are enough to most decision makers. Most metaheuristic papers use genetic algorithms (7 out of 11), which shows open opportunities for other techniques such as iterated local search [34], tabu search [28], or any other metaheuristic [47] or simheuristic [81]. Fig. 4 shows the frequency in which the analyzed papers mix each simulation technique with each solving approach. Open opportunities are identified in the use of artificial neural networks, fuzzy simulation and Monte Carlo simulation. Most papers combine an exact method with DES, although this simulation approach is also frequently combined with a metaheuristic. As an example of the first case, [26] propose a hybrid model that, in early stages, solve independently both the deterministic and the stochastic models for designing a SCN. Then, authors combine these models and compare results with the analytical model and a simulation-based optimization model. The solving time required by this hybrid approach is shorter than the one employed by  traditional simulation-based optimization models. As an example of the second case, [90] design and assess a distribution network through a hybrid sim-opt model. A strategic-tactical MILP model is proposed and a genetic algorithm is used as a solving approach combined with DES. Sim-opt papers make little use of scenarios with probabilities, as well as fuzzy numbers (Table 10). Probability distributions are the most used uncertainty approach (23 out of 32 papers). For instance, Martins et al. [106] propose a sim-opt approach to redesign a pharmaceutical wholesaler SCN. They affirm that literature addressing supply chain network redesign is very scarce, and that a redesign process should be carried out carefully because it is different to the design one -in the former, the company has already a market share that can be severely affected if the redesign process is not performed well. A MILP model is used for strategic and tactical decisions of redesign, and a DES model is also employed for operational decisions related to the evaluation of the impact of redesign in daily activities.
It is very unusual to combine different uncertainty approaches. Only [158] model demand uncertainty through scenarios with probabilities. They also model costs uncertainty through fuzzy numbers. Other modeled uncertain parameters are shown in Table 11, such as cost (28% of the papers) and supply (25% of the papers). Nevertheless, demand is also the most addressed uncertain parameter: 75% of the papers consider it. For instance, a set of 7 strategic-tactical decisions are considered by [151] to design and assess a SCN. Qualitative and policy decisions are tackled by a genetic algorithm and quantitative decisions by a MILP model. Simulation is used to assess the performance of the obtained supply chain configurations.
Only 8 out of 32 papers model a single uncertain parameter. The rest address at least 2 of them. Moreover, some of these parameters are considered by only one paper. For instance, only [30] consider arrival frequency, pick-up time, delivery time and trans- Table 11 Sim-opt references according to the uncertain parameter.

Table 12
Sim-opt references according to objective criterion.

Objective criterion Authors
Minimize Costs [28,34,85,107], [37]*, [40,41], [58]*, [59,79,84], [86]*, [90], [93]*, [95,106], [135]*, [136,137,151,154,158,162,163 An open opportunity is identified in the optimization of criteria different than cost, since cost minimization is the most addressed objective criterion (Table 12): 78% of the papers seek to optimize it, either as a single objective or jointly with other criterion in a multi-objective model (identified with an asterisk in the table). For instance, a paper by [135] minimizes both operation costs and costs associated to global warming impact. The latter objective is important here due to the environmental impact that the designed cold supply chain can yield. Two cases that require warehousing and transportation with a controlled temperature are analyzed through a hybrid sim-opt approach.
Finally, Table 13 shows papers that consider some supply chain special case or a real-world case. The latter is considered by 21 out of 32 papers, which shows the relevance that most authors give to apply their models to real-life cases. For instance, a two-part paper is written by [121] (not included in the table) and [92] (in the table). The former one proposes an integrated refinery supply chain dynamic simulator. The latter combines this simulation tool with a non-dominated sorting genetic algorithm to design and operate a petroleum refinery SCN with the objectives of maximizing profit margin and customer satisfaction.
Only 11 out of 32 papers papers consider explicitly a supply chain special case, being the agricultural SCN the most addressed one. For instance, an agricultural SCN is designed and assessed by de Keizer et al. [85] through a hybrid MILP and DES model. The objective is to minimize the total cost taking into account the high perishability of fresh cut flowers. Therefore, the product quality decay is modeled as a function of time and temperature. Data from a real-world Dutch company that distributes flowers across Europe is used to test the proposed approach.

Insights and future research directions
The increasing concerns about operational and disruption risks in SCND lead to use methods that model them as accurately as possible. As discussed in previous sections, designing and assessing resilient SCNs requires to take into account many factors altogether, from uncertainty in several parameters of the optimization model that need to be considered (e.g., random occurrence of disruptions, random customers' demands or links availability, etc.) to dynamic conditions that might affect daily operations (e.g., continuous changes in availability of raw materials, transport costs, or customers' demands, among others). Consequently, solving methods need to be able to address all these characteristics of real-world SCNs together with the fact that, in most cases, SCNs constitute large-scale complex systems [46]. Modeling these concerns means: (i) considering uncertainty to represent operational and/or disruption risks (inherent in supply chain resiliency research) coherently with real-world features; (ii) optimizing the supply chain design according to suitable criteria, such as costs, profit, environmental impact, or resilience; and (iii) using time-efficient methods when designing and assessing resilient supply chains considering their complexity.
Under these circumstances, pure optimization or pure simulation methods alone do not seem to have the flexibility and power to provide answers to increasingly demanding decision-makers. On the contrary, hybrid sim-opt methods, such as those from stochastic programming [138] or simheuristics, which combine metaheuristic frameworks with simulation, seem to be more appropriate to deal with problems under uncertainty. In particular, simheuristics have shown to be an effective method to deal with large-scale NP-hard optimization problems under uncertainty conditions [82]. For instance, Pagès-Bernaus et al. [117] propose a simheuristic algorithm Table 13 Sim-opt references according to the supply chain special case and real-world case.

Authors
Supply chain special case Real-world case [28] Agricultural A biomass supply chain [29] Sustainable A Colombian first generation biodiesel production from palm oil feedstock [30] Reverse A Colombian city used tire collection process [85] Agricultural A Dutch cut flower retail chain [107] --Distribution of long-lasting insecticidal nets in Ivory Coast [37] --A European automotive production-distribution network [40] Agricultural A Canadian agricultural biomass supply chain [41] Agricultural A supply chain for biocrude production [55] Agricultural A supply chain of prickly pear in Mexico [58] Closed-loop -- [59] --A multinational company in alcohol free beverage sector [84] --Volkswagen distribution system [86] --A white goods retailer who serves the Greek market [88] --A biorefinery network in US [92] --A petroleum refinery supply chain [93] Agricultural Ethanol production from rice straws in Indonesia [95] --A carbon capture, utilization and storage supply chain in Germany [106] --A pharmaceutical wholesaler [135] Green Prepared meats in Canada, A cold supply chain for publicly-funded vaccines in Canada [136] Humanitarian A blood supply chain network in a possible earthquake in Tehran [154] --A wood distribution company in Mexico [166] --A natural gas supply chain to design SCNs in the context of e-commerce, and shows that it tends to outperform classical stochastic programming approaches when solving large-sized instances. Since they are based on the use of simulation and therefore can provide rich information on any design plan, simheuristics are well suited for estimating SCN risk-related properties such as: reliability, robustness, and resilience. Likewise, when dealing with large-scale SCNs under dynamic conditions, the combination of metaheuristics with machine learning methods might also be quite appropriate. In effect, learnheuristics are based on the use of learning mechanisms that allow the metaheuristic algorithm to improve their capacity to adapt to the existence of dynamic inputs [18]. For instance, Calvet et al. [19] address a SCN in which both distribution costs and customers' demands might be influenced by the way customers are assigned to the heterogeneous facilities or retail centers.
Although traditional SCND has focused on long-term and costly to reverse strategic decisions, there might be situations in which the design, re-design and assessment of a SCN needs to be performed in a fast way and several times in a short time period, thus calling for 'agile' SCND. This is the case, for example, of emergency situations associated with natural or human-caused disasters, where a set of mobile facilities (e.g., first-aid centers) need to be quickly deployed over a territory and then re-allocated as new events happen (e.g., some areas get stabilized while others require more attention and resources). In this cases, decisions on the SCND (e.g., facility location, customers' allocation, or transport modes) need to be made almost in real time and are required to be re-evaluated every few days or even hours. In these cases, the use of biased-randomized algorithms [57] constitute an interesting tool yet to be fully explored, specially when they are combined with parallelization techniques in order to generate high-quality solutions in realtime. Finally, with the advent of the internet of things (IoT), real-time information obtained of sensors distributed by all the elements of the supply chain can be used to design SCN. Hence, the design process would not only become more efficient, but also much more reliable, since the IoT provides to supply chain managers a coherent stream of real-time data, by which they can develop flexible contingency plans and strategies to respond to disasters [73]. Furthermore, as IoT allows the continuous self-assessment of the supply chain, it is possible to predict eventualities during supply chain operation. Thus, decision makers can assess and re-design the SCN in function of the time period of the disaster, providing a flexible and fast recuperation of the system, designing intelligent supply chains networks [31].

Conclusions
This paper has provided a literature review on recent works related to the design of resilient supply chain networks via simulation and optimization approaches. A systematic literature review approach was followed. Our review shows that this is an emerging topic, which has been gaining 'momentum' during the last years. Simulation-optimization methods are specially designed to deal with considerations regarding uncertainty, time-efficiency and optimization of suitable criteria. The simulation side provides efficient tools to address uncertainty. Discrete-event simulation stands out in analyzed papers, although Monte Carlo simulation is also a useful tool. Nevertheless, simulation does not allow itself to obtain optimal or near-optimal solutions. Therefore, the optimization side is intended to achieve them. Here, we find that most used mathematical approaches are stochastic programming, mixed-integer linear programming, fuzzy programming, and robust optimization.
Hence, a hybrid simulation-optimization approach is particularly useful due to the following facts: (i) both operational and disruption risks are subject to uncertainty in real-world problems. The use of a deterministic approach would lead to a supply chain design whose resilience is not coherent with this reality, increasing potential high economic losses after a disruption event; and (ii) instead of just measuring resilience or costs, as pure simulation would do, resilience should be optimized in order to face risks properly. However, extremely resilient supply chains design would be highly expensive. A trade-off between resilience and any economic performance indicator would be very useful. Solving methods considering multiple objectives become relevant in these cases.
Analyzed papers show that costs minimization is still the widely preferred optimization objective, but given the contemporary concerns about environment, sustainability, and resilience, other objectives have been taken into account, such as environmental impact or CO 2 emissions minimization. Nevertheless, only a few authors have tackled them. Consequently, the consideration of multiple-objective approaches constitutes an open challenge. In addition, demand is the most addressed uncertain parameter, which shows its relevance when designing and assessing supply chain networks. However, other parameters subject to uncertainty, such as costs, capacity, supply, node disruption, link disruption, and many others should also be considered together with demand. Clearly, these combinations are also open research lines, especially when considering both operational and disruption risks. The uncertainty regarding these parameters is mostly addressed through probability distributions and scenarios with assigned probabilities. Fuzzy numbers are used to a lesser extent.
Six supply chain design special cases were identified: sustainable, closed-loop, agricultural, green, competitive and reverse supply chain. About 37% of the papers address at least one of these. In addition, real-world cases are considered by most papers. Economic sectors, such as the automotive industry, the pharmaceutical industry, or the clothing industry are tackled.
Most real-life supply chain networks are large-sized and associated problems easily become NP-hard as realistic constraints are included into the mathematical models. Furthermore, if several uncertain parameters and multiple objectives are considered, an exact optimization may become time-prohibitive. Hence, it is somewhat surprising that the use of metaheuristic methods is still relatively scarce in sim-opt methods for resilient supply chain network design. Most authors prefer to use exact methods as solving approach. Besides, only about 9% of the papers use hybrid simulation-optimization methods to design resilient supply chain networks. Therefore, the open opportunities are huge when considering the hybridization and metaheuristics to carry out the design process.
In consequence, our paper proposes the use of emerging hybrid methods, such as simheuristics and learnheuristics, to deal with the design of supply chain networks under uncertainty and dynamic conditions. We point out the need of considering agile methods, such as parallelized versions of biased-randomized algorithms, to address a new type of supply chain networks characterized by the need of re-designing facility location, customers' allocation, and transport modes every few hours or days.
Although there are some advantages when following a systematic review protocol in comparison with narrative reviews, such as the reduction of sources of bias and the increase in objectivity for the selection and analysis of research works, there are some limitations as well. Indeed, the combination of terms to search for documents and the selection of databases may lead to the exclusion of some research papers. Unfortunately, it is not possible to provide the list of such excluded studies. In addition, as analyzing papers addressing the use of simulation and optimization techniques for resilient supply chain network design and assessment is a criterion for this paper, some studies on this topic not developing or applying any of these techniques are also excluded.