Integrating Operational and Organizational Aspects in Interdependent Infrastructure Network Recovery

Managing risk in infrastructure systems implies dealing with interdependent physical networks and their relationships with the natural and societal contexts. Computational tools are often used to support operational decisions aimed at improving resilience, whereas economics‐related tools tend to be used to address broader societal and policy issues in infrastructure management. We propose an optimization‐based framework for infrastructure resilience analysis that incorporates organizational and socioeconomic aspects into operational problems, allowing to understand relationships between decisions at the policy level (e.g., regulation) and the technical level (e.g., optimal infrastructure restoration). We focus on three issues that arise when integrating such levels. First, optimal restoration strategies driven by financial and operational factors evolve differently compared to those driven by socioeconomic and humanitarian factors. Second, regulatory aspects have a significant impact on recovery dynamics (e.g., effective recovery is most challenging in societies with weak institutions and regulation, where individual interests may compromise societal well‐being). And third, the decision space (i.e., available actions) in postdisaster phases is strongly determined by predisaster decisions (e.g., resource allocation). The proposed optimization framework addresses these issues by using: (1) parametric analyses to test the influence of operational and socioeconomic factors on optimization outcomes, (2) regulatory constraints to model and assess the cost and benefit (for a variety of actors) of enforcing specific policy‐related conditions for the recovery process, and (3) sensitivity analyses to capture the effect of predisaster decisions on recovery. We illustrate our methodology with an example regarding the recovery of interdependent water, power, and gas networks in Shelby County, TN (USA), with exposure to natural hazards.     

Decentralized planning with an interdependent marketing-production system

An interdependent marketing-production planning model based on control theory is described. The interdependent model is a composition of the Vidale-Wolfe model relating advertising rates to sales rates, and the Holt, Modigliani, Muth & Simon (HMMS) production inventory planning model. An overall optimal marketing-production plan is identified using the interdependent model. This overall optimal plan (resulting from centralized planning) is then used as a reference point to measure the effectiveness of decentralized planning approaches. It is found that in some cases almost no coordination is necessary, in some cases the use of a transfer price leads to good decentralized planning, and in other cases centralized planning must be employed to achieve good results. Several examples are presented to illustrate the cases in which decentralized planning does and does not work well.     

Competitive and Collaborative Quality and Warranty Management in Supply Chains

Product quality and product warranty coverage are two important and closely related operational decisions. A longer warranty protection period can boost sales, but it may also result in dramatically increased warranty cost, if product quality is poor. To investigate how these two decisions interact with each other and influence supply chain performance, we develop a single‐period model with a supplier that provides a product to an original equipment manufacturer, which in turn sells it to customers. Customer demand is random and affected by the length of the product warranty period. Warranty costs are incurred by both the supplier and the manufacturer. We analyze two different scenarios based on which party sets the warranty period: manufacturer warranty and supplier warranty. Product quality is controlled by the supplier, and the manufacturer determines the ordering quantity. We analyze these decentralized systems and provide the structural properties of the equilibrium strategies. We also compare the results of centralized and decentralized systems and identify the conditions under which one system provides a longer warranty and better product quality than the other. Our numerical study further shows that, in decentralized settings, when the warranty period is determined by the firm sharing the larger proportion of total warranty costs, the supply chain can achieve greater system‐wide profit. Both parties can therefore benefit from properly delegating the warranty decision and sharing the resulting additional profit. We further design a supplier‐development and buy‐back contract for coordinating decentralized supply chains. Several extensions are also discussed.     

State of the Art in Risk Analysis of Workforce Criticality Influencing Disaster Preparedness for Interdependent Systems

The objective of this article is to discuss a needed paradigm shift in disaster risk analysis to emphasize the role of the workforce in managing the recovery of interdependent infrastructure and economic systems. Much of the work that has been done on disaster risk analysis has focused primarily on preparedness and recovery strategies for disrupted infrastructure systems. The reliability of systems such as transportation, electric power, and telecommunications is crucial in sustaining business processes, supply chains, and regional livelihoods, as well as ensuring the availability of vital services in the aftermath of disasters. There has been a growing momentum in recognizing workforce criticality in the aftermath of disasters; nevertheless, significant gaps still remain in modeling, assessing, and managing workforce disruptions and their associated ripple effects to other interdependent systems. The workforce plays a pivotal role in ensuring that a disrupted region continues to function and subsequently recover from the adverse effects of disasters. With this in mind, this article presents a review of recent studies that have underscored the criticality of workforce sectors in formulating synergistic preparedness and recovery policies for interdependent infrastructure and regional economic systems.     

Toward Disaster‐Resilient Cities: Characterizing Resilience of Infrastructure Systems with Expert Judgments

Resilient infrastructure systems are essential for cities to withstand and rapidly recover from natural and human‐induced disasters, yet electric power, transportation, and other infrastructures are highly vulnerable and interdependent. New approaches for characterizing the resilience of sets of infrastructure systems are urgently needed, at community and regional scales. This article develops a practical approach for analysts to characterize a community's infrastructure vulnerability and resilience in disasters. It addresses key challenges of incomplete incentives, partial information, and few opportunities for learning. The approach is demonstrated for Metro Vancouver, Canada, in the context of earthquake and flood risk. The methodological approach is practical and focuses on potential disruptions to infrastructure services. In spirit, it resembles probability elicitation with multiple experts; however, it elicits disruption and recovery over time, rather than uncertainties regarding system function at a given point in time. It develops information on regional infrastructure risk and engages infrastructure organizations in the process. Information sharing, iteration, and learning among the participants provide the basis for more informed estimates of infrastructure system robustness and recovery that incorporate the potential for interdependent failures after an extreme event. Results demonstrate the vital importance of cross‐sectoral communication to develop shared understanding of regional infrastructure disruption in disasters. For Vancouver, specific results indicate that in a hypothetical M7.3 earthquake, virtually all infrastructures would suffer severe disruption of service in the immediate aftermath, with many experiencing moderate disruption two weeks afterward. Electric power, land transportation, and telecommunications are identified as core infrastructure sectors.     

需求与回收确定下闭环供应链的竞争与链内协调研究

针对两条分别由单生产商和单零售商组成、零售商负责废品回收的闭环供应链,运用博弈论和均衡理论建立了对应两条闭环供应链均为分散式供应链、均为集中式供应链、一条为分散式供应链一条为集中式供应链的带均衡约束的均衡（EPEC）模型、纳什（Nash）均衡模型和带均衡约束的优化（MPEC）模型,并进行了模型求解。对比三种模式表明：集中式控制是供应链竞争下的占优策略。随后,给出了两条供应链竞争下可协调分散式供应链达到集中式供应链效果的批发价加回收补贴契约。最后的数值算例和敏感性分析表明了模型的合理性、协调契约的有效性、以及相关参数的影响。     

A coordination mechanism with fair cost allocation for divergent multi-echelon inventory systems

In this paper we study the coordination of inventory control in divergent multi-echelon inventory systems under periodic review and decentralized control. Under decentralized control the installations decide upon replenishment policies that minimize their individual inventory costs. In general these policies do not coincide with the optimal policies of the system under centralized control. Hence, the total cost under decentralized control is larger than under centralized control. We present a simple coordination mechanism that removes this cost inefficiency. The upstream installations increases its base stock level while the downstream installations compensate their supplier for increased costs and provide it with additional side payments. We show that this mechanism coordinates the system; the global optimal policy of the system is the unique Nash equilibrium of the corresponding strategic game. Furthermore, the mechanism results in a fair allocation of the costs; all installations enjoy cost savings.     

Inherent Costs and Interdependent Impacts of Infrastructure Network Resilience

Recent studies in system resilience have proposed metrics to understand the ability of systems to recover from a disruptive event, often offering a qualitative treatment of resilience. This work provides a quantitative treatment of resilience and focuses specifically on measuring resilience in infrastructure networks. Inherent cost metrics are introduced: loss of service cost and total network restoration cost. Further, “costs” of network resilience are often shared across multiple infrastructures and industries that rely upon those networks, particularly when such networks become inoperable in the face of disruptive events. As such, this work integrates the quantitative resilience approach with a model describing the regional, multi‐industry impacts of a disruptive event to measure the interdependent impacts of network resilience. The approaches discussed in this article are deployed in a case study of an inland waterway transportation network, the Mississippi River Navigation System.     

Resilience of Cyber Systems with Over‐ and Underregulation

Recent cyber attacks provide evidence of increased threats to our critical systems and infrastructure. A common reaction to a new threat is to harden the system by adding new rules and regulations. As federal and state governments request new procedures to follow, each of their organizations implements their own cyber defense strategies. This unintentionally increases time and effort that employees spend on training and policy implementation and decreases the time and latitude to perform critical job functions, thus raising overall levels of stress. People's performance under stress, coupled with an overabundance of information, results in even more vulnerabilities for adversaries to exploit. In this article, we embed a simple regulatory model that accounts for cybersecurity human factors and an organization's regulatory environment in a model of a corporate cyber network under attack. The resulting model demonstrates the effect of under‐ and overregulation on an organization's resilience with respect to insider threats. Currently, there is a tendency to use ad‐hoc approaches to account for human factors rather than to incorporate them into cyber resilience modeling. It is clear that using a systematic approach utilizing behavioral science, which already exists in cyber resilience assessment, would provide a more holistic view for decisionmakers.     

基于线性分段恢复函数的基础设施韧性分析模型——以C县电力系统网络为例

针对近年来一系列突发事件冲击和破坏着城市关键基础设施系统的正常运行,并造成了较为严重的社会后果的现实问题,提出了如何保护关键基础设施系统的研究问题,以使基础设施系统能够对灾害情景做出迅速的响应,并迅速地处理以恢复到常态。本研究基于三种典型的恢复函数提出了线性分段恢复函数,构建了关键基础设施系统韧性分析模型,并用蒙特卡洛模拟的方法应用到C县的电力系统网络加以验证,得到了该韧性分析模型不仅可以帮助决策者在灾害情境下权衡预算成本和韧性的关系,也可以识别关键基础设施系统网络中需要保护的关键节点,从而实现对关键基础设施系统的针对性保护的结论。本研究构建的韧性分析模型有为灾害情境下对电力系统采取针对性保护的现实价值,和开拓了对基础设施系统进行保护研究的分析模型的理论价值。     

Probabilistic Multiple Hazard Resilience Model of an Interdependent Infrastructure System

Multiple hazard resilience is of significant practical value because most regions of the world are subject to multiple natural and technological hazards. An analysis and assessment approach for multiple hazard spatiotemporal resilience of interdependent infrastructure systems is developed using network theory and a numerical analysis. First, we define multiple hazard resilience and present a quantitative probabilistic metric based on the expansion of a single hazard deterministic resilience model. Second, we define a multiple hazard relationship analysis model with a focus on the impact of hazards on an infrastructure. Subsequently, a relationship matrix is constructed with temporal and spatial dimensions. Further, a general method for the evaluation of direct impacts on an individual infrastructure under multiple hazards is proposed. Third, we present an analysis of indirect multiple hazard impacts on interdependent infrastructures and a joint restoration model of an infrastructure system. Finally, a simplified two‐layer interdependent infrastructure network is used as a case study for illustrating the proposed methodology. The results show that temporal and spatial relationships of multiple hazards significantly influence system resilience. Moreover, the interdependence among infrastructures further magnifies the impact on resilience value. The main contribution of the article is a new multiple hazard resilience evaluation approach that is capable of integrating the impacts of multiple hazard interactions, interdependence of network components (layers), and restoration strategy.     

Impact of Retailers with Knowledge of Supplier's Inventory on Supply Chain Performance

We model a supply chain consisting of a supplier and multiple retailers facing deterministic demand. We denote some retailers as strategic in the sense that given the supplier inventory information, they will implement the optimal stocking policy by incorporating such information. On the other hand, some retailers are denoted as naïve in the sense that they ignore supply information and resort to a simplistic ordering policy. Naïve retailers learn the optimal policy over time and adjust their orders accordingly. We study the dynamics of this game and investigate the impact of such strategic and naïve retailers on the cost, ordering pattern and stocking policies of all parties. We analyze the supply chain under two scenarios: the centralized supply chain where the objective is to minimize the total supply chain cost, and the decentralized supply chain where each self‐interested player minimizes its own cost in a Stackelberg game setting. We fully characterize the optimal policies under both centralized and decentralized scenarios and show that, surprisingly, the supply chain might be better off by virtue of naïve retailers. The result is driven by the fact that strategic and naïve players’ decisions shift the positioning of inventory in the supply chain with its final impact being determined by the relative costs of different retailer‐types. Our results also offer managerial insights into how access to supply information can improve supply chain performance.     

Sequential Hazards Resilience of Interdependent Infrastructure System: A Case Study of Greater Toronto Area Energy Infrastructure System

Coupled infrastructure systems and complicated multihazards result in a high level of complexity and make it difficult to assess and improve the infrastructure system resilience. With a case study of the Greater Toronto Area energy system (including electric, gas, and oil transmission networks), an approach to analysis of multihazard resilience of an interdependent infrastructure system is presented in the article. Integrating network theory, spatial and numerical analysis methods, the new approach deals with the complicated multihazard relations and complex infrastructure interdependencies as spatiotemporal impacts on infrastructure systems in order to assess the dynamic system resilience. The results confirm that the effects of sequential hazards on resilience of infrastructure (network) are more complicated than the sum of single hazards. The resilience depends on the magnitude of the hazards, their spatiotemporal relationship and dynamic combined impacts, and infrastructure interdependencies. The article presents a comparison between physical and functional resilience of an electric transmission network, and finds functional resilience is always higher than physical resilience. The multiple hazards resilience evaluation approach is applicable to any type of infrastructure and hazard and it can contribute to the improvement of infrastructure planning, design, and maintenance decision making.     

Quick response and supply chain structure with strategic consumers

This work explores the impact of quick response on supply chain performance for various supply chain structures with strategic customer behavior. By investigating pricing and inventory decisions in decentralized supply chains under revenue-sharing contracts and in centralized supply chains, we study the performance of four various systems and compare the value of quick response in different supply chain structures. The results show that if the extra cost of quick response is relatively low, the value of quick response would be greater in centralized systems than in decentralized systems. On the other hand, if the extra cost is high, decentralized supply chains reap more incremental profits from adopting quick response. We also find that revenue-sharing contracts enable a decentralized supply chain to outperform a centralized supply chain, but only allow limited flexibility of allocating total profits between a manufacturer and a retailer.     

A Game-Theoretic Approach to Quantity Discount Problems*

The traditional quantity discount problem is analyzed from the perspective of game theory, including both noncooperative and cooperative models. For the noncooperative case, the Stackelberg equilibrium is derived. For the cooperative case, the Pareto Optimality criteria are used to find a group of optimal strategies. Both scenarios are illustrated through an example which quantifies the benefits resulting from cooperation between the buyer and the seller for game-theoretic solutions using geometric programming.     

Who's Who in Networks. Wanted: The Key Player

Finite population noncooperative games with linear‐quadratic utilities, where each player decides how much action she exerts, can be interpreted as a network game with local payoff complementarities, together with a globally uniform payoff substitutability component and an own‐concavity effect. For these games, the Nash equilibrium action of each player is proportional to her Bonacich centrality in the network of local complementarities, thus establishing a bridge with the sociology literature on social networks. This Bonacich–Nash linkage implies that aggregate equilibrium increases with network size and density. We then analyze a policy that consists of targeting the key player, that is, the player who, once removed, leads to the optimal change in aggregate activity. We provide a geometric characterization of the key player identified with an intercentrality measure, which takes into account both a player's centrality and her contribution to the centrality of the others.     

Who Should Pay for Interdependent Risk? Policy Implications for Security Interdependence Among Airports

We study interdependent risks in security, and shed light on the economic and policy implications of increasing security interdependence in presence of reactive attackers. We investigate the impact of potential public policy arrangements on the security of a group of interdependent organizations, namely, airports. Focusing on security expenditures and costs to society, as assessed by a social planner, to individual airports and to attackers, we first develop a game-theoretic framework, and derive explicit Nash equilibrium and socially optimal solutions in the airports network. We then conduct numerical experiments mirroring real-world cyber scenarios, to assess how a change in interdependence impact the airports' security expenditures, the overall expected costs to society, and the fairness of security financing. Our study provides insights on the economic and policy implications for the United States, Europe, and Asia.     

考虑消费者低碳偏好的供应链减排微分博弈模型研究

针对由一个供应商和一个制造商构成的两级供应链,考虑消费者的低碳偏好和碳交易政策,建立分散决策和集中决策两种情形下的微分博弈模型解决供应链动态优化问题,比较两种情形下的最优均衡反馈策略、减排量的最优轨迹及最优利润,提出减排策略。通过数值仿真,进一步验证了命题的有效性;通过对消费者低碳偏好及碳交易价格进行灵敏度分析发现：随着低碳偏好的增加,供应商和制造商的减排量和供应链系统的利润均增加,并且政府在规划期内应及时调整碳交易政策,达到激励企业减排的效果。     

THE EFFECTS OF TWO NORMATIVE STRUCTURAL INTERVENTIONS ON ESTABLISHED AND AD HOC GROUPS: IMPLICATIONS FOR IMPROVING DECISION MAKING EFFECTIVENESS1

This paper focuses on a direct comparison of consensual, nominal, and conventional decision making techniques in established and ad hoc groups. The impact of the structural interventions on group decision quality and group attitudes is examined, and the appropriateness of the techniques in various situations is discussed.     

Strategic Preparedness for Recovery from Catastrophic Risks to Communities and Infrastructure Systems of Systems

Natural and human‐induced disasters affect organizations in myriad ways because of the inherent interconnectedness and interdependencies among human, cyber, and physical infrastructures, but more importantly, because organizations depend on the effectiveness of people and on the leadership they provide to the organizations they serve and represent. These human–organizational–cyber–physical infrastructure entities are termed systems of systems. Given the multiple perspectives that characterize them, they cannot be modeled effectively with a single model. The focus of this article is: (i) the centrality of the states of a system in modeling; (ii) the efficacious role of shared states in modeling systems of systems, in identification, and in the meta‐modeling of systems of systems; and (iii) the contributions of the above to strategic preparedness, response to, and recovery from catastrophic risk to such systems. Strategic preparedness connotes a decision‐making process and its associated actions. These must be: implemented in advance of a natural or human‐induced disaster, aimed at reducing consequences (e.g., recovery time, community suffering, and cost), and/or controlling their likelihood to a level considered acceptable (through the decisionmakers’ implicit and explicit acceptance of various risks and tradeoffs). The inoperability input‐output model (IIM), which is grounded on Leontief's input/output model, has enabled the modeling of interdependent subsystems. Two separate modeling structures are introduced. These are: phantom system models (PSM), where shared states constitute the essence of modeling coupled systems; and the IIM, where interdependencies among sectors of the economy are manifested by the Leontief matrix of technological coefficients. This article demonstrates the potential contributions of these two models to each other, and thus to more informative modeling of systems of systems schema. The contributions of shared states to this modeling and to systems identification are presented with case studies.