Facility Location: A Robust Optimization Approach

In this research, we apply robust optimization (RO) to the problem of locating facilities in a network facing uncertain demand over multiple periods. We consider a multi‐period fixed‐charge network location problem for which we find (1) the number of facilities, their location and capacities, (2) the production in each period, and (3) allocation of demand to facilities. Using the RO approach we formulate the problem to include alternate levels of uncertainty over the periods. We consider two models of demand uncertainty: demand within a bounded and symmetric multi‐dimensional box, and demand within a multi‐dimensional ellipsoid. We evaluate the potential benefits of applying the RO approach in our setting using an extensive numerical study. We show that the alternate models of uncertainty lead to very different solution network topologies, with the model with box uncertainty set opening fewer, larger facilities. Through sample path testing, we show that both the box and ellipsoidal uncertainty cases can provide small but significant improvements over the solution to the problem when demand is deterministic and set at its nominal value. For changes in several environmental parameters, we explore the effects on the solution performance.     

质量预防水平不确定下供应链质量控制鲁棒设计模型

研究了由一个制造商和一个购买商构成的多产品、多阶段供应链质量控制鲁棒运作问题.将制造商、购买商质量收益最大和制造商交付量等于购买商订货量三个运作目标整合成目标函数,以制造商和购买商的质量运作能力限制为基本约束条件,采用基于区间分析法描述制造商质量预防水平不确定性,建立目标规划模型,并进行优化求解.模型能够实现供应链协调运作和制造商、购买商的利润目标,并且在制造商质量预防水平不确定的情况下具有鲁棒性.数值算例的结果表明,制造商质量预防水平在一定范围内波动不改变供应链的质量控制运作策略,仅对其运作性能产生一定影响,即所提出的质量控制模型是鲁棒的.     

Managing Disruption Risks in Supply Chains

There are two broad categories of risk affecting supply chain design and management: (1) risks arising from the problems of coordinating supply and demand, and (2) risks arising from disruptions to normal activities. This paper is concerned with the second category of risks, which may arise from natural disasters, from strikes and economic disruptions, and from acts of purposeful agents, including terrorists. The paper provides a conceptual framework that reflects the joint activities of risk assessment and risk mitigation that are fundamental to disruption risk management in supply chains. We then consider empirical results from a rich data set covering the period 1995–2000 on accidents in the U. S. Chemical Industry. Based on these results and other literature, we discuss the implications for the design of management systems intended to cope with supply chain disruption risks.     

基于EVA与经营风险偏好的供应链鲁棒优化模型

在由一个制造商和多个外部供应商构成的多产品、多阶段供应链中,将经济增加值（EVA）作为体现价值创造的绩效指标,并考虑决策者的经营风险偏好,采用已知概率的离散情景描述资本成本与需求的波动情况,利用鲁棒随机规划方法,建立了以价值创造为目标的供应链鲁棒优化模型。应用分析的结果表明,模型能够将供应链的绩效与风险管理结合起来,减少资本成本与需求不确定对目标值的影响,得到具有鲁棒性的最优解,而且越是风险厌恶型的决策者越会为了保持较低的经营风险而放弃较大的EVA值。同时,决策者可选择不同的权重系数侧重于解鲁棒或模型鲁棒,保证供应链运作的鲁棒性,实现价值创造的目标。     

Cyber Risk Management for Critical Infrastructure: A Risk Analysis Model and Three Case Studies

Managing cyber security in an organization involves allocating the protection budget across a spectrum of possible options. This requires assessing the benefits and the costs of these options. The risk analyses presented here are statistical when relevant data are available, and system‐based for high‐consequence events that have not happened yet. This article presents, first, a general probabilistic risk analysis framework for cyber security in an organization to be specified. It then describes three examples of forward‐looking analyses motivated by recent cyber attacks. The first one is the statistical analysis of an actual database, extended at the upper end of the loss distribution by a Bayesian analysis of possible, high‐consequence attack scenarios that may happen in the future. The second is a systems analysis of cyber risks for a smart, connected electric grid, showing that there is an optimal level of connectivity. The third is an analysis of sequential decisions to upgrade the software of an existing cyber security system or to adopt a new one to stay ahead of adversaries trying to find their way in. The results are distributions of losses to cyber attacks, with and without some considered countermeasures in support of risk management decisions based both on past data and anticipated incidents.     

Evacuation Risks: A Tentative Approach for Quantification

This study tries to assess the risk of deaths and injuries from motor vehicle accidents associated with an evacuation of population groups in case of nuclear plant accidents. The risk per person–km is evaluated using: (a) data from previous evacuation: information from Soufriere evacuation (Guadeloupe Island 1976) and Mississauga (1979), added to Hans and Sell's data: no road accident occurred for a sample of 1,500,000 persons; (b) national recording system for motor vehicle accident: the rates of 2.2 10 ^-8 deaths per person–km and 32 10^-8 injuries per person–km is calculated as an average. These last rates in France overestimate the number of casualties. A reasonable hypothesis is to assume that the probability of road accident occurrence follows a Poisson distribution, as these events are independent and unfrequent, as no accident was observed in a sample of 1,500,000 persons the probability is between 0 and an upper value of 0.24 10^-8 deaths per person-km and 3.29 10^-8 injuries per person–km. The average and maximum population involved within different radii around French and U.S. Nuclear power sites are taken as a sample size in order to study the total risk of deaths and injuries in the hypothesis of an evacuation being necessary to protect the populations.     

Bounds of Relative Regret Limit in p‐Robust Supply Chain Network Design

This research studies the p‐robust supply chain network design with uncertain demand and cost scenarios. The optimal design integrates the supplier selection together with the facility location and capacity problem. We provide a new framework to obtain the relative regret limit, which is critical in the robust supply chain design but is assumed to be a known value in the existing literature. We obtain lower and upper bounds for relative regret limit and obtain a sequence of optimal solutions for series relative regret limits between the upper and lower bounds. An algorithm for p‐robust supply chain network design is provided. A series of numerical examples are designed to find the properties of the bottleneck scenarios. A scenario with low probability and a low optimal objective function value for the scenario has a greater chance of being a bottleneck. To focus only on the influence from the relative regret, we also introduce three separate new objective functions in p‐robust design. The proposed new theories and approaches provide a sequence of options for decision makers to reduce the marketing risks effectively in supply chain network design.     

Robustness of Optimal Investment Decisions in Mixed Insurance/Investment Cyber Risk Management

An integrated risk management strategy, combining insurance and security investments, where the latter contribute to reduce the insurance premium, is investigated to assess whether it can lead to reduced overall security expenses. The optimal investment for this mixed strategy is derived under three insurance policies, covering, respectively, all the losses (total coverage), just those below the limit of maximum liability (partial coverage), and those above a threshold but below the maximum liability (partial coverage with deductibles). Under certain conditions (e.g., low potential loss, or either very low or very high vulnerability), the mixed strategy reverts however to insurance alone, because investments do not provide an additional benefit. When the mixed strategy is the best choice, the dominant component in the overall security expenses is the insurance premium in most cases. Optimal investment decisions require an accurate estimate of the vulnerability, whereas larger estimation errors may be tolerated for the investment-effectiveness coefficient.     

供需不确定条件下基于CVaR的零售商库存鲁棒优化模型

在经典报童模型下考虑供应和需求不确定性,研究了具有风险厌恶的零售商库存优化问题。采用条件风险值(CVaR)对库存绩效进行度量,构建了基于CVaR的零售商库存运作模型;在此基础上,考虑上游供应商供货能力和下游市场需求不确定性,并采用一系列未知概率的离散情景进行描述,给出了供需不确定条件下基于CVaR的零售商库存鲁棒优化模型。进一步,采用区间不确定集对未知情景概率进行建模,给出了基于最大最小准则的鲁棒对应模型。针对同时考虑供需不确定性导致的模型非凸性,采用标准对偶理论将其转化为易于求解的数学规划问题。最后,通过数值计算分析了不同风险厌恶程度和不确定性程度对零售商库存决策以及库存绩效的影响。结果表明,供需不确定性的存在虽然会导致零售商库存绩效损失,但损失值较小。特别地,依据文中模型得到的鲁棒库存策略在多数情况下能够保证零售商获得更优的库存绩效。此外,不确定性和风险厌恶程度的增加虽然会影响零售商库存决策和运作绩效,但在同等风险厌恶态度下,随着不确定性程度的增加,基于文中方法得到的鲁棒库存策略仍能确保零售商获得理想的库存绩效,表明文中所建模型在应对供需不确定性方面具有良好的鲁棒性。     

Financial Instruments for Mitigation of Flood Risks: The Case of Florence

This article analyzes the mechanisms and effects of innovative financial instruments that a central public administration (CPA) may adopt to minimize the flood risk in particularly exposed regions. The pattern we suggest assumes that in risky areas the CPA can issue two financial instruments, called project options and CAT‐bonds, producing a dynamic interaction among three types of agents: the CPA itself, the local public administrations, and private investors. We explore the possible scenarios of such interaction and the conditions under which the CPA's goal of maximal risk reduction is attained. This pattern is proposed for flood risk mitigation in the city of Florence, where the model dynamics are tested assuming parameters obtained from engineering studies.     

基于鲁棒优化模型的项目调度策略遗传算法

针对任务工期不确定的资源受限项目调度问题,提出了求解该问题的鲁棒优化数学模型。在随机规划基础上,针对该鲁棒优化模型设计了遗传算法。算法通过多种任务优先规则生成初始种群以保证种群多样性。应用该遗传算法对项目实例进行了求解,分析表明所求得的项目调度策略能够有效应对任务工期不确定性导致的随机差异,具有较强的鲁棒性。参数分析表明决策者可以通过调节模型权重系数有效平衡解的可行性与最优性,有助于决策者根据风险偏好进行选择。     

一种有限信息共享的全局寻优供应链双边协同计划方法

针对有限信息共享条件下,供应链协同计划难以实现计划调整的收敛性和达到全局最优的问题,提出一种具有多点搜索舜口概率搜索特征的协同计划方法.将协商中交流的备选计划及其所产生的成本变化信息融入到计划调整算法中.以遗传算法的选择、交叉和变异过程为调整机制,将算法的迭代过程与计划协商过程结合在一起.在确定上下游企业能力约束多产品批量计划模型和最小累积需求求解方法及其模型的基础上,分析了协同计划过程中的编码、适应度函数、初始计划组生成和选择、交叉、变异算法等主要要素,并给出协同计划流程.通过仿真实验验证了该方法的有效性和相对的优越性.     

不确定需求下考虑大数据投资决策的供应链鲁棒优化及协调模型

针对由数据公司、制造商和零售商组成的三级供应链系统,在仅知需求均值和方差信息下,建立了集中和分散两种决策情况下的供应链鲁棒优化模型。集中决策下,全体供应链成员共同决定产品零售价和产品生产数量;分散决策下,数据公司作为主方,决定需求信息零售价,制造商和零售商作为从方,分别决定产品批发价和产品订货数量。针对两种决策下的供应链鲁棒优化模型,给出了相应的最优决策,分析了大数据投资成本、消费者异质性需求满足程度等系统参数对供应链决策的影响。进一步,设计了能实现三级供应链完美协调的利润共享契约。最后,通过数值算例验证了所建模型和契约协调的有效性。研究表明,在集中和分散决策下,大数据投资成本只有在满足一定条件下,投资大数据才有利于供应链成员及系统利润的改善。特别地,与无协调时的情况相比,虽然协调机制下相关系统参数对供应链成员决策及利润绩效的作用机制存在差异,但文中提出的利润共享契约在一定条件下能够显著改进供应链成员利润且实现供应链完美协调。     

基于条件风险值理论的供应链优化与协调模型研究

本文将近年来发展起来的金融风险控制工具--条件风险值,引入具有风险规避特性的供应链优化与协调问题的研究.建立了随机需求下由具有不同风险规避特性的单个供应商与单个零售商组成的两级供应链的条件风险值模型和基于条件风险值的最优订购量模型及协调供应链的收入共享契约模型,并对模型进行了分析,揭示了供应商和零售商的风险规避程度对最优订购量、批发价格及供应链协调的影响.最后通过一个算例对模型进行了仿真,仿真结果进一步验证了本文的研究结论.     

有限需求信息下基于回购契约的供应链鲁棒协调策略

研究了仅知需求均值和区间信息条件下,基于最小最大后悔值准则的供应链回购契约协调问题。针对未知需求具体分布形式的两级供应链系统,在回购契约框架下,建立了以鲁棒决策和最优决策下的供应链及其成员绩效之差为目标函数的供应链协调模型。在仅知需求区间和均值信息条件下,采用鲁棒优化方法求解了最小最大后悔值准则下的集成供应链鲁棒订货策略和分散供应链鲁棒契约协调策略及其绩效偏差。分析了不同服务水平和契约参数条件下,由于信息缺失而未能实现最优运作的供应链及其成员绩效损失情况。最后,进行了数值计算,验证了通过鲁棒优化方法得到的供应链回购契约协调策略的鲁棒性和有效性。结果表明,基于回购契约的供应链鲁棒协调策略能够有效抑制需求不确定性对系统及其成员运作绩效的影响,同仅知需求区间信息相比,额外获得需求均值信息能够有效改进供应链运作绩效。     

The Complementary Roles of Mitigation and Insurance in Managing Catastrophic Risks

This paper examines the impact that insurance coupled with specific risk mitigation measures (RMMs) could have on reducing losses from hurricanes and earthquakes as well as improving the solvency position of insurers who provide coverage against these hazards. We first explore why relatively few individuals adopt cost-effective RMMs by reporting on the results of empirical studies and controlled laboratory studies. We then investigate the impact that an RMM has on both the expected losses and those from a worst case scenario in two model cities—Oakland (an earthquake-prone area) and Miami/Dade County (a hurricane-prone area) which were constructed respectively with the assistance of two modeling firms. The paper then explores three programs for forging a meaningful public-private sector partnership: well-enforced building codes, insurance premium reductions linked with long-term loans, and lower deductibles on insurance policies tied to mitigation. We conclude by briefly examining four issues for future research on linking mitigation with insurance.     

Quality Risk Ratings in Global Supply Chains

Extended enterprises face many challenges in managing the product quality of their suppliers. Consequently characterizing the quality risk posed by value‐chain partners has become increasingly important. There have been several recent efforts to develop frameworks for rating the quality risk posed by suppliers. We develop an analytical model to examine the impact of such quality ratings on suppliers, manufacturers, and social welfare. While it might seem that quality ratings would benefit high‐quality suppliers and hurt low‐quality suppliers, we show that this is not always the case. We find that such quality ratings can hurt both types of suppliers or benefit both, depending on the market conditions. We also find that quality ratings do not always benefit the most demanding manufacturers who desire high‐quality suppliers. Finally, we find that social welfare is not always improved by risk ratings. These results suggest that public policy initiatives addressing risk ratings must be carefully considered.     

基于产品寿命次数的闭环供应链生产优化问题研究

本文研究了单一厂商制造/再制造集成系统的多期生产优化问题.首先,基于闭环供应链的全生命周期思想,通过引入产品寿命次数的概念构造了不超过产品寿命次数而能够进行再制造的回收产品与新制造产品之间的数量关系;接着,验证了将可再制造产品全部用于再制造时能够实现利润最大化的目标;然后,给出了几个有关解的性质;最后,通过算例对本文模型的性质和规律作进一步分析.     

信用评估中的鲁棒赋权自适应Lp最小二乘支持向量机方法

消费者信用评估是金融风险管理和信用产业竞争的一个重要方面.信用评估数据中常带有噪声点,并且其类别是不均衡的.最小二乘支持向量机是一个被广泛应用的分类模型,其模型简单,求解速度快,但鲁棒性差.本文提出了一个鲁棒赋权自适应L_p最小二乘支持向量机模型,能够适应信用评估样本数据库类别不均衡的特点,可以有效处理信用评估数据中带有噪声点的问题.在仿真数据和三个信用数据库上的实证分析表明,本文所提出的模型具有较好的鲁棒性和分类能力.     

Traceability and Risk Analysis Strategies for Addressing Counterfeit Electronics in Supply Chains for Complex Systems

Within the microelectronics industry, there is a growing concern regarding the introduction of counterfeit electronic parts into the supply chain. Even though this problem is widespread, there have been limited attempts to implement risk‐based approaches for testing and supply chain management. Supply chain risk management tends to focus on the highly visible disruptions of the supply chain instead of the covert entrance of counterfeits; thus counterfeit risk is difficult to mitigate. This article provides an overview of the complexities of the electronics supply chain, and highlights some gaps in risk assessment practices. In particular, this article calls for enhanced traceability capabilities to track and trace parts at risk through various stages of the supply chain. Placing the focus on risk‐informed decision making through the following strategies is needed, including prioritization of high‐risk parts, moving beyond certificates of conformance, incentivizing best supply chain management practices, adoption of industry standards, and design and management for supply chain resilience.