灾后不确定需求下应急医疗移动医院鲁棒选址问题研究

我国灾害医学救援主要采用"现场救治"模式，应急医疗移动医院的选址是否合理直接影响救援效率，但各受灾点伤员数量的不确定性增加了决策的困难。本文引入多面体不确定集合刻画伤员数量的不确定性，同时考虑伤员分类及移动医院分型，构建一个以伤员总生存概率最大化为目标的鲁棒选址模型。利用鲁棒优化理论，将模型转化为等价的混合整数规划问题，通过GAMS软件编程并调用CPLEX求解器求解。最后，以四川芦山地震应急医疗救援为例，验证模型和求解方法的可行性和鲁棒性。结果表明，扰动比例和不确定水平对移动医院的选址和伤员的分配方案有显著影响，决策者可根据自己对不确定性风险的偏好程度选择最佳的扰动比例和不确定水平组合，以获得最优的选址分配方案。     

具有遗憾值约束的鲁棒供应链网络设计模型研究

考虑不确定性环境,研究战略层次的供应链网络鲁棒设计问题,目标是设计参数发生摄动时,供应链性能能够保持稳健性。基于鲁棒解的定义,建立从上游供应商选择到下游设施选址-需求分配的供应链网络设计鲁棒优化模型;提出确定遗憾值限定系数上限和下限的方法,允许决策者调节鲁棒水平,选择多种供应链网络结构;通过模型分解与协调,设计了供应链节点配置的禁忌搜索算法。算例的计算结果表明了禁忌搜索算法具有良好的收敛特性,以及在处理大规模问题上的优越性;同时也反映了利用鲁棒优化模型进行供应链网络设计,可以有效规避投资风险。     

碳交易政策下多式联运路径选择问题的鲁棒优化研究

针对碳交易政策下的多式联运路径选择问题,考虑运输时间和单位运费率不确定且其概率分布未知的情况,引入鲁棒优化建模方法对其进行研究。首先利用box不确定集合刻画分布未知的运输时间和运费率,然后在碳交易政策下确定模型的基础上,构建鲁棒性可调节的多式联运路径选择模型,并通过对偶转化得到相对易求解的鲁棒等价模型。实例分析表明,鲁棒模型能较好地处理参数概率分布未知的多式联运路径选择问题,方便决策者根据偏好调整不确定预算水平进行决策。运输时间和单位运费率的不确定性都会影响多式联运路径决策,但是作用机理有所不同。将上述碳交易政策下的模型拓展到其他低碳政策,结果表明多种低碳政策的组合能更好实现多式联运减排。     

不确定需求下考虑供应商参与机制的应急资源配置鲁棒优化研究

突发事件应急资源优化配置是突发事件发生后救援工作有效开展的前提和基本保障。本文在调研国内外相关研究的基础上，以应对地震灾难为背景研究考虑供应商参与机制的应急资源保障策略，在灾前选择供应商建立政府与供应商的合作机制完成政府储备仓库的选址与资源配置，突发事件发生后依托政府储备仓库和供应商生产能力共同满足应急救援对应急资源的分时段需求，以期协调供应商与政府储备、灾前实物采购与灾后生产能力采购的比例，在保障救援效率的同时降低应急资源保障体系的成本。同时由于地震灾难发生具有需求不确定性的特点，本文引入L1范数描述需求的不确定性，建立了备灾与灾害救援两阶段决策的鲁棒优化模型，并给出了鲁棒模型对应问题的转化方法。最后通过算例仿真验证了模型和对应问题转换方法的有效性，为地震的应对提供理论指导和决策支持。     

基于鲁棒优化的人力资源规划模型研究

本文分析了企业人力资源流动问题的特点,考虑到因企业内外部环境带来的不确定性因素,建立了基于鲁棒优化的人力资源规划模型,从而在人员流动确定性模型的基础上,分析了当其中某些因素产生不确定性的波动时,人员流动如何变化,以求更加贴近实际问题,使研究结果更具有实际参考价值.     

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。     

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。     

军队技术人才培养规划的鲁棒优化研究

本文针对军队发展带来技术人才需求的动态变化,通过将技术人才各方面素质需求的不确定性离散成三种不同情景,采用鲁棒优化方法构建了军队人才培养的鲁棒优化模型,以军队信息化建设人才需求为背景,以某部人才队伍为研究对象进行了实证求解,并比较了基于单一情景的规划结果与鲁棒优化模型的结果。研究结果表明,鲁棒优化模型对于军队人才培养规划制定具有更好的稳定性和可行性。     

基于信息更新的两阶段鲁棒-随机优化调配模型研究

在突发事件的应对中,应急决策过程的灾情信息具有动态性、不确定性等特征,从而使得整个应急救援过程中的决策都必须随信息更新而不断调整,本文在调研国内外相关研究的基础上,以地震为背景提出了基于信息更新的资源调配决策问题。文章结合灾情信息更新的特征,给出了应急救援响应的阶段划分;以此为基础建立了两阶段鲁棒-随机优化模型,通过虚拟储备库点及虚拟临时分发中心点的设计,实现了第一阶段调配结果对第二阶段调配决策的后效性调整决策;根据鲁棒优化及随机优化的特点,设计了相应的原始-对偶及L-Shaped Method算法对模型进行求解;最后,通过CPLEX软件编程求解,并进行情景生成下的算例分析,与其他方法比较分析,证明了文章所设计的模型在灾情信息更新下的优势。     

不确定环境下两阶段应急供应链网络建模与优化求解

为制订有效的应急供应链网络规划方案,提升应急组织救援效率、实现资源物质合理配置,考虑供应和需求的不确定性,采用多运输方式联合的配送模式,以最小化网络响应时间、成本和碳排为优化目标,构建两阶段应急供应链混合整数规划模型,同时,基于鲁棒优化理论构建可调节鲁棒优化模型,增强网络应对不确定因素的能力,通过线性对偶理论对含不确定参数的约束进行转化;为提升模型的求解效果,提出一种优化布谷鸟搜索（optimize cuckoo search,OCS）算法,引入基准实例,以验证OCS算法求解多目标函数的优越性和适用性;最后,利用武汉新冠疫期期间应急物资配送数据,研究带有不确定参数的应急供应链网络决策问题,并通过敏感性分析证明鲁棒控制系数对不确定扰动的有效抑制作用。     

An adjustable robust optimization model for the resource-constrained project scheduling problem with uncertain activity durations

This paper addresses the resource-constrained project scheduling problem with uncertain activity durations. An adaptive robust optimization model is proposed to derive the resource allocation decisions that minimize the worst-case makespan, under general polyhedral uncertainty sets. The properties of the model are analyzed, assuming that the activity durations are subject to interval uncertainty where the level of robustness is controlled by a protection factor related to the risk aversion of the decision maker. A general decomposition approach is proposed to solve the robust counterpart of the resource-constrained project scheduling problem, further tailored to address the uncertainty set with the protection factor. An extensive computational study is presented on benchmark instances adapted from the PSPLIB.     

Application of the Fuzzy Weighted Average in Strategic Portfolio Management*

We propose a systematic approach that incorporates fuzzy set theory in conjunction with portfolio matrices to assist managers in reaching a better understanding of the overall competitiveness of their business portfolios. Integer linear programming is also accommodated in the proposed integrated approach to help select strategic plans by using the results derived from the previous portfolio analysis and other financial data. The proposed integrated approach is designed from a strategy‐oriented perspective for portfolio management at the corporate level. It has the advantage of dealing with the uncertainty problem of decision makers in doing evaluation, providing a technique that presents the diversity of confidence and optimism levels of decision makers. Furthermore, integer linear programming is used because it offers an effective quantitative method for managers to allocate constrained resources optimally among proposed strategies. An illustration from a real‐world situation demonstrates the integrated approach. Although a particular portfolio matrix model has been adopted in our research, the procedure proposed here can be modified to incorporate other portfolio matrices.     

Staffing and scheduling flexible call centers by two-stage robust optimization

We study the shift scheduling problem in a multi-shift, flexible call center. Differently from previous approaches, the staffing levels ensuring the desired quality of service are considered uncertain, leading to a two-stage robust integer program with right-hand-side uncertainty. We show that, in our setting, modeling the correlation of the demands in consecutive time slots is easier than in other staffing approaches. The complexity issues of a Benders type reformulation are investigated and a branch-and-cut algorithm is devised. The approach can efficiently solve real-world problems from an Italian call center and effectively support managers decisions. In fact, we show that robust shifts have very similar costs to those evaluated by the traditional (deterministic) method while ensuring a higher level of protection against uncertainty.     

When do Public Managers Imitate Each Other? Mimetic Decision Making in Contracting Decisions of Danish Municipalities

Using organizational new institutional theory, this paper explores a core mechanism underlying contracting decisions in public organizations. A central proposition of this branch of institutional theory is that uncertainty leads to organizational isomorphism. The present study investigates this proposition by asking: When does perceived uncertainty lead public managers to imitative behavior in contracting out decisions? Contrary to most previous studies, we apply an individual level approach and relate different types of perceived uncertainty of decision makers to mimetic decision making. We define mimetic decision making as when decision makers deliberately obtain information about other organizations in order to possibly imitate them. In a survey of Danish municipal managers facing important and complex contracting decisions, we test our hypotheses about three types of perceived uncertainty and mimetic decision making. The results show that technological uncertainty is strongly related to mimetic decision making among public managers. However, we do not find significant results for either volume uncertainty or performance uncertainty. The paper illustrates how uncertainty, through mimetic decision making, is connected to organizational isomorphism. It further highlights that future studies should pay attention to the multidimensionality of uncertainty and its consequences.     

A robust approach to the share-of-choice product design problem

A critical issue when solving the share-of-choice product design problem is the reliability of the optimal solution in the presence of partworth uncertainty. Existing approaches use point estimates of an individual's partworth utilities as input to the product optimization stage, ignoring within-person variability in estimates. Post-optimality sensitivity analysis is occasionally performed to assess the degree to which a solution is negatively impacted by partworth uncertainty. We propose a robust optimization model that explicitly captures variation in partworth estimates during the optimization process. Using a large, commercial dataset, we benchmark our model's performance against its deterministic counterpart. We also present inferential theory to guide the selection of model parameters controlled by the analyst. Results reveal that the new approach produces robust solutions in the face of measurement error. Out-of-sample coverage for individuals drawn from the target population is significantly higher than corresponding solutions from published methods.     

基于随机p-鲁棒优化的国家血液战略储备库选址-库存模型

以往的救灾实践对建立国家血液战略储备体系提出了迫切要求。国家血液战略储备库的建设问题亟待解决。由于血液产品特性以及应急血液保障特性的存在，使得国家血液战略储备库的选址决策具有一定的复杂性。本文将问题定位为选址-库存问题。首先，以应急条件下血液保障及时度最高为目标，构建了一个不确定环境下考虑多情景、多血型、多阶段、带提前期、有容量限制、日常随机需求、有预算约束及协同定位的国家血液战略储备库选址-库存模型。同时，为了规避应急条件下的不确定风险，进一步构建了国家血液战略储备库选址-库存问题的随机p-鲁棒优化模型。该模型为离散非线性混合整数规划模型，难以快速精确求解。故基于模型性质，设计了相应的遗传算法。最后，设计了两组算例验证模型与算法的有效性。其中，第1组算例基于我国大陆地区31个省级血液中心与省级行政区的数据，并根据不同预算值给出6个算例，得到了国家血液战略储备库的选址-库存决策方案。第2组算例为6个不同规模的模拟算例，用来测试不同规模下的算法性能。算例结果表明：遗传算法的性能更好；鲁棒解与确定性模型最优值相差不大（最大差距≤1.08%），可降低不确定性导致的风险。实践中，可对本文所建模型稍作改进，应用于具有类似特征的易腐品（药品、粮食等）应急物资储备库选址-库存决策。     

α-鲁棒随机截流选址问题的模型和算法

由于选址决策的长期性,相关参数会随着时间而变化,所以选址问题存在很多不确定因素。本文通过不同的情景来处理截流问题中流量的不确定性,并结合随机优化和鲁棒优化,提出α-鲁棒随机截流选址模型。该模型规定了在各情景下的相对后悔值不超过α的条件下,使截得的流量的期望值最大,该条件称为α-鲁棒约束。本文将该模型建立成为一个线性0-1整数规划,并给出了改进型贪婪算法和拉格朗日启发式算法。最后,本文使用这两种算法对不同规模的截流选址问题进行了研究。