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A decision support approach employing the PROMETHEE method and risk factors for critical supply assessment in large-scale projects 采用PROMETHEE方法和风险因素进行大型项目关键供应评估的决策支持方法
IF 2.5 4区 管理学 Q1 Mathematics Pub Date : 2022-01-01 DOI: 10.1016/j.orp.2022.100238
Richard Alex da Cunha , Luís Alberto Duncan Rangel , Christian A. Rudolf , Luiza dos Santos

The purpose of this article is twofold: to identify the critical risk factors (RFs) that impact supply chains (SC) in the engineering, procurement, and construction of large-scale projects (EPC-LSP) of the oil and gas industry (OGI) and to apply these RFs in a mathematical model developed, based on multiple-criteria decision-making (MCDM) methods in an expert group. The mathematical model was developed in MATLAB and was based on the Preference Ranking Organization Method for Enrichment Evaluations (PROMÉTHÉE) II and (PROMÉTHÉE GDSS) Group Decision Support System methods. The model's criteria were defined with the RF mapping identified using 33 years of literature and the application of questionnaires to specialists. The evaluation process of the alternatives concerning the defined criteria was conducted through questionnaires to specialists. Finally, the functionality and results of the model were validated by the specialists in the field through interviews. As a contribution, managers, companies, and industry could adopt this solution as a practical and dynamic tool to support decision-making. This fact especially holds true in possible critical supply scenarios, where it is necessary to direct resources to minimize risks and other impacts to EPC-LSP SC. Another novelty refers to the critical risk factors identified, originating from an extensive literature mapping covering the three pillars of sustainability. Moreover, this research was to fill the literature gap, given the lack of studies that propose clear, practical, and specific tools for SCRM in EPC-LSP.

本文的目的有两个:确定影响石油和天然气行业(OGI)大型项目(EPC-LSP)工程、采购和建设中的供应链(SC)的关键风险因素(rf),并将这些rf应用于基于专家组多标准决策(MCDM)方法开发的数学模型中。数学模型基于富集评价偏好排序组织方法(PROMÉTHÉE) II和(PROMÉTHÉE GDSS)群体决策支持系统方法,在MATLAB中开发。该模型的标准是通过33年的文献和专家问卷调查确定的射频映射来定义的。关于确定的标准的备选方案的评价过程是通过向专家进行问卷调查进行的。最后,由该领域的专家通过访谈对模型的功能和结果进行验证。作为贡献,管理人员、公司和行业可以采用此解决方案作为支持决策的实用和动态工具。这一事实在可能的关键供应情况下尤其适用,在这种情况下,有必要引导资源以最大限度地减少风险和对EPC-LSP SC的其他影响。另一个新颖之处是,根据涵盖可持续性三大支柱的广泛文献映射,确定了关键风险因素。此外,鉴于缺乏研究为EPC-LSP中的SCRM提供明确、实用和具体的工具,本研究是为了填补文献空白。
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引用次数: 5
Originating multiple-objective portfolio selection by counter-COVID measures and analytically instigating robust optimization by mean-parameterized nondominated paths 通过反covid措施发起多目标投资组合选择,并通过平均参数化非主导路径解析引发鲁棒优化
IF 2.5 4区 管理学 Q1 Mathematics Pub Date : 2022-01-01 DOI: 10.1016/j.orp.2022.100252
Yue Qi , Kezhi Liao , Tongyang Liu , Yu Zhang

The COVID-19 pandemic is unleashing crises of humanity, economy, and finance. Portfolio selection is widely recognized as the foundation of modern financial economics. Therefore, it is naturally crucial and inviting to utilize portfolio selection in order to counter COVID-19 in stock markets. We originate a counter-COVID measure for stocks, extend portfolio selection, and construct multiple-objective portfolio selection. Because of the uncertainty in measuring counter-COVID, we perform robust optimization. Specifically, we analytically compute the optimal solutions as a trail of an optimal portfolio due to the change of counter-COVID. We call the trail as mean-parameterized nondominated path. Moreover, the path is a continuous function of the change, so the portfolio relatively mildly varies for the change. In contrast, researchers typically still focus on 2-objective robust illustrations and infrequently explicitly compute the optimal solutions for multiple-objective portfolio optimization.

To the best of our knowledge, there is limited research for multiple-objective portfolio selection of COVID and for the robust optimization of multiple-objective portfolio selection. In such an area, this paper contributes to the literature. The implications to fight COVID are that investors minimize risk, maximize return, and maximize counter-COVID in stock markets and that investors ascertain the multiple-objective portfolio selection as relatively robust.

新冠肺炎大流行正在引发人类、经济和金融危机。投资组合选择被广泛认为是现代金融经济学的基础。因此,为了在股市中应对COVID-19,利用投资组合选择自然是至关重要的。我们提出了股票的抗covid措施,扩展了投资组合选择,构建了多目标投资组合选择。由于测量抗covid的不确定性,我们进行了鲁棒优化。具体来说,我们分析计算了最优解决方案,作为由于counter-COVID变化的最优投资组合的踪迹。我们称这条轨迹为平均参数化非支配路径。此外,路径是变化的连续函数,因此投资组合相对温和地随变化而变化。相比之下,研究人员通常仍然集中在两目标的鲁棒性说明上,很少明确地计算多目标投资组合优化的最优解。据我们所知,关于COVID的多目标投资组合选择和多目标投资组合鲁棒优化的研究有限。在这方面,本文有一定的文献贡献。对抗COVID的含义是投资者在股票市场中最大限度地降低风险,最大限度地提高回报,最大限度地提高抗COVID能力,并且投资者确定多目标投资组合选择相对稳健。
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引用次数: 1
Identifying and correcting the defects of the Saaty analytic hierarchy/network process: A comparative study of the Saaty analytic hierarchy/network process and the Markov chain-based analytic network process 萨提分析层次/网络过程的缺陷识别与修正:萨提分析层次/网络过程与基于马尔可夫链的分析网络过程的比较研究
IF 2.5 4区 管理学 Q1 Mathematics Pub Date : 2022-01-01 DOI: 10.1016/j.orp.2022.100244
Qizhi Liu

The Saaty analytic network process (Saaty-ANP) is a generalization of the analytic hierarchy process. The Markov chain-based ANP (MC-ANP) is another decision-making approach suitable for general structures. Both ANPs use a relative measurement (paired comparisons with ratio scales) to estimate tangible and intangible factors, use a stochastic matrix (SM) to solve feedback problems and obtain the same results under some conditions. The Saaty-ANP does not define the basic concepts, nor does it check the rationality of the structure, which may lead to meaningless solutions and ignore a subclass of feedback decision problems. MC-ANP separates the alternatives from the criteria and defines the attributes, criteria, criterion dominated relations (CDRs) and reasonable constraints of the CDRs by means of digraphs; it also represents CDRs as Markov chain transition diagrams and corresponding (stochastic) adjacency matrices and obtains solutions from a system of linear equations. With the MC-ANP, for the real alternative problems (Class I), the solutions are priorities of the alternatives obtained by the parametric positive left eigenvectors of the SM, and for the nominal alternative problems (Class II), the solutions are priorities of the criteria obtained by the nonnegative right eigenvector of the SM. We analyze the conditions and causes of rank reversal; note that rank reversal does not appear in Class II problems; the study offers a rank reversal ANP example (with feedback) and presents a rank-preserving method for Class I problems. We discuss the contribution of MC-ANP, how to compensate for the defects of Saaty-AHP/ANP, and present issues that need further consideration.

安全分析网络过程(Saaty- anp)是层次分析法的推广。基于马尔可夫链的ANP (MC-ANP)是另一种适用于一般结构的决策方法。两种anp都使用相对测量(与比例量表配对比较)来估计有形和无形因素,使用随机矩阵(SM)来解决反馈问题,并在某些条件下获得相同的结果。Saaty-ANP没有定义基本概念,也没有检查结构的合理性,这可能导致无意义的解,忽略了反馈决策问题的一个子类。MC-ANP将备选方案从准则中分离出来,通过有向图的方式定义了准则的属性、准则、准则主导关系(cdr)和合理约束;它还将cdr表示为马尔可夫链转移图和相应的(随机)邻接矩阵,并从线性方程组中得到解。利用MC-ANP,对于第一类实际可选问题,其解是由SM的参数正左特征向量得到的可选方案的优先级;对于第二类标称可选问题,其解是由SM的非负右特征向量得到的准则的优先级。分析了排名颠倒的条件和原因;注意,等级反转不会出现在第二类问题中;本文给出了一个带反馈的秩反转ANP实例,并给出了一类问题的秩保持方法。我们讨论了MC-ANP的贡献,以及如何弥补safety - ahp /ANP的缺陷,并提出了需要进一步考虑的问题。
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引用次数: 1
Analysis of Vaccine efficacy during the COVID-19 pandemic period using CSF-ELECTRE-I approach 应用csf - electre -1方法分析COVID-19大流行期间疫苗的疗效
IF 2.5 4区 管理学 Q1 Mathematics Pub Date : 2022-01-01 DOI: 10.1016/j.orp.2022.100251
Samayan Narayanamoorthy , Subramaniam Pragathi , Meshal Shutaywi , Ali Ahmadian , Daekook Kang

COVID-19 vaccinations have been shown to be safe, efficacious, and life-saving. They, like other vaccines, do not entirely protect everyone who receives them, and no one knows how effectively they can prevent people from spreading the virus to others or whether the booster dosage is dangerous to some vulnerable people. So, in addition to getting vaccinated, we must continue with additional efforts to combat the pandemic. Quantitatively, the pragmatic, appropriate, and phenomenal mechanism of the complex spherical fuzzy set enhances the decision-making efficacy and the ordering quality of the ELECTRE I method to include a profitable and optimal approach for MAGDM. In the CSF environment, critically ill patients are investigated systematically using a pairwise comparison based ELECTRE-I technique. In this paper, we improve the precision of the CSF-based ELECTRE-I approach to an unique score function. The suggested approach’s comparability is examined with techniques that should provide equal importance to the alternatives, and the presented score function’s reliability is validated using the existing score function with the two cases.

COVID-19疫苗接种已被证明是安全、有效和挽救生命的。与其他疫苗一样,它们并不能完全保护所有接种者,也没有人知道它们能在多大程度上有效地防止人们将病毒传播给他人,也没有人知道加强剂量是否对某些脆弱人群有危险。因此,除了接种疫苗外,我们还必须继续作出更多努力来防治这一流行病。定量地说,复杂球面模糊集的实用、适宜和现象性机制提高了ELECTRE方法的决策效率和排序质量,使其包含了一个有利可图的最优MAGDM方法。在脑脊液环境中,使用基于成对比较的ELECTRE-I技术系统地调查危重患者。在本文中,我们提高了基于csf的elecre - i方法的精度,以获得唯一的分数函数。建议的方法的可比性是通过技术来检验的,这些技术应该对备选方案提供同等的重要性,并且使用现有的得分函数对两种情况进行可靠性验证。
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引用次数: 1
Nonconvex multicommodity near equilibrium models: Energy markets perspective 非凸多商品近均衡模型:能源市场视角
IF 2.5 4区 管理学 Q1 Mathematics Pub Date : 2022-01-01 DOI: 10.1016/j.orp.2022.100243
J. David Fuller, Mehrdad Pirnia

In this paper we explore the application of the minimum total opportunity cost (MTOC) model of Fuller and Celebi (2017) to multicommodity market planning models containing binary variables and price sensitive demands, with or without substitution among commodities. We present a greatly simplified derivation of the MTOC approximation of Fuller and Celebi (2017), here called the near equilibrium (NE) model, a mixed integer program with nonlinearities only in the objective function. For some models, the NE solution achieves the MTOC solution exactly, as in an example. We provide a simple example of capacity expansion in gas and electricity markets that are linked through substitution in demand and in the possibility of using gas to produce electricity. In several cases, we compare the NE solution to the social welfare (SW) maximization solution calculated by a sequential optimization algorithm. In one case, the sequential optimization algorithm fails to converge, due to the binary variables. For the other cases, the NE model has smaller producer opportunity costs – in particular, in most cases, smaller make whole payments that bring negative producer profits up to zero – at some sacrifice of social welfare. We suggest that the NE model could be useful to government regulators as a supplementary tool along with SW models, as the NE solution usually reduces subsidies needed for make whole payments, and sometimes benefits consumers compared to the SW solution.

在本文中,我们探讨了Fuller和Celebi(2017)的最小总机会成本(MTOC)模型在包含二元变量和价格敏感需求的多商品市场规划模型中的应用,包括商品之间是否存在替代。我们提出了Fuller和Celebi(2017)的MTOC近似的极大简化推导,这里称为近平衡(NE)模型,这是一个仅在目标函数中具有非线性的混合整数程序。对于某些模型,网元解决方案完全实现了MTOC解决方案,如示例所示。我们提供了一个简单的例子,说明天然气和电力市场的产能扩张是通过需求替代和使用天然气发电的可能性联系在一起的。在一些情况下,我们将NE解决方案与通过顺序优化算法计算的社会福利(SW)最大化解决方案进行了比较。在一种情况下,由于二元变量,顺序优化算法不能收敛。在其他情况下,以牺牲一些社会福利为代价,东北模式的生产者机会成本更小——特别是,在大多数情况下,更少的生产者支付全部费用,使生产者的负利润接近于零。我们建议,作为SW模型的补充工具,NE模型可能对政府监管机构有用,因为NE解决方案通常会减少支付所需的补贴,与SW解决方案相比,有时会使消费者受益。
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引用次数: 0
The impact of preservation technology investments on lot-sizing and shipment strategies in a three-echelon food supply chain involving growing and deteriorating items 在涉及生长和变质物品的三级食品供应链中,保存技术投资对批量和运输策略的影响
IF 2.5 4区 管理学 Q1 Mathematics Pub Date : 2022-01-01 DOI: 10.1016/j.orp.2022.100241
Makoena Sebatjane

Food production systems are complex industrial operations that often involve multiple parties. This study proposes inventory management strategies for a multi-echelon perishable food supply chain with growing and deteriorating items. The upstream end of the proposed food supply chain is the farming echelon where newborn growing items are reared to maturity. Following this, the items are sent to the processing echelon for processing, a term that collectively describes activities such as slaughtering, cutting and packaging. The aim of the processing echelon is to transform live growing items into processed food products that are suitable for human consumption. The downstream end of the supply chain is the retail echelon where consumer demand for processed food products is met. Once the items are processed, they are subject to deterioration at both the processing and retail echelons. In light of this, an integrated inventory model aimed at optimising the performance of the entire food supply chain is formulated. The impact of investing in preservation technologies is also investigated due to the perishable nature of food products. To do this, a secondary model that incorporates an investment in preservation technologies is formulated. The model, representing a simplified industrial food production system, is aimed at jointly optimising the lot-size, number of shipments, growing cycle duration, processing cycle duration and the preservation technology investment amount. The results from the numerical example demonstrate that the preservation technology investment is worthwhile because it results in reduced inventory management costs across the supply chain.

食品生产系统是复杂的工业操作,通常涉及多方。本研究提出了一个多层次易腐烂食品供应链的库存管理策略。所提出的食品供应链的上游端是农业梯队,在那里,新生生长的物品被饲养到成熟。在此之后,这些物品被送到加工梯队进行加工,这个术语统称为屠宰、切割和包装等活动。加工梯队的目的是将活的种植项目转化为适合人类消费的加工食品。供应链的下游是零售梯队,消费者对加工食品的需求在这里得到满足。一旦物品被加工,它们就会在加工和零售梯队中变质。基于此,本文提出了一个旨在优化整个食品供应链绩效的综合库存模型。由于食品的易腐性,对保鲜技术投资的影响也进行了调查。为了做到这一点,我们制定了一个包含保存技术投资的二级模型。该模型代表了一个简化的工业食品生产系统,旨在共同优化批量、发货量、生长周期、加工周期和保鲜技术投资金额。数值算例的结果表明,在整个供应链中,仓储技术的投资是值得的,因为它降低了库存管理成本。
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引用次数: 10
Multi-period portfolio decision analysis: A case study in the infrastructure management sector 多时期投资组合决策分析:基础设施管理部门的案例研究
IF 2.5 4区 管理学 Q1 Mathematics Pub Date : 2022-01-01 DOI: 10.1016/j.orp.2021.100213
Gaia Gasparini, Matteo Brunelli, Marius Dan Chiriac

This paper presents an approach to select and plan the optimal execution of potential investment activities. The model is composed by a computational part, in the form of a combinatorial optimization problem, coupled with a preference elicitation module used to capture subjective judgments. In particular, the structure of the elicitation module draws from portfolio decision analysis and Multi-Attribute Value Theory and shows how their use can be integrated with a multi-period optimization problem with activities durations and constraints on their overlaps. The problem formulation was inspired by a real-world infrastructure management case in the energy distribution sector and tested on a dataset of more than three hundred activities of improvement of infrastructure conditions. Finally, the approach proposed in this paper is validated by analyzing its results and its robustness concerning the input data of the real-world case study.

本文提出了一种选择和规划潜在投资活动的最佳执行的方法。该模型由计算部分组成,以组合优化问题的形式,加上用于捕获主观判断的偏好激发模块。特别地,启发模块的结构借鉴了投资组合决策分析和多属性价值理论,并展示了如何将它们的使用与具有活动持续时间和重叠约束的多周期优化问题相结合。该问题的提出受到了能源分配部门现实世界基础设施管理案例的启发,并在300多个改善基础设施条件的活动的数据集上进行了测试。最后,通过分析本文所提出的方法的结果及其对实际案例输入数据的鲁棒性进行了验证。
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引用次数: 2
Modeling Bayesian inspection game for non-performing loan problems 不良贷款问题的贝叶斯检验对策建模
IF 2.5 4区 管理学 Q1 Mathematics Pub Date : 2022-01-01 DOI: 10.1016/j.orp.2021.100218
Erwin Widodo , Oryza Akbar Rochmadhan , Lukmandono , Januardi

This study compiled a Bayesian inspection game as a branch in game theory to deal with non-performing loans (NPLs). Three types of games are analyzed, which are false alarm (FA), non-detection (ND), and bull's eye (BE). A Bayesian Nash equilibrium calculation process took place to formulate the player's strategy proportion. The equilibrium solution indicates the causative factors and develops the strategies to anticipate NPLs. The identified factors causing NPLs include customers' utility and disutility, inspection error in the form of false alarm and non-detection, operational costs to conduct an inspection, and bank utility related to inspection. The results showed that some examinations of type I and II errors to the game model could provide more comprehensive and interesting insights in managing NPL problems.

本研究编制了一个贝叶斯检查博弈作为博弈论的一个分支来处理不良贷款。本文分析了三种类型的游戏,即假警报(FA)、非检测(ND)和靶心(BE)。通过贝叶斯纳什均衡计算过程来确定玩家的策略比例。均衡解指出了不良贷款的成因,并制定了预测不良贷款的策略。已确定的导致不良贷款的因素包括客户的效用和负效用,以虚警和未检测形式出现的检查错误,进行检查的运营成本,以及与检查相关的银行效用。结果表明,对博弈模型的I型和II型错误的一些检查可以为管理不良实验室问题提供更全面和有趣的见解。
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引用次数: 0
The impact of penalty and subsidy mechanisms on the decisions of the government, businesses, and consumers during COVID-19 ——Tripartite evolutionary game theory analysis 新冠肺炎期间惩罚和补贴机制对政府、企业和消费者决策的影响——三方进化博弈论分析
IF 2.5 4区 管理学 Q1 Mathematics Pub Date : 2022-01-01 DOI: 10.1016/j.orp.2022.100255
Yuxun Zhou, Mohammad Mafizur Rahman, Rasheda Khanam, Brad R. Taylor

Purpose

Based on the fact that punishment and subsidy mechanisms affect the anti-epidemic incentives of major participants in a society, the issue of this paper is how the penalty and subsidy mechanisms affect the decisions of governments, businesses, and consumers during Corona Virus Disease 2019 (COVID-19).

Design/Methodology/approach

- This paper proposes a tripartite evolutionary game theory, involving governments, businesses, and consumers, to analyze the evolutionary stable strategies and the impact of penalty and subsidy mechanism on their strategy selection during COVID-19. We then uses numerical analysis to simulate the strategy formation process of governments, businesses, and consumers for the results of tripartite evolutionary game theory.

Findings

This paper suggests that there are four evolutionary stable strategies corresponding to the actual anti-epidemic situations. We find that different subsidy and penalty mechanisms lead to different evolutionary stable strategies. High penalties for businesses and consumers can prompt them to choose active prevention strategies no matter what the subsidy mechanism is. For the government, the penalty mechanism is better than the subsidy mechanism, because the excessive subsidy mechanism will raise the government expenditure. The punishment mechanism is more effective than the subsidy mechanism in realizing the tripartite joint prevention of the COVID-19. Therefore, the implementation of strict punishment mechanism should be a major government measure under COVID-19.

Originality/value

- Our paper extends the existing theoretical work. We use political economy to make the preference hypothesis, and we explicitly state the effect of subsidy and penalty mechanisms on the decision making of participants and compare their applicability. This is the work that the existing literature did not complete before. Our findings can provide an important theoretical and decision-making basis for COVID-19 prevention and control.

基于惩罚和补贴机制影响社会主要参与者的抗疫激励这一事实,本文的问题是在2019冠状病毒病(COVID-19)期间,惩罚和补贴机制如何影响政府、企业和消费者的决策。设计/方法/途径——本文提出了政府、企业和消费者三方参与的进化博弈理论,分析了新冠肺炎期间企业的进化稳定策略,以及惩罚和补贴机制对其策略选择的影响。然后,我们用数值分析模拟了政府、企业和消费者三方博弈的策略形成过程。研究发现——本文提出了四种与实际抗疫形势相适应的进化稳定策略。研究发现,不同的补贴和惩罚机制导致不同的进化稳定策略。无论补贴机制是什么,对企业和消费者的高额处罚都可以促使他们选择积极的预防策略。对于政府来说,惩罚机制优于补贴机制,因为过度的补贴机制会增加政府支出。在实现新冠肺炎三方联防方面,惩罚机制比补贴机制更有效。因此,实施严格的惩罚机制应成为新冠疫情下政府的一项重大举措。原创性/价值——本文是对已有理论工作的延伸。本文运用政治经济学的方法提出了偏好假设,明确阐述了补贴机制和惩罚机制对参与者决策的影响,并比较了它们的适用性。这是现有文献之前没有完成的工作。研究结果可为新冠肺炎疫情防控提供重要的理论和决策依据。
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引用次数: 5
Industrial-size job shop scheduling with constraint programming 具有约束规划的工业规模作业车间调度
IF 2.5 4区 管理学 Q1 Mathematics Pub Date : 2022-01-01 DOI: 10.1016/j.orp.2022.100249
Giacomo Da Col , Erich C. Teppan

The job shop scheduling problem is one of the most studied optimization problems to this day and it becomes more and more important in the light of the fourth industrial revolution (Industry 4.0) that aims at fully automated production processes. For a long time exact methods like constraint programming had problems to solve real large-scale problem instances and methods of choice were to be found in the area of (meta-) heuristics. However, developments during the last decade improved the performance of state-of-the-art constraint solvers dramatically, to the point that they can be applied also on large-scale instances. The presented work’s main target is to elaborate the performance of state-of-the-art constraint solvers with respect to industrial-size job shop scheduling problem instances. To this end, we analyze and compare the performance of two cutting-edge constraint solvers: OR-Tools, an open-source solver developed by Google and recurrent winner of the MiniZinc Challenge, and CP Optimizer, a proprietary constraint solver from IBM targeted at industrial optimization problems. In order to reflect real-world industrial scenarios with heavy workloads like found in the semi-conductor domain, we use novel benchmarks that comprise up to one million operations to be scheduled on up to one thousand machines. The comparison is based on the best makespan (i.e. completion time) achieved and the time required to solve the problem instances. We test the solvers on single-core and quad-core configurations.

作业车间调度问题是当今研究最多的优化问题之一,鉴于第四次工业革命(工业4.0)旨在实现全自动化生产过程,它变得越来越重要。长期以来,像约束规划这样的精确方法在解决实际的大规模问题实例时存在问题,而选择方法则是在(元)启发式领域找到的。然而,过去十年的发展极大地提高了最先进的约束求解器的性能,以至于它们也可以应用于大规模实例。提出的工作的主要目标是详细说明关于工业规模的作业车间调度问题实例的最先进的约束求解器的性能。为此,我们分析并比较了两种前沿约束求解器的性能:OR-Tools(谷歌开发的开源求解器,也是MiniZinc挑战赛的多次获奖者)和CP Optimizer (IBM针对工业优化问题的专有约束求解器)。为了反映在半导体领域中发现的具有繁重工作负载的真实工业场景,我们使用了新的基准测试,其中包括多达一千台机器上安排的多达一百万个操作。比较是基于实现的最佳makespan(即完成时间)和解决问题实例所需的时间。我们在单核和四核配置上测试求解器。
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引用次数: 7
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Operations Research Perspectives
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