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Metaheuristic  Algorithms for Solving Roman {2}-Domination Problem 解决罗马人{2}配位问题的元启发式算法
Pub Date : 2024-03-26 DOI: 10.1051/ro/2024074
Alfred Raju M, Venkata Subba Reddy P
A Roman ${2}$-dominating function ($Rom2DF$) on a graph $G(V,E)$ is a function $g:V rightarrow {0,1,2}$ of  $G$ such that for every vertex $xin V$ with $g(x)=0,$ either there exists a neighbor $y$ of $x$ with $g(y)=2$ or at least two neighbors, $u,v$  with $g(u)=g(v)=1$. The value $w(g)=sum_{xin V}g(x)$ is the weight of the Rom2DF. The minimum weight of a Rom2DF of $G$ is called the textit{Roman ${2}$-domination number} denoted by textit{$gamma_{{R2}}(G)$}. Since determining  textit{$gamma_{{R2}}(G)$} of a graph $G$ is NP-hard and no metaheuristic algorithms have been proposed for the same, two procedures based on genetic algorithm are proposed as a solution for the Roman {2}-domination problem. One of the proposed methods employs a random initial population, while the other uses a population generated using heuristics. Experiments have been carried out on graphs generated using textit{Erdős–Rényi} model, a popular model for graph generation and $Harwell ;Boeing (HB)$ dataset. The experimental results demonstrate that both approaches provide a near optimal solution which is well within the known lower and upper bounds for the problem. The experimental results further show that the procedure based on random initial population has outperformed the heuristic based procedure.
图 $G(V,E)$上的罗马${2}$支配函数($Rom2DF$)是$G$的函数$g:V rightarrow {0,1,2}$,使得V$中每个顶点$xin V$的$g(x)=0,$要么存在$x$的邻居$y$的$g(y)=2$,要么存在至少两个邻居$u,v$的$g(u)=g(v)=1$。值 $w(g)=sum_{xin V}g(x)$ 是 Rom2DF 的权重。$G$的Rom2DF的最小权重称为textit{Roman ${2}$-domination number},用textit{$gamma_{{R2}}(G)$表示。}由于确定一个图 $G$ 的 textit{$gamma_{{R2}}(G)$} 是 NP 难的,而且还没有元启发式算法被提出来,因此我们提出了两种基于遗传算法的程序作为解决 Roman {2}-domination 问题的方法。其中一种方法使用随机初始种群,另一种方法使用启发式算法生成的种群。实验在使用 textit{Erdős-Rényi} 模型(一种流行的图形生成模型)和 $Harwell ;Boeing (HB)$ 数据集生成的图形上进行。实验结果表明,这两种方法都提供了接近最优的解决方案,而且都在问题的已知下限和上限范围内。实验结果进一步表明,基于随机初始群体的程序优于基于启发式的程序。
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引用次数: 0
Italian, 2-rainbow and Roman domination numbers in middle graphs 中图中的意大利、2-rainbow 和罗马统治数字
Pub Date : 2024-03-25 DOI: 10.1051/ro/2024072
Kijung Kim
Given a graph $G$, we considerthe Italian domination number $gamma_I(G)$,the $2$-rainbow domination number $gamma_{r2}(G)$ andthe Roman domination number $gamma_R(G)$.It is known that $gamma_I(G) leq gamma_{r2}(G) leq gamma_R(G)$ holds for any graph $G$.In this paper, we prove that $gamma_I(M(G)) =gamma_{r2}(M(G)) =gamma_R(M(G)) =n$ for the middle graph $M(G)$ of a graph $G$ of order $n$, which gives an answer for an open problem posed by Mustapha Chellali et al. [Discrete Applied Mathematics 204 (2016) 22--28].Moreover, we give a complete characterization of Roman domination stable middle graphs, 2-rainbow domination stable middle graphs and Italian domination stable middle graphs.
给定一个图 $G$,我们考虑意大利支配数 $gamma_I(G)$、2$-彩虹支配数 $gamma_{r2}(G)$和罗马支配数 $gamma_R(G)$。众所周知,对于任何图 $G$,$gamma_I(G) leq gamma_{r2}(G) leq gamma_R(G)$ 都成立。本文证明了对于阶数为 $n$ 的图 $G$ 的中间图 $M(G)$,$gamma_I(M(G)) =gamma_{r2}(M(G)) =gamma_R(M(G)) =n$,这给出了 Mustapha Chellali 等人提出的一个开放问题的答案。[此外,我们还给出了罗马支配稳定中间图、2-虹支配稳定中间图和意大利支配稳定中间图的完整表征。
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引用次数: 0
Sales model and logistics selections for a manufacturer considering carbon emission and logistics levels 考虑碳排放和物流水平的制造商的销售模式和物流选择
Pub Date : 2024-03-19 DOI: 10.1051/ro/2024070
Xiaojie Wu, Xin Liu, Xiaogang Lin
Improving logistics levels requires mobilizing more resources, resulting in more carbon emissions. We consider a manufacturer selling its products through an e-commerce platform that sells them to customers (reselling) or directly accessing customers via the platform by paying a proportional fee (agency selling). Under reselling, the manufacturer first sets a wholesale price and then the platform sets a retail price and a logistics level. Under agency selling, if using third-party logistics, the manufacturer sets the retail price and logistics level. When using the platform logistics, the manufacturer sets the retail price and the platform sets the logistics level; moreover, the manufacturer bears part of the logistics cost. This study examines the manufacturer's sales model and logistics selection and its impact on the platform's profit and consumer surplus. We find that if the logistics-improving efficiency is sufficiently high (low), the manufacturer should employ reselling (agency selling and third-party logistics) when the manufacturer bears a sufficient small or large part of the logistics cost. However, regardless of the size of the logistics-improving efficiency, the manufacturer should adopt agency selling and platform logistics when the logistics cost borne by the manufacturer is intermediate. If consumers become more sensitive to carbon emission levels, the manufacturer is less (more) likely to adopt the reselling model and platform logistics (agency selling model and platform logistics). Choosing reselling or agency selling and platform logistics, or agency selling and third-party logistics could benefit both the platform and consumers, generating a ``win-win-win" outcome.
提高物流水平需要调动更多的资源,从而产生更多的碳排放。我们考虑制造商通过电子商务平台向客户销售产品(转售),或通过平台支付一定比例的费用直接与客户接触(代理销售)。在转售情况下,制造商首先设定批发价,然后由平台设定零售价和物流水平。在代理销售中,如果使用第三方物流,则由制造商确定零售价和物流水平。使用平台物流时,制造商确定零售价格,平台确定物流水平;此外,制造商还承担部分物流成本。本研究探讨了制造商的销售模式和物流选择及其对平台利润和消费者剩余的影响。我们发现,如果物流改进效率足够高(低),当制造商承担足够小或足够大的物流成本时,制造商应采用转售(代理销售和第三方物流)。然而,无论物流改进效率的大小如何,当制造商承担的物流成本处于中间水平时,制造商应采用代理销售和平台物流。如果消费者对碳排放水平越来越敏感,制造商就不太可能(更可能)采用转售模式和平台物流(代理销售模式和平台物流)。选择转售或代理销售和平台物流,或代理销售和第三方物流,都会使平台和消费者受益,产生 "三赢 "结果。
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引用次数: 0
An improved sequential insertion initialization algorithm and Tabu search to vehicle routing problem with time windows 一种改进的顺序插入初始化算法和 Tabu 搜索,用于有时间窗的车辆路由问题
Pub Date : 2024-03-19 DOI: 10.1051/ro/2024069
Bin Yue, Jie Yang, Junxu Ma, Jinfa Shi, Linjian Shangguan
The vehicle routing problem (VRP) is a well-researched problem in the operations research literature. This paper studies a vehicle routing problem with time windows. Based on Solomon’s re-search, an improved sequential initialization algorithm, Solomon i1 with DTWC (Solomon i1 with Dynamic Time Windows Compatibility), is proposed in this paper to construct feasible initial solutions with higher quality in less calculation time. A tabu search with VNS (Variable Neighborhood Search) and the Metropolis criterion is used to further optimize the solutions that the proposed initialization algorithm provides. We run computational experiments on cases of well-known problems. Results show that compared to the initialization method before the change, our improved initialization approach performs well in terms of providing a better feasible initialization solution in less time, with an average 10 % improvement in solution quality and an average 34 % computational time savings. The proposed initialization algorithm’s superiority is also demonstrated by the tabu search’s better performance on the initial solutions it produces.
车辆路由问题(VRP)是运筹学文献中研究较多的一个问题。本文研究的是带有时间窗口的车辆路由问题。在所罗门再搜索的基础上,本文提出了一种改进的顺序初始化算法,即具有动态时间窗口兼容性的所罗门 i1 算法(Solomon i1 with DTWC),它能在更短的计算时间内构造出质量更高的可行初始解。我们使用带有 VNS(可变邻域搜索)和 Metropolis 准则的 tabu 搜索来进一步优化所提初始化算法提供的解。我们对一些众所周知的问题进行了计算实验。结果表明,与改变前的初始化方法相比,我们改进后的初始化方法表现出色,能在更短的时间内提供更好的可行初始化解决方案,解决方案的质量平均提高了 10%,计算时间平均节省了 34%。tabu 搜索所产生的初始解决方案性能更佳,这也证明了所提出的初始化算法的优越性。
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引用次数: 0
The hardness of recognising poorly matchable graphs and the hunting of the d-snark 识别匹配性差的图形的难度和猎取 d-snark
Pub Date : 2024-03-18 DOI: 10.1051/ro/2024068
L. Zatesko, Renato Carmo, André L. P. Guedes, Raphael C. S. Machado, Celina M. H. Figueiredo
Abstract. An r-graph is an r-regular graph G on an even number of vertices where every odd set X ⊆V(G) is connected by at least r edges to its complement V(G)  X. Every r-graph has a perfect matching and in a poorly matchable r-graph every pair of perfect matchings intersect, which implies that poorly matchable r-graphs are not r-edge-colourable. We prove, for each fixed r ≥ 3, that poorly matchable r-graph recognition is coNP-complete, an indication that, for each odd d ≥ 3, it may be a hard problem to recognise d-regular (d−1)-edge-connected non-d-edge-colourable graphs, referred to as d-snarks in this paper. We show how to construct, for every fixed odd d ≥ 5, an infinite family of d-snarks. These families provide a natural extension to the well-known Loupekine snarks. We also discuss how the hunting of the smallest d-snarks may help in strengthening and better understanding the major Overfull Conjecture on edge-colouring simple graphs.
摘要r图是偶数顶点上的r正则图G,其中每个奇数集X⊆V(G)至少有r条边与其补集V(G) X相连。每个r图都有一个完美匹配,而在一个差匹配r图中,每一对完美匹配都相交,这意味着差匹配r图不是r-edge-colourable。我们证明,对于每个固定的 r ≥ 3,可差匹配 r 图的识别是 coNP-complete,这表明对于每个奇数 d ≥ 3,识别 d-regular (d-1)-edge-connected non-d-edge-colourable graphs(本文中称为 d-snarks)可能是一个难题。我们展示了如何为每一个固定奇数 d ≥ 5 构建一个无穷的 d-snarks 族。这些族是对著名的卢佩金星形的自然扩展。我们还讨论了寻找最小 d-snarks 如何有助于加强和更好地理解关于边着色简单图的主要 Overfull 猜想。
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引用次数: 0
A sustainable manufacturing-remanufacturing inventory model with price and green sensitive demand for defective and usable items 一种可持续的制造-再制造库存模型,对缺陷和可用物品的价格和绿色需求敏感
Pub Date : 2024-03-12 DOI: 10.1051/ro/2024067
Rakibul Haque, Magfura Pervin, Sankar Prasad Mondal
A sustainable manufacturing-remanufacturing inventory model with two production phases is presented in this study. In this two phases model, the first phase is used for manufacturing whereas the second phase is used for both manufacturing and remanufacturing. Keeping in mind about environment and price of products, it is presumed that market demand rate is influenced by the greenness of item and unit selling price simultaneously. Remanufacturing is performed for non-serviceable items i.e., defective items which are produced from imperfect production and used items that are purchased from the market. But the products for which remanufacturing cost is more than manufacturing cost are scraped off. In the production process carbon releases from setting up, manufacture and holding of the perfect items. To mitigate the carbon emission carbon tax regulation is imposed. Next, concavity of the profit function is driven through the pseudo concavity. Profit is maximized by minimizing the economic, environmental, and social effect. The models are illustrated by a numerical example and a sensitivity analysis is also elaborated for fixed parameters. Special cases are provided to compare the result with previous literature. The results shows that manufacturer wishes to engage in remanufacturing as remanufacturing cost continuously increases with respect time. Another important finding is that the manufacturer can choose remanufacturing as the cost is lower than manufacturing for saving environment. Finally, mathematical findings are listed and managerial implications are recorded.
本研究提出了一种具有两个生产阶段的可持续制造-再制造库存模型。在这个两阶段模型中,第一阶段用于制造,第二阶段用于制造和再制造。考虑到环境和产品价格,假定市场需求率同时受到产品绿色程度和单位售价的影响。再制造针对的是不可维修的产品,即不完善生产中产生的缺陷产品和从市场上购买的旧产品。但再制造成本高于制造成本的产品将被报废。在生产过程中,完美产品的设置、制造和持有都会产生碳排放。为了减少碳排放,需要征收碳税。其次,利润函数的凹性是通过伪凹性实现的。通过最小化经济、环境和社会影响来实现利润最大化。模型通过数值示例进行了说明,并对固定参数进行了敏感性分析。还提供了一些特殊案例,以便将结果与以前的文献进行比较。结果表明,由于再制造成本随着时间的推移不断增加,制造商希望从事再制造。另一个重要发现是,制造商可以选择再制造,因为再制造成本比制造成本更低,更环保。最后,列出了数学结论,并记录了对管理的影响。
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引用次数: 0
Dual channel sales in supply chain: live streaming or traditional e-commerce 供应链中的双渠道销售:直播还是传统电子商务
Pub Date : 2024-03-12 DOI: 10.1051/ro/2024066
Xuejun Zhou, Zhibing Liu, Jie Liu, Chen Pan
In recent years, live streaming is becoming a popular channel to sell products all over the world. Compared to traditional e-commerce channel, live streaming channel may not only bring consumers more shopping convenience, but also pose consumers more privacy concern. This paper considers a supply chain consisting of a manufacturer and an e-tailer who sells through dual channels (i.e., live streaming and traditional e-commerce) to explore how shopping convenience and privacy concern affect the optimal decisions. We build game models of two pricing (exogenous and endogenous) and two incentive contracts (wholesale price and two-part tariff).We find that the optimal promotion efforts are decreasing in shopping convenience while increasing in privacy concerns under the wholesale price contract, and independent of them under the two-part tariff contract when pricing is not a decision (such as iPhone); the optimal promotion efforts are increasing in shopping convenience while decreasing in privacy concern when pricing is a decision (such as the seasonal products). Whether the retail pricing is a decision or not, supply chain coordination can be achieved by the two-part tariff contract, but not through the wholesale price contract. Further, the two-part tariff contract is more favorable to the manufacturer if the exogenously given retail price is low, and the wholesale price contract is more favorable to the manufacturer if the retail price is high; the two-part tariff contract is always more beneficial for the supply chain than the wholesale price contract. Finally, we extend our analysis to relax a more realistic form with a variable effort elasticity and verify the robustness of the theoretical results.
近年来,直播正在成为世界各地销售产品的热门渠道。与传统电子商务渠道相比,直播渠道不仅会给消费者带来更多购物便利,也会给消费者带来更多隐私方面的担忧。本文考虑了一个由制造商和网络零售商组成的供应链,该供应链通过双渠道(即直播和传统电子商务)进行销售,以探讨购物便利性和隐私顾虑如何影响最优决策。我们建立了两种定价(外生性和内生性)和两种激励合约(批发价和两部分关税)的博弈模型。我们发现,在批发价合约下,最优促销力度在购物便利性上递减,而在隐私关注度上递增,而在两部分关税合约下,当定价不是决定因素时(如 iPhone),最优促销力度与购物便利性无关;当定价是决定因素时(如季节性产品),最优促销力度在购物便利性上递增,而在隐私关注度上递减。无论零售定价是否是决定性的,供应链协调都可以通过两部分关税合同来实现,但不能通过批发价格合同来实现。此外,如果外生给定的零售价格较低,两部分关税合同对制造商更有利;如果零售价格较高,批发价格合同对制造商更有利;两部分关税合同总是比批发价格合同更有利于供应链。最后,我们将分析扩展到更现实的可变努力弹性形式,并验证了理论结果的稳健性。
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引用次数: 0
Abstract generalized epsilon-descent algorithm 抽象广义ε-后裔算法
Pub Date : 2024-03-08 DOI: 10.1051/ro/2024060
Estéfany Castillo Ventura, Erik ALEX PAPA QUIROZ
Given the problem of minimizing a possibly nonconvex and nonsmooth function in a real Hilbert space, we present a generalized $epsilon$-descent algorithm motivated from the abstract descent method introduced by Attouch et al.(2013} with two essential addition, we consider scalar errors on the sufficient descent condition, as well as, on the relativeinexact optimality condition. Under general conditions on the function to be minimized, we obtain that all the accumulation points of the sequences generated by the algorithm, if they exist, are generalized critical limit points of the objective function.
给定在实希尔伯特空间中最小化一个可能非凸和非光滑函数的问题,我们提出了一种广义的$epsilon$-下降算法,该算法源于Attouch等人(2013年)提出的抽象下降方法,并增加了两个基本条件:我们考虑了充分下降条件上的标量误差,以及相对精确最优条件上的标量误差。在待最小化函数的一般条件下,我们得到算法生成序列的所有堆积点(如果存在的话)都是目标函数的广义临界极限点。
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引用次数: 0
Hybrid quantitative-qualitative method for technology portfolio selection: A case study of Iran space industry 技术组合选择的定量-定性混合方法:伊朗航天工业案例研究
Pub Date : 2024-03-07 DOI: 10.1051/ro/2024055
Emad Chizari, Seyed Hassan Sedighy, Mirsaman Pishvaee, Adel Azar
The space industry is known as an important driver for many world economies. In Iran, the acquisition of satellite technology knowledge is one of the achievements of the country's scientific and technological indicators in the recent years, but the position and importance of optimal investment in this industry has been not considered, effectively. The optimal technology portfolio is one of the tools that can cover this gap and lead to better decision making by policy makers. In this paper, the optimum technology portfolio determination regarding its goals, attributes and challenges is addressed for Iran space industry with a hybrid quantitative-qualitative method in two short and medium term periods. We formulate a technology portfolio selection model with these multi-objectives functions: maximization of benefits in using different technologies comprising of both short and medium term portfolios, maximizing the total summation of all technology readiness levels (TRLs), maximizing the acquisition speed for the technologies, and minimizing the acquisition risk of technologies in each portfolio. In the proposed model, the usability, acquisition cost, and complexity of each technology are considered, meticulously. Also, the goal programming method is used to integrate the objective functions. Another novelty of this paper is formulation of two portfolios with two different time periods which their corresponding inputs and outputs affect each other’s. This research can significantly help in directing the country’s investment in the space industry, spatial ecosystem orientation, facilitating the creation of space-based businesses, improving economic growth, also provides guidelines to improve the related policies in this area. In addition, it can be considered as an inspiration for other developing countries in the space industry.
众所周知,航天工业是世界许多经济体的重要驱动力。在伊朗,获取卫星技术知识是该国近年来科技指标取得的成就之一,但对该行业最佳投资的地位和重要性却没有进行有效的考虑。优化技术组合是弥补这一不足的工具之一,可以帮助决策者做出更好的决策。本文采用定量与定性相结合的方法,针对伊朗航天工业的目标、属性和挑战,从短期和中期两个阶段来确定最佳技术组合。我们制定了一个具有以下多目标功能的技术组合选择模型:在短期和中期组合中使用不同技术的效益最大化、所有技术就绪水平(TRL)的总和最大化、技术获取速度最大化以及每个组合中技术的获取风险最小化。在建议的模型中,每项技术的可用性、获取成本和复杂性都得到了细致的考虑。此外,还采用了目标编程法来整合目标函数。本文的另一个新颖之处在于提出了两个不同时间段的组合,其相应的输入和输出相互影响。这项研究对引导国家对太空产业的投资、空间生态系统的定位、促进太空企业的创建、改善经济增长有很大帮助,也为完善该领域的相关政策提供了指导。此外,它还可被视为对其他发展中国家航天工业的启示。
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引用次数: 0
Green design strategies for sustainable supply chain considering channel leadership 考虑渠道领导力的可持续供应链绿色设计战略
Pub Date : 2024-03-07 DOI: 10.1051/ro/2024056
Fengmin Yao, Yingluo Yan, Likun Liu, Jiayi Sun
We have observed from practice that both the upstream and downstream firms in sustainable supply chain are motivated to invest in green design to create new economic and environmental values. Channel leadership as an important factor affecting the channel profit distribution will reshape the investment motivation of enterprises. In this paper, we construct six kinds of pricing and green design decision models to explore the optimal green design strategies for sustainable supply chain consisting of one manufacturer and one retailer under different channel leadership, and investigate the interaction between channel leadership and green design strategy, and their impact on sustainable supply chain performance, environment and consumer surplus. We find that regardless of the channel leadership, the wholesale and retail prices of products under different green design strategies are always affected by the cost effect of green design. In terms of boosting the green design level and market demand, increasing the consumer surplus and enterprises profits, only when the manufacturer is the channel leader and the green design cost effect is small, the retailer can implement green design better. Moreover, when the manufacturer implements green design, the better channel structure between the retailer-led and Nash equilibrium game depends on the green design cost effect, but both are better than the manufacturer-led. However, when the retailer implements green design, the channel structure of Nash equilibrium game is always better. We finally illustrate that under different channel leadership, which green design strategy is more conducive to reducing the total environment impact of products depends on the joint effect of green design cost effect and green design environment effect.
我们从实践中观察到,可持续供应链的上下游企业都有投资绿色设计的动机,以创造新的经济和环境价值。渠道领导力作为影响渠道利润分配的重要因素,将重塑企业的投资动机。本文构建了六种定价与绿色设计决策模型,探讨了不同渠道领导力下由一个制造商和一个零售商组成的可持续供应链的最优绿色设计策略,并研究了渠道领导力与绿色设计策略之间的互动关系,以及它们对可持续供应链绩效、环境和消费者剩余的影响。我们发现,无论渠道领导力如何,不同绿色设计策略下的产品批发价和零售价都会受到绿色设计成本效应的影响。在提升绿色设计水平和市场需求、增加消费者剩余和企业利润方面,只有当制造商是渠道领导者且绿色设计成本效应较小时,零售商才能更好地实施绿色设计。此外,当制造商实施绿色设计时,零售商主导的渠道结构与纳什均衡博弈的优劣取决于绿色设计成本效应,但都优于制造商主导的渠道结构。然而,当零售商实施绿色设计时,纳什均衡博弈的渠道结构总是更好。最后,我们说明了在不同的渠道主导下,哪种绿色设计策略更有利于降低产品对环境的总影响取决于绿色设计成本效应和绿色设计环境效应的共同作用。
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引用次数: 0
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RAIRO - Operations Research
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