Junfeng Dong, Mengyuan Wang, Li Jiang, Wenxing Lu, Changyong Liang
This study considers two government subsidy policies, namely, supply-side (subsidising elderly service companies) and demand-side (subsidising elderly customers) subsidies. A Nash game model consisting of elderly customers and two elderly service providers with different levels of infrastructure is developed to present the effects of government subsidies on the price, quality and quantity of demand for elderly services under different subsidy policies. The results show that the economic situation of the region and the strategic objectives of the local government are important factors influencing the effectiveness of the government’s subsidy strategy. For areas with good regional economic conditions, subsidies should be biased in favour of elderly care institutions with poorer infrastructure; for areas with poorer economic conditions, subsidies should be biased in favour of institutions with better infrastructure. Moreover, if the government plans to reduce prices more effectively, then it should adopt a demand-side subsidy policy for areas with a small or large elderly population and a supply-side subsidy policy for areas with a medium elderly population.
{"title":"Decision-making model of elderly service companies under government subsidies\u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000\u0000 ","authors":"Junfeng Dong, Mengyuan Wang, Li Jiang, Wenxing Lu, Changyong Liang","doi":"10.1051/ro/2024043","DOIUrl":"https://doi.org/10.1051/ro/2024043","url":null,"abstract":"This study considers two government subsidy policies, namely, supply-side (subsidising elderly service companies) and demand-side (subsidising elderly customers) subsidies. A Nash game model consisting of elderly customers and two elderly service providers with different levels of infrastructure is developed to present the effects of government subsidies on the price, quality and quantity of demand for elderly services under different subsidy policies. The results show that the economic situation of the region and the strategic objectives of the local government are important factors influencing the effectiveness of the government’s subsidy strategy. For areas with good regional economic conditions, subsidies should be biased in favour of elderly care institutions with poorer infrastructure; for areas with poorer economic conditions, subsidies should be biased in favour of institutions with better infrastructure. Moreover, if the government plans to reduce prices more effectively, then it should adopt a demand-side subsidy policy for areas with a small or large elderly population and a supply-side subsidy policy for areas with a medium elderly population.","PeriodicalId":506995,"journal":{"name":"RAIRO - Operations Research","volume":"51 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139838517","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this study, we investigate a heterogeneous queueing model with intermittent server availability, server catastrophes, and a hybrid vacation policy. Our focus is on a specific scenario: Server 1 is always available, while Server 2 may experience breakdowns or vacations, making it intermittently accessible. Using the matrix-geometric approach (MGA), we derive matrix-based expressions for the stationary probability distribution of the number of customers in the system and various system performance measures. Additionally, we evaluate the cost function per unit of time to determine optimal values for the system’s decision variables. Furthermore, we employ an adaptive neural fuzzy inference system (ANFIS) based on soft computing technology to compare and analyze the numerical results obtained. Through this comprehensive analysis, our study contributes to the understanding and optimization of this complex queueing system, attracting the attention of researchers in the field and offering practical insights for real-world applications.
{"title":"Performance analysis and ANFIS computing of a Markovian queueing model with intermittently accessible server under a hybrid vacation policy.","authors":"D. K., I. K.","doi":"10.1051/ro/2024044","DOIUrl":"https://doi.org/10.1051/ro/2024044","url":null,"abstract":"In this study, we investigate a heterogeneous queueing model with intermittent server availability, server catastrophes, and a hybrid vacation policy. Our focus is on a specific scenario: Server 1 is always available, while Server 2 may experience breakdowns or vacations, making it intermittently accessible. Using the matrix-geometric approach (MGA), we derive matrix-based expressions for the stationary probability distribution of the number of customers in the system and various system performance measures. Additionally, we evaluate the cost function per unit of time to determine optimal values for the system’s decision variables. Furthermore, we employ an adaptive neural fuzzy inference system (ANFIS) based on soft computing technology to compare and analyze the numerical results obtained. Through this comprehensive analysis, our study contributes to the understanding and optimization of this complex queueing system, attracting the attention of researchers in the field and offering practical insights for real-world applications.","PeriodicalId":506995,"journal":{"name":"RAIRO - Operations Research","volume":"29 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139778246","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Junfeng Dong, Mengyuan Wang, Li Jiang, Wenxing Lu, Changyong Liang
This study considers two government subsidy policies, namely, supply-side (subsidising elderly service companies) and demand-side (subsidising elderly customers) subsidies. A Nash game model consisting of elderly customers and two elderly service providers with different levels of infrastructure is developed to present the effects of government subsidies on the price, quality and quantity of demand for elderly services under different subsidy policies. The results show that the economic situation of the region and the strategic objectives of the local government are important factors influencing the effectiveness of the government’s subsidy strategy. For areas with good regional economic conditions, subsidies should be biased in favour of elderly care institutions with poorer infrastructure; for areas with poorer economic conditions, subsidies should be biased in favour of institutions with better infrastructure. Moreover, if the government plans to reduce prices more effectively, then it should adopt a demand-side subsidy policy for areas with a small or large elderly population and a supply-side subsidy policy for areas with a medium elderly population.
{"title":"Decision-making model of elderly service companies under government subsidies\u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000\u0000 ","authors":"Junfeng Dong, Mengyuan Wang, Li Jiang, Wenxing Lu, Changyong Liang","doi":"10.1051/ro/2024043","DOIUrl":"https://doi.org/10.1051/ro/2024043","url":null,"abstract":"This study considers two government subsidy policies, namely, supply-side (subsidising elderly service companies) and demand-side (subsidising elderly customers) subsidies. A Nash game model consisting of elderly customers and two elderly service providers with different levels of infrastructure is developed to present the effects of government subsidies on the price, quality and quantity of demand for elderly services under different subsidy policies. The results show that the economic situation of the region and the strategic objectives of the local government are important factors influencing the effectiveness of the government’s subsidy strategy. For areas with good regional economic conditions, subsidies should be biased in favour of elderly care institutions with poorer infrastructure; for areas with poorer economic conditions, subsidies should be biased in favour of institutions with better infrastructure. Moreover, if the government plans to reduce prices more effectively, then it should adopt a demand-side subsidy policy for areas with a small or large elderly population and a supply-side subsidy policy for areas with a medium elderly population.","PeriodicalId":506995,"journal":{"name":"RAIRO - Operations Research","volume":"25 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139778656","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this study, we investigate a heterogeneous queueing model with intermittent server availability, server catastrophes, and a hybrid vacation policy. Our focus is on a specific scenario: Server 1 is always available, while Server 2 may experience breakdowns or vacations, making it intermittently accessible. Using the matrix-geometric approach (MGA), we derive matrix-based expressions for the stationary probability distribution of the number of customers in the system and various system performance measures. Additionally, we evaluate the cost function per unit of time to determine optimal values for the system’s decision variables. Furthermore, we employ an adaptive neural fuzzy inference system (ANFIS) based on soft computing technology to compare and analyze the numerical results obtained. Through this comprehensive analysis, our study contributes to the understanding and optimization of this complex queueing system, attracting the attention of researchers in the field and offering practical insights for real-world applications.
{"title":"Performance analysis and ANFIS computing of a Markovian queueing model with intermittently accessible server under a hybrid vacation policy.","authors":"D. K., I. K.","doi":"10.1051/ro/2024044","DOIUrl":"https://doi.org/10.1051/ro/2024044","url":null,"abstract":"In this study, we investigate a heterogeneous queueing model with intermittent server availability, server catastrophes, and a hybrid vacation policy. Our focus is on a specific scenario: Server 1 is always available, while Server 2 may experience breakdowns or vacations, making it intermittently accessible. Using the matrix-geometric approach (MGA), we derive matrix-based expressions for the stationary probability distribution of the number of customers in the system and various system performance measures. Additionally, we evaluate the cost function per unit of time to determine optimal values for the system’s decision variables. Furthermore, we employ an adaptive neural fuzzy inference system (ANFIS) based on soft computing technology to compare and analyze the numerical results obtained. Through this comprehensive analysis, our study contributes to the understanding and optimization of this complex queueing system, attracting the attention of researchers in the field and offering practical insights for real-world applications.","PeriodicalId":506995,"journal":{"name":"RAIRO - Operations Research","volume":"107 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139837846","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This work studies the problem of semi-online scheduling on two uniform parallel machines with speeds 1 and s≥2, respectively. We introduce a novel concept of initial lookahead in which any deterministic online algorithm has the full knowledge of the first k jobs at the beginning, while the remaining jobs are released one-by-one in the online over-list mode. The objective of the considered problem is to minimize the makespan. We focus on the case where the first k jobs are of a total processing time not less than (s+1)Δ where Δ is the largest job length, and it is assumed that s is an integer. We prove a lower bound of (s2+s+1)/(s2+s), and propose a deterministic online algorithm with competitive ratio of (s+1)2/(s2+s+1). The ratio is at most 9/7 and much less than that of 1.618 for the basic case without initial lookahead (Cho and Sahni [7]). Our results demonstrate that a finite ability of initial lookahead can greatly improve the competitiveness of online algorithms.
这项工作研究的是速度分别为 1 和 s≥2 的两台均匀并行机器上的半联机调度问题。我们引入了一个新颖的初始前瞻概念，在这个概念中，任何确定性在线算法在开始时都完全知道前 k 个作业，而其余作业则在在线超列表模式下逐个释放。所考虑问题的目标是最小化作业间隔。我们关注的是前 k 个作业的总处理时间不小于 (s+1)Δ 的情况，其中 Δ 是最大作业长度，假设 s 为整数。我们证明了 (s2+s+1)/(s2+s) 的下限，并提出了一种确定性在线算法，其竞争比率为 (s+1)2/(s2+s+1) 。该比率最多为 9/7，远小于无初始前瞻的基本情况下的 1.618（Cho 和 Sahni [7]）。 我们的结果表明，有限的初始前瞻能力可以大大提高在线算法的竞争力。
{"title":"Semi-online scheduling on two uniform parallel machines with initial lookahead\u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 ","authors":"Feifeng Zheng, Yuhong Chen, Ming Liu","doi":"10.1051/ro/2024042","DOIUrl":"https://doi.org/10.1051/ro/2024042","url":null,"abstract":"This work studies the problem of semi-online scheduling on two uniform parallel machines with speeds 1 and s≥2, respectively. We introduce a novel concept of initial lookahead in which any deterministic online algorithm has the full knowledge of the first k jobs at the beginning, while the remaining jobs are released one-by-one in the online over-list mode. The objective of the considered problem is to minimize the makespan. We focus on the case where the first k jobs are of a total processing time not less than (s+1)Δ where Δ is the largest job length, and it is assumed that s is an integer. We prove a lower bound of (s2+s+1)/(s2+s), and propose a deterministic online algorithm with competitive ratio of (s+1)2/(s2+s+1). The ratio is at most 9/7 and much less than that of 1.618 for the basic case without initial lookahead (Cho and Sahni [7]). Our results demonstrate that a finite ability of initial lookahead can greatly improve the competitiveness of online algorithms.","PeriodicalId":506995,"journal":{"name":"RAIRO - Operations Research","volume":"142 34","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139780511","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jose Javier Cerda Hernández, Artem Logachov, Anatoly Yambartsev
We propose a simple continuous-time stochastic model for capturing the dynamics of a limit order book in the presence of liquidity fluctuations, manifested by gaps in filled price levels within the OB. Inspired by Farmer et al. (2004), we define a model for the dynamics of spread that incorporates liquidity fluctuations and undertake a comprehensive theoretical study of the model's properties, providing rigorous proofs of several key asymptotic theorems. Furthermore, we show how large deviations manifest in the spread under this regime.
我们提出了一个简单的连续时间随机模型，用于捕捉限价订单簿在流动性波动情况下的动态变化，流动性波动表现为 OB 内部成交价格水平的差距。受 Farmer 等人（2004 年）的启发，我们定义了一个包含流动性波动的价差动态模型，并对模型的特性进行了全面的理论研究，提供了几个关键渐近定理的严格证明。此外，我们还展示了在这一机制下利差的大偏差表现。
{"title":"Bid-ask spread dynamics: large upward jump with geometric catastrophes","authors":"Jose Javier Cerda Hernández, Artem Logachov, Anatoly Yambartsev","doi":"10.1051/ro/2024039","DOIUrl":"https://doi.org/10.1051/ro/2024039","url":null,"abstract":"We propose a simple continuous-time stochastic model for capturing the dynamics of a limit order book in the presence of liquidity fluctuations, manifested by gaps in filled price levels within the OB. Inspired by Farmer et al. (2004), we define a model for the dynamics of spread that incorporates liquidity fluctuations and undertake a comprehensive theoretical study of the model's properties, providing rigorous proofs of several key asymptotic theorems. Furthermore, we show how large deviations manifest in the spread under this regime.","PeriodicalId":506995,"journal":{"name":"RAIRO - Operations Research","volume":"353 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139841616","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper aims to coordinate a shipment lead time hedging (SLTH) problem between a building contractor and a logistics provider in the prefabricated construction supply chain (PCSC). In the PCSC, untimely (early or late) delivery of prefabs will result in project time and cost overrun. To mitigate this challenge, the building contractor requires the logistics provider to reduce the shipping time variability, which is termed the SLTH strategy. Though it benefits the building contractor, this strategy puts more investment and operational pressures on the logistics provider. To solve this conflict, a coordination mechanism is introduced. Two terms are involved in this mechanism: an SLTH level related cost term is charged by the logistic provider to the building contractor and a constant transfer term is adopted to fairly allocate the system surplus. Three decentralized models are investigated: i.e. two Stackelberg game models with alternative decision-making sequences and an equal power model. Further comparative analysis and numerical studies reveal that the proposed coordination mechanism increases the SLTH level and ensures a win-win situation. Moreover, some interesting managerial implications are derived.
{"title":"Shipment lead time hedging and coordination in prefabricated construction supply chain","authors":"Zhenyi Wang, Haizi Wang, Shibin Zhang, Shuai Qiu","doi":"10.1051/ro/2024041","DOIUrl":"https://doi.org/10.1051/ro/2024041","url":null,"abstract":"This paper aims to coordinate a shipment lead time hedging (SLTH) problem between a building contractor and a logistics provider in the prefabricated construction supply chain (PCSC). In the PCSC, untimely (early or late) delivery of prefabs will result in project time and cost overrun. To mitigate this challenge, the building contractor requires the logistics provider to reduce the shipping time variability, which is termed the SLTH strategy. Though it benefits the building contractor, this strategy puts more investment and operational pressures on the logistics provider. To solve this conflict, a coordination mechanism is introduced. Two terms are involved in this mechanism: an SLTH level related cost term is charged by the logistic provider to the building contractor and a constant transfer term is adopted to fairly allocate the system surplus. Three decentralized models are investigated: i.e. two Stackelberg game models with alternative decision-making sequences and an equal power model. Further comparative analysis and numerical studies reveal that the proposed coordination mechanism increases the SLTH level and ensures a win-win situation. Moreover, some interesting managerial implications are derived.","PeriodicalId":506995,"journal":{"name":"RAIRO - Operations Research","volume":"48 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139781640","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper aims to coordinate a shipment lead time hedging (SLTH) problem between a building contractor and a logistics provider in the prefabricated construction supply chain (PCSC). In the PCSC, untimely (early or late) delivery of prefabs will result in project time and cost overrun. To mitigate this challenge, the building contractor requires the logistics provider to reduce the shipping time variability, which is termed the SLTH strategy. Though it benefits the building contractor, this strategy puts more investment and operational pressures on the logistics provider. To solve this conflict, a coordination mechanism is introduced. Two terms are involved in this mechanism: an SLTH level related cost term is charged by the logistic provider to the building contractor and a constant transfer term is adopted to fairly allocate the system surplus. Three decentralized models are investigated: i.e. two Stackelberg game models with alternative decision-making sequences and an equal power model. Further comparative analysis and numerical studies reveal that the proposed coordination mechanism increases the SLTH level and ensures a win-win situation. Moreover, some interesting managerial implications are derived.
{"title":"Shipment lead time hedging and coordination in prefabricated construction supply chain","authors":"Zhenyi Wang, Haizi Wang, Shibin Zhang, Shuai Qiu","doi":"10.1051/ro/2024041","DOIUrl":"https://doi.org/10.1051/ro/2024041","url":null,"abstract":"This paper aims to coordinate a shipment lead time hedging (SLTH) problem between a building contractor and a logistics provider in the prefabricated construction supply chain (PCSC). In the PCSC, untimely (early or late) delivery of prefabs will result in project time and cost overrun. To mitigate this challenge, the building contractor requires the logistics provider to reduce the shipping time variability, which is termed the SLTH strategy. Though it benefits the building contractor, this strategy puts more investment and operational pressures on the logistics provider. To solve this conflict, a coordination mechanism is introduced. Two terms are involved in this mechanism: an SLTH level related cost term is charged by the logistic provider to the building contractor and a constant transfer term is adopted to fairly allocate the system surplus. Three decentralized models are investigated: i.e. two Stackelberg game models with alternative decision-making sequences and an equal power model. Further comparative analysis and numerical studies reveal that the proposed coordination mechanism increases the SLTH level and ensures a win-win situation. Moreover, some interesting managerial implications are derived.","PeriodicalId":506995,"journal":{"name":"RAIRO - Operations Research","volume":"393 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139841487","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
For a simple undirected connected graph G = (V,E), a maximal Roman dominating function (MRDF) of G is a function f : V (G) → {0,1,2} with the following properties: (i) For every vertex v ∈ {v ∈ V |f(v) = 0}, there exists a vertex u ∈ N(v) such that f(u) = 2. (ii) The set {v ∈ V |f(v) = 0} is not a dominating set of G; In other words, there exists a vertex v ∈ {v ∈ V |f(v) = 0} such that N(v) ∩ {u ∈ V |f(u) = 0} = ∅. The weight of an MRDF of G is the sum of its function values over all vertices, denoted as f(G) =Σv∈V (G)f(v), and the maximal Roman domination number of G, denoted by γmR(G), is the minimum weight of an MRDF of G. In this paper, we establish some bounds of the maximal Roman domination number of graphs. Additionally, we develop an integer linear programming formulation to compute the maximal Roman domination number of any graph. Furthermore, we prove that maximal Roman domination problem (MRD) is NP-complete even restricted to star convex bipartite graphs and chordal bipartite graphs. Lastly, we show the maximal Roman domination number of threshold graphs, trees, and block graphs can be computed in linear time.
对于简单无向连通图 G = (V,E)，G 的最大罗马支配函数（MRDF）是一个函数 f : V (G) → {0,1,2}，具有以下性质：(i) 对于每个顶点 v∈ {v∈ V |f(v) = 0}，存在一个顶点 u∈ N(v)，使得 f(u) = 2。(ii) 集合 {v∈V |f(v) = 0} 不是 G 的支配集；换句话说，存在一个顶点 v∈ {v∈V |f(v) = 0}，使得 N(v) ∩ {u∈V |f(u) = 0} = ∅。G 的 MRDF 权重是其在所有顶点上的函数值之和，表示为 f(G) =Σv∈V (G)f(v)，而 G 的最大罗马支配数（表示为 γmR(G)）是 G 的 MRDF 的最小权重。此外，我们还开发了一种整数线性规划公式来计算任意图的最大罗马支配数。此外，我们还证明了最大罗马支配数问题（MRD）即使仅限于星凸双方形图和弦双方形图也是 NP-完备的。最后，我们证明了可以在线性时间内计算阈值图、树和块图的最大罗马支配数。
{"title":"On maximal Roman domination in graphs: complexity and algorithms","authors":"Zehui Shao, Yonghao Song, Qiyun Liu, Zhixing Duan, Huiqin Jiang","doi":"10.1051/ro/2024038","DOIUrl":"https://doi.org/10.1051/ro/2024038","url":null,"abstract":"For a simple undirected connected graph G = (V,E), a maximal Roman dominating function (MRDF) of G is a function f : V (G) → {0,1,2} with the following properties: (i) For every vertex v ∈ {v ∈ V |f(v) = 0}, there exists a vertex u ∈ N(v) such that f(u) = 2. (ii) The set {v ∈ V |f(v) = 0} is not a dominating set of G; In other words, there exists a vertex v ∈ {v ∈ V |f(v) = 0} such that N(v) ∩ {u ∈ V |f(u) = 0} = ∅. The weight of an MRDF of G is the sum of its function values over all vertices, denoted as f(G) =Σv∈V (G)f(v), and the maximal Roman domination number of G, denoted by γmR(G), is the minimum weight of an MRDF of G. In this paper, we establish some bounds of the maximal Roman domination number of graphs. Additionally, we develop an integer linear programming formulation to compute the maximal Roman domination number of any graph. Furthermore, we prove that maximal Roman domination problem (MRD) is NP-complete even restricted to star convex bipartite graphs and chordal bipartite graphs. Lastly, we show the maximal Roman domination number of threshold graphs, trees, and block graphs can be computed in linear time.","PeriodicalId":506995,"journal":{"name":"RAIRO - Operations Research","volume":"59 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139840206","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
To reduce carbon emissions, many countries and regions have implemented carbon cap-and-trade regulation. The main objective of this paper is to explore the economic and environmental impacts of carbon cap-and-trade regulation on two competing supply chains. This paper considers two cases: (i) in the absence of cap-and-trade regulation and (ii) with carbon cap-and-trade regulation. For each case, there are three structures: centralized-centralized (C-C) structure, decentral-ized-decentralized (D-D) structure, and hybrid centralized-decentralized (C-D) structure. First, this paper analyzes the optimal pricing decisions of two competing supply chains for the two cases, and then explore the impacts of cap-and-trade regulation on the sale price, market demand, economy (include enterprise profits and consumer surplus), environment (i.e., carbon emission) and total social welfare. Finally, numerical examples are provided to illustrate the theoretical results. By comparing the two cases, the main conclusions are as follows: (i) cap-and-trade regulation leads to the increase of unit price and the decrease of the market demand, (ii) cap-and-trade regulation leads to the reduction of both carbon emission and the consumer surplus, (iii) the impacts of cap-and-trade regulation on the profit and social welfare depend on the carbon cap.
{"title":"Comparison of competing supply chains with different structures under cap-and-trade regulation","authors":"Yuyu Chen, Qingguo Bai, Jianteng Xu","doi":"10.1051/ro/2024040","DOIUrl":"https://doi.org/10.1051/ro/2024040","url":null,"abstract":"To reduce carbon emissions, many countries and regions have implemented carbon cap-and-trade regulation. The main objective of this paper is to explore the economic and environmental impacts of carbon cap-and-trade regulation on two competing supply chains. This paper considers two cases: (i) in the absence of cap-and-trade regulation and (ii) with carbon cap-and-trade regulation. For each case, there are three structures: centralized-centralized (C-C) structure, decentral-ized-decentralized (D-D) structure, and hybrid centralized-decentralized (C-D) structure. First, this paper analyzes the optimal pricing decisions of two competing supply chains for the two cases, and then explore the impacts of cap-and-trade regulation on the sale price, market demand, economy (include enterprise profits and consumer surplus), environment (i.e., carbon emission) and total social welfare. Finally, numerical examples are provided to illustrate the theoretical results. By comparing the two cases, the main conclusions are as follows: (i) cap-and-trade regulation leads to the increase of unit price and the decrease of the market demand, (ii) cap-and-trade regulation leads to the reduction of both carbon emission and the consumer surplus, (iii) the impacts of cap-and-trade regulation on the profit and social welfare depend on the carbon cap.","PeriodicalId":506995,"journal":{"name":"RAIRO - Operations Research","volume":"65 11","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139841627","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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