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An optimization method to solve a fully intuitionistic fuzzy non-linear separable programming problem 求解全直觉模糊非线性可分规划问题的优化方法
4区 管理学
Rairo-Operations Research Pub Date : 2023-09-21 DOI: 10.1051/ro/2023152
Kirti Sharma, VISHNU PRATAP SINGH, Bhavin Poojara, Ali Ebrahimnejad, Debjani Chakraborty
{"title":"An optimization method to solve a fully intuitionistic fuzzy non-linear separable programming problem","authors":"Kirti Sharma, VISHNU PRATAP SINGH, Bhavin Poojara, Ali Ebrahimnejad, Debjani Chakraborty","doi":"10.1051/ro/2023152","DOIUrl":"https://doi.org/10.1051/ro/2023152","url":null,"abstract":"This paper presents an optimization method to solve a non-linear separable programming problem with coefficients and variables as generalized trapezoidal intuitionistic fuzzy numbers. Such optimization problems are known as fully intuitionistic fuzzy non-linear separable programming problems. The optimization method is based on the linear approximation of fully intuitionistic fuzzy non-linear separable functions. The concept of an intuitionistic fuzzy line segment between two intuitionistic fuzzy points is introduced to find the required linear approximation. In this way, a fully intuitionistic fuzzy non-linear programming problem is converted into an intuitionistic fuzzy linear programming problem. The defuzzification and component-wise comparison techniques are then used to convert the fully intuitionistic fuzzy linear programming problem to a linear programming problem with crisp coefficients which can then be solved by using traditional optimization techniques. The application of the proposed approach in an investment problem faced by a businessman has been presented.","PeriodicalId":54509,"journal":{"name":"Rairo-Operations Research","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136155443","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Modular design of new products and remanufacturing of used products under mass customization 大规模定制下的新产品模块化设计与旧产品再制造
4区 管理学
Rairo-Operations Research Pub Date : 2023-09-21 DOI: 10.1051/ro/2023151
Honglin Yang, Lan Jiang
{"title":"Modular design of new products and remanufacturing of used products under mass customization","authors":"Honglin Yang, Lan Jiang","doi":"10.1051/ro/2023151","DOIUrl":"https://doi.org/10.1051/ro/2023151","url":null,"abstract":"Modular architecture design can not only increase the product variety and thus make mass customization (MC) easier, but also improve interchangeability and then lower the remanufacturing cost. This paper models a remanufacturing MC supply chain with one manufacturer and one retailer. The manufacturer, as a Stackelberg game leader, designs and then sells the new and modular MC products via its brand retailer, and meanwhile the remanufacturing of used MC products would be carried out by either the manufacturer or the retailer. We study the optimal modular design for new MC products and the best remanufacturing mode for used MC products. One centralized and two decentralized decision models are formulated, and the equilibrium solutions of proposed models are compared and analyzed. Findings show that, compared to the retailer-remanufacturing mode, the manufacturer-remanufacturing mode can be superior in terms of the ability to cope with customer customization requirements (i.e., the modularity level), total supply chain profit, and consumer surplus. Moreover, both supply chain members and consumers would prefer the manufacturer-remanufacturing mode when the parameters meet certain conditions. We also extend the model to two scenarios: the remanufacturing is bounded by cores supply and the retailer acts a leader, so as to verify the robustness of main results. Numerical examples demonstrate the theoretical results.","PeriodicalId":54509,"journal":{"name":"Rairo-Operations Research","volume":"75 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136155435","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the degree of trees with Game Chromatic Number 4 论游戏色数为4的树的度
4区 管理学
Rairo-Operations Research Pub Date : 2023-09-19 DOI: 10.1051/ro/2023150
Ana Luísa C. Furtado, Miguel Alfredo Del Rio Palma, Simone Dantas, Celina M. H. de Figueiredo
{"title":"On the degree of trees with Game Chromatic Number 4","authors":"Ana Luísa C. Furtado, Miguel Alfredo Del Rio Palma, Simone Dantas, Celina M. H. de Figueiredo","doi":"10.1051/ro/2023150","DOIUrl":"https://doi.org/10.1051/ro/2023150","url":null,"abstract":"The coloring game is played by Alice and Bob on a finite graph $G$. They take turns properly coloring the vertices with $t$ colors. The goal of Alice is to color the input graph with t colors, and Bob does his best to prevent it. If at any point there exists an uncolored vertex without available color, then Bob wins; otherwise Alice wins. The game chromatic number $chi_g(G)$ of $G$ is the smallest number $t$ such that Alice has a winning strategy. In 1991, Bodlaender showed the smallest tree $T$ with $chi_g(T)$ equal to $4$, and in 1993 Faigle et al. proved that every tree $T$ satisfies the upper bound $chi_g(T) leq 4$. The stars $T = K_{1,p}$ with $pgeq 1$ are the only trees satisfying $chi_{g}(T)=2$; and the paths $T= P_n$, $ngeq 4$, satisfy $chi_{g}(T)=3$. Despite the vast literature in this area, there does not exist a characterization of trees with $chi_g(T) = 3$ or $4$. We answer a question about the required degree to ensure $chi_g(T) = 4$, by exhibiting infinitely many trees with maximum degree 3 and game chromatic number 4.","PeriodicalId":54509,"journal":{"name":"Rairo-Operations Research","volume":"143 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135059495","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On two variants of split graphs: 2-unipolar graph and k-probe-split graph 关于分裂图的两个变体:2-单极图和k-探针分裂图
4区 管理学
Rairo-Operations Research Pub Date : 2023-09-15 DOI: 10.1051/ro/2023149
Luciano N. Grippo, Verónica A. Moyano
{"title":"On two variants of split graphs: 2-unipolar graph and k-probe-split graph","authors":"Luciano N. Grippo, Verónica A. Moyano","doi":"10.1051/ro/2023149","DOIUrl":"https://doi.org/10.1051/ro/2023149","url":null,"abstract":"A graph is called split if its vertex set can be partitioned into a stable set and a clique. In this article, we studied two variants of split graphs. A graph G is polar if its vertex set can be partitioned into two sets A and B such that G[A] is a complete multipartite graph and G[B] is a disjoint union of complete graphs. A 2-unipolar graph is a polar graph G such that G[A] is a clique and G[B] is the disjoint union of complete graphs with at most two vertices. We present a minimal forbidden induced subgraph characterization for 2-unipolar graphs. In addition, we show that they can be represented as an intersection of substars of special cacti. Let G be a graph class, the G-width of a graph G is the minimum positive integer k such that there exist k independent sets N1,...,Nk such that a set F of nonedges of G, whose endpoints belong to some Ni with i = 1,...,k, can be added so that the resulting graph G0 belongs to G. We say that a graph G is k-probe-G if it has G-width at most k and when G is the class of split graphs it is denominated k-probe-split. We prove that deciding, given a graph G and a positive integer k, whether G is a h-probe-split graph for some h ≤ k is NP-complete. Besides, a characterization by minimal forbidden induced subgraphs for 2-probesplit cographs is presented.","PeriodicalId":54509,"journal":{"name":"Rairo-Operations Research","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135437003","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Modelling the forest harvesting tour problem 森林采伐旅游问题的建模
4区 管理学
Rairo-Operations Research Pub Date : 2023-09-11 DOI: 10.1051/ro/2023142
Víctor Viana, Héctor Cancela, Lorena Pradenas
{"title":"Modelling the forest harvesting tour problem","authors":"Víctor Viana, Héctor Cancela, Lorena Pradenas","doi":"10.1051/ro/2023142","DOIUrl":"https://doi.org/10.1051/ro/2023142","url":null,"abstract":"In a globalized market, forest management plans play an important role in the sustainability of forest enterprises. Several optimization processes have therefore been developed to support decision-making in forestry operations. However, important issues remain to be addressed, such as planning the allocation of harvesting areas and scheduling the harvesting teams that are contracted for these purposes. Harvesting schedules include different time scales and natural constraints, so that finding optimal or even good quality ones constitutes a highly complex combinatorial optimization problem. Efficient planning of harvesting operations can significantly reduce the costs associated with logistics and improve the economic performance of companies in the sector. In Uruguay, almost 75% of total forest harvesting operations for pulp production are carried out by contractor companies, so they are an important player in the supply chain. This study aims to optimize the allocation and routing of the harvesting equipment of forest contractors, which must be located at the sites to be harvested during the year. Numerical experiments over a case study based on realistic data have shown that realistic-sized instances can be resolved by standard mathematical programming software in a reasonable time. The mathematical programming model can also be useful to evaluate potential gains in joint planning by several contractors with respect to the costs incurred by separate planning; as illustrated also with numerical examples over the same case study. This model can be used to support annual forest harvest scheduling and equipment allocation for corporate contractors, leading to better quality plans and improvement opportunities.","PeriodicalId":54509,"journal":{"name":"Rairo-Operations Research","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135981534","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Bounds for Aα-eigenvalues a α-特征值的界
4区 管理学
Rairo-Operations Research Pub Date : 2023-09-11 DOI: 10.1051/ro/2023144
João Domingos Gomes da Silva Júnior, Carla Silva Oliveira, Liliana Manuela G. C. da Costa
{"title":"Bounds for Aα-eigenvalues","authors":"João Domingos Gomes da Silva Júnior, Carla Silva Oliveira, Liliana Manuela G. C. da Costa","doi":"10.1051/ro/2023144","DOIUrl":"https://doi.org/10.1051/ro/2023144","url":null,"abstract":"Let G be a graph with adjacency matrix A(G) and degree diagonal matrix D(G). In 2017, Nikiforov [1] defined the matrix Aα(G), as a convex combination of A(G) and D(G), the following way, Aα(G) = αA(G) + (1 − α)D(G), where α ∈ [0,1]. In this paper we present some new upper and lower bounds for the largest, second largest and the smallest eigenvalue of Aα-matrix. Moreover, extremal graphs attaining some of these bounds are characterized.","PeriodicalId":54509,"journal":{"name":"Rairo-Operations Research","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135937977","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Optimal strategies for green supply chains with competition between green and traditional suppliers 绿色供应商与传统供应商竞争下的绿色供应链优化策略
4区 管理学
Rairo-Operations Research Pub Date : 2023-09-11 DOI: 10.1051/ro/2023141
Jing Cong, Tao Pang, Hongjun Peng
{"title":"Optimal strategies for green supply chains with competition between green and traditional suppliers","authors":"Jing Cong, Tao Pang, Hongjun Peng","doi":"10.1051/ro/2023141","DOIUrl":"https://doi.org/10.1051/ro/2023141","url":null,"abstract":"We consider a green supply chain that consists of a traditional supplier, a green supplier, and a manufacturer. We investigate the optimal strategies for the suppliers' raw material prices, and the manufacturer's production and green raw material ordering. In particular, we consider three price competition models: the traditional supplier-led model, the green supplier-led model, and the Nash game model. The results indicate that the more dominant the green supplier, the more likely the green material price will be higher than the traditional material price. In addition, the manufacturers' product greenness level is the lowest under the green supplier-led model and the highest under the traditional supplier-led model. We also find that, as the manufacturer's yield uncertainty increases, the prices of traditional and green raw materials both decrease with respect to the manufacturer's product greenness level. Moreover, as customers' green preference increases, the price of green raw materials increases, the price of traditional raw materials decreases, and the product greenness level increases.","PeriodicalId":54509,"journal":{"name":"Rairo-Operations Research","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135937973","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Frèchet normal cone for nonsmooth mathematical programming problems with switching constraints                           具有切换约束的非光滑数学规划问题的fr<s:1>切法线锥
IF 1.8 4区 管理学
Rairo-Operations Research Pub Date : 2023-09-08 DOI: 10.1051/ro/2023138
Balendu Bhooshan Upadhyay, Zahra Jafariani, Nader Kanzi, Maryam Naderi Parizi
{"title":"On Frèchet normal cone for nonsmooth mathematical programming problems with switching constraints\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":"Balendu Bhooshan Upadhyay, Zahra Jafariani, Nader Kanzi, Maryam Naderi Parizi","doi":"10.1051/ro/2023138","DOIUrl":"https://doi.org/10.1051/ro/2023138","url":null,"abstract":"This paper is devoted to the study of a class of nonsmooth programming problems with switching constraints (abbreviated as, (NMPSC)), where all the involved functions in the switching constraints are assumed to be locally Lipschitz. We investigate the properties of Frèchet normal cone of (NMPSC). In particular, we introduce two Guignard type constraint qualifications for (NMPSC) in terms of Michel-Penot subdifferential. Moreover, we derive two estimates for the Fr‘echet normal cone of (NMPSC) and further establish stationarity conditions at an optimal solution for (NMPSC). To the best of our knowledge, this is for the first time Frèchet normal cone for (NMPSC) have been studied in the setting of Euclidean spaces.","PeriodicalId":54509,"journal":{"name":"Rairo-Operations Research","volume":"3 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82113068","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Optimal investment and consumption strategies for an investor with stochastic economic factor in a defaultable market 违约市场中具有随机经济因素的投资者的最优投资与消费策略
IF 1.8 4区 管理学
Rairo-Operations Research Pub Date : 2023-09-08 DOI: 10.1051/ro/2023139
Weiwei Shen, Juliang Yin
{"title":"Optimal investment and consumption strategies for an investor with stochastic economic factor in a defaultable market","authors":"Weiwei Shen, Juliang Yin","doi":"10.1051/ro/2023139","DOIUrl":"https://doi.org/10.1051/ro/2023139","url":null,"abstract":"This paper considers the issue of optimal investment and consumption strategies for an investor with stochastic economic factor in a defaultable market. In our model, the price process is composed of a money market account and a default-free risky asset, assuming they rely on a stochastic economic factor described by a diffusion process. A defaultable perpetual bond is depicted by the reduced-form model, and both the default risk premium and the default intensity of it rely on the stochastic economic factor. Our goal is to maximize the infinite horizon expected discounted power utility of the consumption. Applying the dynamic programming principle, we derive the Hamilton--Jacobi--Bellman (HJB) equations and analyze them using the so-called sub-super solution method to prove the existence and uniqueness of their classical solutions. Next, we use a verification theorem to derive the explicit formula for optimal investment and consumption strategies. Finally, we provide a sensitivity analysis.","PeriodicalId":54509,"journal":{"name":"Rairo-Operations Research","volume":"32 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73521029","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Optimizing retailer's order and financing decisions on an e-commercial platform considering cash flow 考虑现金流的电子商务平台上零售商订单和融资决策优化
IF 1.8 4区 管理学
Rairo-Operations Research Pub Date : 2023-09-07 DOI: 10.1051/ro/2023137
Honglin Yang, Yue Yu
{"title":"Optimizing retailer's order and financing decisions on an e-commercial platform considering cash flow","authors":"Honglin Yang, Yue Yu","doi":"10.1051/ro/2023137","DOIUrl":"https://doi.org/10.1051/ro/2023137","url":null,"abstract":"The mismatch in cash flow often distorts business operational decisions and even lead to bankruptcy for enterprises. This paper investigates the order and financing decisions of a capital-constrained retailer who borrows from an e-commerce platform to fund its business operations. The e-commercial platform, which has full capital, provides three financing schemes: (1) lump-sum repayment (scheme L), (2) average capital plus interest repayment (scheme P), and (3) average capital repayment (scheme A). We first model the financing behaviors of the retailer and determine the circumstances in which the retailer favors a specific financing scheme. Then, we propose a viable cash flow matching strategy in which the retailer retains a portion of its initial capital to address potential repayment shortfalls in each period. To the best of our knowledge, this paper is the first to integrate the capital-constrained retailer’s cash flow management into the platform financing scheme. The results show that: In the absence of cash flow considerations, the retailer prefers scheme L since selecting scheme P or A may lead to bankruptcy. In contrast, if the cash flow matching is efficiently realized, the retailer always prefers scheme P to enhance its performance. Numerical examples are used to validate the theoretical results.","PeriodicalId":54509,"journal":{"name":"Rairo-Operations Research","volume":"14 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72711123","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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