The Assignment Problem (AP) can be stated as n activities to be assigned to n resources in such a way that the overall cost of assignment is minimized and each activity is assigned to one and only one resource. In real-life, the parameters of the AP are presented as uncertain numbers due to the lack of knowledge, experiences or any other (internal or external) factor. In this paper, the AP is considered under intuitionistic triangular fuzzy number and solved by the novel constructive heuristic Dhouib-Matrix-AP1 (DM-AP1) with a time complexity of O(n). Actually, this paper presents the first enhancement of the novel heuristic DM-AP1 to solve the AP under intuitionistic triangular fuzzy environment. DM-AP1 is composed of three simple steps: computing the total cost, selecting the highest value and finding the minimal element. These steps are repeated in n iterations with the use of a standard deviation statistical metric. Two case studies of AP under intuitionistic triangular fuzzy set are taken from the literature and a step-by-step application of the novel DM-AP1 heuristic is presented for more clarification.
{"title":"Unravelling the assignment problem under intuitionistic triangular fuzzy environment by the novel heuristic Dhouib-Matrix-AP1","authors":"S. Dhouib","doi":"10.2298/yjor220915005d","DOIUrl":"https://doi.org/10.2298/yjor220915005d","url":null,"abstract":"The Assignment Problem (AP) can be stated as n activities to be assigned to n resources in such a way that the overall cost of assignment is minimized and each activity is assigned to one and only one resource. In real-life, the parameters of the AP are presented as uncertain numbers due to the lack of knowledge, experiences or any other (internal or external) factor. In this paper, the AP is considered under intuitionistic triangular fuzzy number and solved by the novel constructive heuristic Dhouib-Matrix-AP1 (DM-AP1) with a time complexity of O(n). Actually, this paper presents the first enhancement of the novel heuristic DM-AP1 to solve the AP under intuitionistic triangular fuzzy environment. DM-AP1 is composed of three simple steps: computing the total cost, selecting the highest value and finding the minimal element. These steps are repeated in n iterations with the use of a standard deviation statistical metric. Two case studies of AP under intuitionistic triangular fuzzy set are taken from the literature and a step-by-step application of the novel DM-AP1 heuristic is presented for more clarification.","PeriodicalId":52438,"journal":{"name":"Yugoslav Journal of Operations Research","volume":"56 Pt 7 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83894147","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}
Decision-making problems can often be effectively solved using traditional optimization methods that have a clearly defined configuration. However, in real-world scenarios, decision-makers frequently encounter doubt or hesitation, making it challenging to precisely specify certain parameters. As a result, they often seek input from different experts, leading to conflicting values and varying levels of satisfaction among decision-makers. This uncertainty and lack of crisp values make decision-making problems inherently non-deterministic. In this paper, a novel Pythagorean hesitant fuzzy (PHF) programming method is designed to address the challenges of optimization problems with multiple objectives. Here PHF aggregation operators are used to aggregate the PHF memberships and non-memberships of the objectives. Additionally, to account the uncertainties of the parameters of the optimization problem Parabolic Pythagorean fuzzy number is used and centroid method is applied for defuzzification. We solved an example of multi objective optimization problem of manufacturing system to demonstrate our proposed method and finally, presented a case study on reliability optimization model for Life Support Systems, where the primary objectives are to maximize system reliability and minimize cost. The result is compared with other existing methods by degree of closeness.
{"title":"A pythagorean hesitant fuzzy programming approach and its application to multi objective reliability optimization problem","authors":"Swarup Jana, Sahidul Islam","doi":"10.2298/yjor230417024j","DOIUrl":"https://doi.org/10.2298/yjor230417024j","url":null,"abstract":"Decision-making problems can often be effectively solved using traditional optimization methods that have a clearly defined configuration. However, in real-world scenarios, decision-makers frequently encounter doubt or hesitation, making it challenging to precisely specify certain parameters. As a result, they often seek input from different experts, leading to conflicting values and varying levels of satisfaction among decision-makers. This uncertainty and lack of crisp values make decision-making problems inherently non-deterministic. In this paper, a novel Pythagorean hesitant fuzzy (PHF) programming method is designed to address the challenges of optimization problems with multiple objectives. Here PHF aggregation operators are used to aggregate the PHF memberships and non-memberships of the objectives. Additionally, to account the uncertainties of the parameters of the optimization problem Parabolic Pythagorean fuzzy number is used and centroid method is applied for defuzzification. We solved an example of multi objective optimization problem of manufacturing system to demonstrate our proposed method and finally, presented a case study on reliability optimization model for Life Support Systems, where the primary objectives are to maximize system reliability and minimize cost. The result is compared with other existing methods by degree of closeness.","PeriodicalId":52438,"journal":{"name":"Yugoslav Journal of Operations Research","volume":"83 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135952772","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}
Consumers today use green, fresh, perishable products because of their freshness, healthfulness, and sustainability. In this article, we developed the continuous production inventory model for the producer who produces and sells fresh perishable products with the input of green efforts. There are two distinct kinds of product decay to take into account: products whose physical condition gradually deteriorates over time at a constant rate, and products whose freshness quality declines with time. Product demand is influenced by the selling price of the product, its freshness level, and its greening efforts. In order to increase the sales of inventory and enhance the profit from clearing stocks at the end of their life, we have adopted the markdown policy. Due to freshness degradation, a markdown strategy is adopted after a period of product deterioration to boost demand. The objectives of the study are to find out the optimal period for replenishment cycle time, the optimal value of greening efforts, and the optimal markdown percentage such that the producer?s total profit is maximum. A numerical example is used to validate a mathematical formulation that reflects real-world circumstances. A sensitivity analysis of the parameters is done to determine the model's reliability. Some significant managerial results are provided, and the article concludes with a consideration of the future scope of related research.
{"title":"An EPQ model for delay deteriorating products with price, freshness and greening efforts dependent demand under markdown strategy","authors":"Dharmesh Katariya, Kunal Shukla","doi":"10.2298/yjor230515023k","DOIUrl":"https://doi.org/10.2298/yjor230515023k","url":null,"abstract":"Consumers today use green, fresh, perishable products because of their\u0000 freshness, healthfulness, and sustainability. In this article, we developed\u0000 the continuous production inventory model for the producer who produces and\u0000 sells fresh perishable products with the input of green efforts. There are\u0000 two distinct kinds of product decay to take into account: products whose\u0000 physical condition gradually deteriorates over time at a constant rate, and\u0000 products whose freshness quality declines with time. Product demand is\u0000 influenced by the selling price of the product, its freshness level, and its\u0000 greening efforts. In order to increase the sales of inventory and enhance\u0000 the profit from clearing stocks at the end of their life, we have adopted\u0000 the markdown policy. Due to freshness degradation, a markdown strategy is\u0000 adopted after a period of product deterioration to boost demand. The\u0000 objectives of the study are to find out the optimal period for replenishment\u0000 cycle time, the optimal value of greening efforts, and the optimal markdown\u0000 percentage such that the producer?s total profit is maximum. A numerical\u0000 example is used to validate a mathematical formulation that reflects\u0000 real-world circumstances. A sensitivity analysis of the parameters is done\u0000 to determine the model's reliability. Some significant managerial results\u0000 are provided, and the article concludes with a consideration of the future\u0000 scope of related research.","PeriodicalId":52438,"journal":{"name":"Yugoslav Journal of Operations Research","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135953384","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}
The carbon footprints are increasing in the environment at an alarming rate mainly due to unplanned human activities. The world?s population will continue to grow at a rapid pace in the future. As a result, our future generations may find it difficult to live on this planet in a healthy manner. The world?s developed and developing countries began to investigate various methods for reducing their carbon footprint. However, it will not be sustainable if it is also not economically viable. In this scenario, maintaining a good profit for businesses while reducing their carbon footprint necessitates a pragmatic strategy. In this article, we will try to find a way out that will provide us with a practical solution. We will simulate the profitability of an upstream oil manufacturer that has invested heavily in green technologies. Under a carbon tax system, we will use the production-inventory model. This system assumes that capital investment in green technology can reduce emissions, and increase profits. We used data from the Oil and Natural Gas Corporation of India, available in its annual reports. As a matter of fact, the Oil and Natural Gas Corporation of India accounts for 70% of crude oil production in India and is a major player in India?s upstream oil companies. The results were quite encouraging, with deviations between expected and actual values being less than 10%. 2 Sen, Dutta Choudhury and Datta / Effect of Green Technology The findings also led us to believe that the excise duty and the pollution control tax levied in India can be regarded as a Green Tax or Carbon Tax. We used a published research model to find the optimal solution.
环境中的碳足迹正以惊人的速度增长，这主要是由于计划外的人类活动。世界吗?未来，美国人口将继续快速增长。因此，我们的后代可能会发现很难以健康的方式生活在这个星球上。世界吗?发达国家和发展中国家开始研究各种减少碳足迹的方法。然而，如果它在经济上也不可行，它将是不可持续的。在这种情况下，为企业保持良好的利润，同时减少碳足迹，需要一个务实的战略。在本文中，我们将尝试找到一条能为我们提供实际解决方案的出路。我们将模拟上游石油制造商在绿色技术上投入巨资的盈利能力。在碳税制度下，我们将使用生产-库存模型。这一体系假定对绿色技术的资本投资可以减少排放，增加利润。我们使用的数据来自印度石油和天然气公司的年度报告。事实上，印度石油天然气公司(Oil and Natural Gas Corporation of India)占印度原油产量的70%，是印度的主要参与者。美国上游石油公司。结果非常令人鼓舞，期望值和实际值之间的偏差小于10%。2 Sen, Dutta Choudhury和Datta /绿色技术的影响研究结果还使我们相信印度征收的消费税和污染控制税可以被视为绿色税或碳税。我们使用已发表的研究模型来寻找最优解。
{"title":"Effect of green technology investment on crude oil inventory system - a case study based on ONGC data","authors":"Abhibasu Sen, Karabi Dutta Choudhury, Tapan Datta","doi":"10.2298/yjor230415025s","DOIUrl":"https://doi.org/10.2298/yjor230415025s","url":null,"abstract":"The carbon footprints are increasing in the environment at an alarming rate mainly due to unplanned human activities. The world?s population will continue to grow at a rapid pace in the future. As a result, our future generations may find it difficult to live on this planet in a healthy manner. The world?s developed and developing countries began to investigate various methods for reducing their carbon footprint. However, it will not be sustainable if it is also not economically viable. In this scenario, maintaining a good profit for businesses while reducing their carbon footprint necessitates a pragmatic strategy. In this article, we will try to find a way out that will provide us with a practical solution. We will simulate the profitability of an upstream oil manufacturer that has invested heavily in green technologies. Under a carbon tax system, we will use the production-inventory model. This system assumes that capital investment in green technology can reduce emissions, and increase profits. We used data from the Oil and Natural Gas Corporation of India, available in its annual reports. As a matter of fact, the Oil and Natural Gas Corporation of India accounts for 70% of crude oil production in India and is a major player in India?s upstream oil companies. The results were quite encouraging, with deviations between expected and actual values being less than 10%. 2 Sen, Dutta Choudhury and Datta / Effect of Green Technology The findings also led us to believe that the excise duty and the pollution control tax levied in India can be regarded as a Green Tax or Carbon Tax. We used a published research model to find the optimal solution.","PeriodicalId":52438,"journal":{"name":"Yugoslav Journal of Operations Research","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135448851","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 paper, we investigate bounds on eigenvalues of real symmetric interval matrices. We present a method that computes bounds on eigenvalues of real symmetric interval matrices. It outperforms many methods developed in the literature and produces as sharp as possible bounds on eigenvalues of real symmetric interval matrices. The aim is to apply the proposed method to compute lower bounds on eigenvalues of a symmetric interval hessian matrix of a nonconvex function in the ?BB method and use them to produce a tighter underestimator that improves the ?BB algorithm for solving global optimization problems. In the end, we illustrate by example, the comparison of various approaches of bounding eigenvalues of real symmetric interval matrices. Moreover, a set of test problems found in the literature are solved efficiently and the performances of the proposed method are compared with those of other methods.
{"title":"Bounds on eigenvalues of real symmetric interval matrices for αBB method in global optimization","authors":"Djamel Zerrouki, Mohand Ouanes","doi":"10.2298/yjor230315019z","DOIUrl":"https://doi.org/10.2298/yjor230315019z","url":null,"abstract":"In this paper, we investigate bounds on eigenvalues of real symmetric interval matrices. We present a method that computes bounds on eigenvalues of real symmetric interval matrices. It outperforms many methods developed in the literature and produces as sharp as possible bounds on eigenvalues of real symmetric interval matrices. The aim is to apply the proposed method to compute lower bounds on eigenvalues of a symmetric interval hessian matrix of a nonconvex function in the ?BB method and use them to produce a tighter underestimator that improves the ?BB algorithm for solving global optimization problems. In the end, we illustrate by example, the comparison of various approaches of bounding eigenvalues of real symmetric interval matrices. Moreover, a set of test problems found in the literature are solved efficiently and the performances of the proposed method are compared with those of other methods.","PeriodicalId":52438,"journal":{"name":"Yugoslav Journal of Operations Research","volume":"56 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77177446","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}
The agricultural production system composes of several conflicting resources that must be combined to yield the desired product output. However, some goals are not conflicting in the system; therefore, this study presents a multi-objective optimization problem using a multi-fractional fuzzy programming concept. The objective is to optimize the profit ratio to cash expenditure and production of crops in different seasons under the restriction of fertilizer, machine, manpower, water consumption, and land utilization. The proposed model is illustrated with numerical examples for validation from an agrirean village in northern Nigeria. The result shows meaningful achievements and improvement in six crops out of the seven crops for both the dry and rainy seasons. Thus the concept is recommended for decision-makers for proper planning and productive yield in the agricultural industry for ensuring food security and the global sustainable developments.
{"title":"Multi-fractional fuzzy programming for sustainable agricultural multi-cropping bi-seasonal planning","authors":"Umar Muhammad Modibbo","doi":"10.2298/yjor220516026m","DOIUrl":"https://doi.org/10.2298/yjor220516026m","url":null,"abstract":"The agricultural production system composes of several conflicting resources that must be combined to yield the desired product output. However, some goals are not conflicting in the system; therefore, this study presents a multi-objective optimization problem using a multi-fractional fuzzy programming concept. The objective is to optimize the profit ratio to cash expenditure and production of crops in different seasons under the restriction of fertilizer, machine, manpower, water consumption, and land utilization. The proposed model is illustrated with numerical examples for validation from an agrirean village in northern Nigeria. The result shows meaningful achievements and improvement in six crops out of the seven crops for both the dry and rainy seasons. Thus the concept is recommended for decision-makers for proper planning and productive yield in the agricultural industry for ensuring food security and the global sustainable developments.","PeriodicalId":52438,"journal":{"name":"Yugoslav Journal of Operations Research","volume":"96 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75896482","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}
Redundancy-allocation problem i.e. RAP is among the reliability optimization problems which make use of non-linear programming method to improve the reliability of complex system. The objective of this research paper is reliability optimization through the application of Genetic Algorithm i.e. GA and Hybrid Genetic & Particle Swarm Optimization (H-GAPSO) on a RAP. Certain shortcomings have been seen when results are obtained by application of single algorithms. In order to get rid of these shortcomings, HGA-PSO is introduced where attractive properties of GA and PSO are combined. This hybrid method makes use of iterative process of GA after obtaining initial best population from PSO. Comparative Analysis of results of GA and H-GAPSO is done with respect to reliability and computation (CPU) time and it is observed that H-GAPSO improved system reliability up to maximum by 63.10%. MATLprogramming has been used for computation of results from GA and HGA-PSO algorithms.
{"title":"Reliability optimization using hybrid genetic and particle swarm optimization algorithm","authors":"Tripti Dahiya, D. Garg","doi":"10.2298/yjor220316020d","DOIUrl":"https://doi.org/10.2298/yjor220316020d","url":null,"abstract":"Redundancy-allocation problem i.e. RAP is among the reliability optimization problems which make use of non-linear programming method to improve the reliability of complex system. The objective of this research paper is reliability optimization through the application of Genetic Algorithm i.e. GA and Hybrid Genetic & Particle Swarm Optimization (H-GAPSO) on a RAP. Certain shortcomings have been seen when results are obtained by application of single algorithms. In order to get rid of these shortcomings, HGA-PSO is introduced where attractive properties of GA and PSO are combined. This hybrid method makes use of iterative process of GA after obtaining initial best population from PSO. Comparative Analysis of results of GA and H-GAPSO is done with respect to reliability and computation (CPU) time and it is observed that H-GAPSO improved system reliability up to maximum by 63.10%. MATLprogramming has been used for computation of results from GA and HGA-PSO algorithms.","PeriodicalId":52438,"journal":{"name":"Yugoslav Journal of Operations Research","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82113176","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 paper a special kind of variational programming problem involving fractional interval-valued objective function is considered. For such type of problem, insights into LU optimal solutions have been discussed. Using the LU optimal concept, we established optimality conditions for the considered problem. Further, We formulated a Mond-Weir dual problem and discussed appropriate duality theorems for the relationship between dual and primal problems.
{"title":"Necessary and sufficient optimality conditions for fractional interval-valued variational problems","authors":"Vivekananda Rayanki, K. Kummari","doi":"10.2298/yjor210815028r","DOIUrl":"https://doi.org/10.2298/yjor210815028r","url":null,"abstract":"In this paper a special kind of variational programming problem involving fractional interval-valued objective function is considered. For such type of problem, insights into LU optimal solutions have been discussed. Using the LU optimal concept, we established optimality conditions for the considered problem. Further, We formulated a Mond-Weir dual problem and discussed appropriate duality theorems for the relationship between dual and primal problems.","PeriodicalId":52438,"journal":{"name":"Yugoslav Journal of Operations Research","volume":"31 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75951208","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 paper, we discuss a batch arrival bulk service queue with rework for the faculty item, possibility of breakdown, repair, and two kinds of multiple vacation with different threshold policy. The server serves the remaining service after repair completion. This type of queueing model has a lot of applications in the manufacturing/production industries. Performance measures and stability conditions are obtained. Numerical illustrations are made to examine the validity of analytical results.
{"title":"Analysis of bulk service queuing system with rework, unreliable server, resuming service and two kinds of multiple vacation","authors":"S. Karpagam","doi":"10.2298/yjor210719009k","DOIUrl":"https://doi.org/10.2298/yjor210719009k","url":null,"abstract":"In this paper, we discuss a batch arrival bulk service queue with rework for the faculty item, possibility of breakdown, repair, and two kinds of multiple vacation with different threshold policy. The server serves the remaining service after repair completion. This type of queueing model has a lot of applications in the manufacturing/production industries. Performance measures and stability conditions are obtained. Numerical illustrations are made to examine the validity of analytical results.","PeriodicalId":52438,"journal":{"name":"Yugoslav Journal of Operations Research","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74650555","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}
We consider the following 2-clustering problem. Given N points in Euclidean space, partition it into two subsets (clusters) so that the sum of squared distances between the elements of the clusters and their centers would be minimum. The center of the first cluster coincides with its centroid (mean) while the center of the second cluster should be chosen from the set of the initial points (medoid). It is known that this problem is NP-hard if the cardinalities of the clusters are given as a part of the input. In this paper we prove that the problem remains NP-hard in the case of arbitrary clusters sizes and suggest a 2-approximation polynomial-time algorithm for this problem.
{"title":"1-mean and 1-medoid 2-clustering problem with arbitrary cluster sizes: Complexity and approximation","authors":"A. Pyatkin","doi":"10.2298/yjor211018008p","DOIUrl":"https://doi.org/10.2298/yjor211018008p","url":null,"abstract":"We consider the following 2-clustering problem. Given N points in Euclidean space, partition it into two subsets (clusters) so that the sum of squared distances between the elements of the clusters and their centers would be minimum. The center of the first cluster coincides with its centroid (mean) while the center of the second cluster should be chosen from the set of the initial points (medoid). It is known that this problem is NP-hard if the cardinalities of the clusters are given as a part of the input. In this paper we prove that the problem remains NP-hard in the case of arbitrary clusters sizes and suggest a 2-approximation polynomial-time algorithm for this problem.","PeriodicalId":52438,"journal":{"name":"Yugoslav Journal of Operations Research","volume":"46 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85469440","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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