In this study, we investigate multi-objective decision making problems with respect to a variable domination structure. In order to solve such problems, we introduce two types of solutions from vector optimization problems with respect to a variable domination structure; afterward, we characterize them. These solution concepts are helpful in multi-objective decision making problems where different preferences or restrictions of objective functions for different alternatives are at hand; or where different preferences of objective functions with respect to different objective functions are assumed. These solution concepts are proposed for multi-objective location problems where there are different preferences of objective functions at each location; our results are applied for selecting a location to establish an outlet store.
{"title":"Multi-Objective Decision Making Problems with Variable Domination Structure","authors":"Bettina Zargini","doi":"10.15807/jorsj.65.105","DOIUrl":"https://doi.org/10.15807/jorsj.65.105","url":null,"abstract":"In this study, we investigate multi-objective decision making problems with respect to a variable domination structure. In order to solve such problems, we introduce two types of solutions from vector optimization problems with respect to a variable domination structure; afterward, we characterize them. These solution concepts are helpful in multi-objective decision making problems where different preferences or restrictions of objective functions for different alternatives are at hand; or where different preferences of objective functions with respect to different objective functions are assumed. These solution concepts are proposed for multi-objective location problems where there are different preferences of objective functions at each location; our results are applied for selecting a location to establish an outlet store.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41726637","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}
{"title":"STRONG CONDORCET CRITERION FOR THE LINEAR ORDERING PROBLEM","authors":"Kazutoshi Ando, Noriyoshi Sukegawa, S. Takagi","doi":"10.15807/jorsj.65.67","DOIUrl":"https://doi.org/10.15807/jorsj.65.67","url":null,"abstract":"","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49444391","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}
Abstract This paper considers the computation of the transient-state probabilities in time-inhomogenous continuous-time Markov chains. We first introduce a new class of time-inhomogenous Markov chains, which is closely related to the phase-type representation of non-negative probability distributions. We show that the introduced class of Markov chains covers a wide-class of time-inhomogenous Markov chains. We then develop a computational method of the transient-state probabilities in Markov chains of this class, which is an extension of the uniformization method in time-homogeneous Markov chains. The developed computational method has a remarkable feature that the time-discretization of the generator is not necessary, as opposed to previously known methods in the literature.
{"title":"A NEW APPROACH TO COMPUTING THE TRANSIENT-STATE PROBABILITIES IN TIME-INHOMOGENEOUS MARKOV CHAINS","authors":"Yoshiaki Inoue","doi":"10.15807/jorsj.65.48","DOIUrl":"https://doi.org/10.15807/jorsj.65.48","url":null,"abstract":"Abstract This paper considers the computation of the transient-state probabilities in time-inhomogenous continuous-time Markov chains. We first introduce a new class of time-inhomogenous Markov chains, which is closely related to the phase-type representation of non-negative probability distributions. We show that the introduced class of Markov chains covers a wide-class of time-inhomogenous Markov chains. We then develop a computational method of the transient-state probabilities in Markov chains of this class, which is an extension of the uniformization method in time-homogeneous Markov chains. The developed computational method has a remarkable feature that the time-discretization of the generator is not necessary, as opposed to previously known methods in the literature.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43324733","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 1991, Adler and Cosares proposed a strongly polynomial time algorithm for an LP problem with a pre-Leontief coefficient matrix and pointed out that the algorithm can be efficiently applied to a generalized transshipment problem. In their generalized transshipment problem, a given demand is satisfied at each vertex except for a distinguished one while we impose the demand condition on all the vertices. Their approach is as follows: By using Veinott’s matrix partition theorem, they partitioned the coefficient matrix into four submatrices including a Leontief submatrix, and these partitioned matrices were utilized in their algorithm. We suggest that the theorem needs more refinement. In order to clarify the suggestion, we refined the theorem to a new one by incorporating trivialities/nontrivialities of the rows and columns of a matrix whose notions were introduced by Veinott. With the help of the refined theorem, we have developed a new strongly polynomial time flow-based algorithm for a broader class of problems including their problem. In the paper by Adler and Cosares, we can not see any algorithm for finding how to divide the columns of the coefficient matrix into two sets when we partition the matrix. Given a coefficient matrix partitioned, our comlexity is the same as theirs. Our main contribution is the following two: 1) The developed algorithm can also determine the feasibility of the generalized transshipment problem, and our complexity is much smaller than theirs; 2) We showed an efficient algorithm for partitioning the given coefficient matrix into such four submatrices by introducing the trivialities/nontrivialities explained above.
{"title":"A STRONGLY POLYNOMIAL TIME ALGORITHM FOR AN LP PROBLEM WITH A PRE-LEONTIEF COEFFICIENT MATRIX","authors":"A. Nakayama, T. Anazawa, Yudai Iwaki","doi":"10.15807/jorsj.65.23","DOIUrl":"https://doi.org/10.15807/jorsj.65.23","url":null,"abstract":"In 1991, Adler and Cosares proposed a strongly polynomial time algorithm for an LP problem with a pre-Leontief coefficient matrix and pointed out that the algorithm can be efficiently applied to a generalized transshipment problem. In their generalized transshipment problem, a given demand is satisfied at each vertex except for a distinguished one while we impose the demand condition on all the vertices. Their approach is as follows: By using Veinott’s matrix partition theorem, they partitioned the coefficient matrix into four submatrices including a Leontief submatrix, and these partitioned matrices were utilized in their algorithm. We suggest that the theorem needs more refinement. In order to clarify the suggestion, we refined the theorem to a new one by incorporating trivialities/nontrivialities of the rows and columns of a matrix whose notions were introduced by Veinott. With the help of the refined theorem, we have developed a new strongly polynomial time flow-based algorithm for a broader class of problems including their problem. In the paper by Adler and Cosares, we can not see any algorithm for finding how to divide the columns of the coefficient matrix into two sets when we partition the matrix. Given a coefficient matrix partitioned, our comlexity is the same as theirs. Our main contribution is the following two: 1) The developed algorithm can also determine the feasibility of the generalized transshipment problem, and our complexity is much smaller than theirs; 2) We showed an efficient algorithm for partitioning the given coefficient matrix into such four submatrices by introducing the trivialities/nontrivialities explained above.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44417928","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 discrete convex analysis, various convexity concepts are considered for discrete functions such as separable convexity, L-convexity, M-convexity, integral convexity, and multimodularity. These concepts of discrete convex functions are not mutually independent. For example, M-natural-convexity is a special case of integral convexity, and the combination of L-natural-convexity and M-natural-convexity coincides with separable convexity. This paper aims at a fairly comprehensive analysis of the inclusion and intersection relations for various classes of discrete convex functions. Emphasis is put on the analysis of multimodularity in relation to L-natural-convexity and M-natural-convexity.
{"title":"INCLUSION AND INTERSECTION RELATIONS BETWEEN FUNDAMENTAL CLASSES OF DISCRETE CONVEX FUNCTIONS","authors":"Satoko Moriguchi, K. Murota","doi":"10.15807/jorsj.66.187","DOIUrl":"https://doi.org/10.15807/jorsj.66.187","url":null,"abstract":"In discrete convex analysis, various convexity concepts are considered for discrete functions such as separable convexity, L-convexity, M-convexity, integral convexity, and multimodularity. These concepts of discrete convex functions are not mutually independent. For example, M-natural-convexity is a special case of integral convexity, and the combination of L-natural-convexity and M-natural-convexity coincides with separable convexity. This paper aims at a fairly comprehensive analysis of the inclusion and intersection relations for various classes of discrete convex functions. Emphasis is put on the analysis of multimodularity in relation to L-natural-convexity and M-natural-convexity.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45826141","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 presents an analytical model for determining the height and shape of a building. The average travel distances of external and internal traffic are obtained for a multi-story building with rectangular floors. The analytical expressions for the average distances demonstrate how the number of floors and the total floor area affect the travel distance in the building. The optimal number of floors that minimizes the average distance is then obtained. The effects of the shape of floors and the locations of the escalator and entrance on the average distance and the optimal number of floors are also examined. The result shows that a one-story building can be optimal if the total floor area is small and the internal traffic is dominant and that the diamond floor is superior to the square and rectangular floors.
{"title":"OPTIMAL HEIGHT AND SHAPE OF A BUILDING WITH EXTERNAL AND INTERNAL TRAFFIC","authors":"M. Miyagawa","doi":"10.15807/jorsj.64.203","DOIUrl":"https://doi.org/10.15807/jorsj.64.203","url":null,"abstract":"This paper presents an analytical model for determining the height and shape of a building. The average travel distances of external and internal traffic are obtained for a multi-story building with rectangular floors. The analytical expressions for the average distances demonstrate how the number of floors and the total floor area affect the travel distance in the building. The optimal number of floors that minimizes the average distance is then obtained. The effects of the shape of floors and the locations of the escalator and entrance on the average distance and the optimal number of floors are also examined. The result shows that a one-story building can be optimal if the total floor area is small and the internal traffic is dominant and that the diamond floor is superior to the square and rectangular floors.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45848517","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}
An interval game is an extension of characteristic function form games in which players are assumed to face payoff uncertainty and thus the characteristic function assigns a closed interval, instead of a real number. In this study, we propose a new solution mapping of two-person interval games. We provide a collection of four axioms, consisting of Efficiency, Individual Rationality, and interval game versions of Shapley’s Additivity and Nash’s Independence of Irrelevant Alternatives, and show that the new solution mapping uniquely satisfies these axioms.
{"title":"A SOLUTION MAPPING AND ITS AXIOMATIZATION IN TWO-PERSON INTERVAL GAMES","authors":"S. Ishihara, Junnosuke Shino","doi":"10.15807/jorsj.64.214","DOIUrl":"https://doi.org/10.15807/jorsj.64.214","url":null,"abstract":"An interval game is an extension of characteristic function form games in which players are assumed to face payoff uncertainty and thus the characteristic function assigns a closed interval, instead of a real number. In this study, we propose a new solution mapping of two-person interval games. We provide a collection of four axioms, consisting of Efficiency, Individual Rationality, and interval game versions of Shapley’s Additivity and Nash’s Independence of Irrelevant Alternatives, and show that the new solution mapping uniquely satisfies these axioms.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46029578","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}
Robin Schneider, H. Hirakawa, Noboru Hosoda, Rong Jin, J. Imai
{"title":"ESTIMATING PARAMETERS FOR TECHNOLOGY INVESTMENTS: AN APPLICATION TO 3D PRINTING","authors":"Robin Schneider, H. Hirakawa, Noboru Hosoda, Rong Jin, J. Imai","doi":"10.15807/jorsj.64.129","DOIUrl":"https://doi.org/10.15807/jorsj.64.129","url":null,"abstract":"","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42600102","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 consider fuzzy matrix games, namely, two-person zero-sum games with fuzzy payoffs. For such games, we define three kinds of concepts of minimax equilibrium strategies based on fuzzy max order, and their properties are investigated. Then, these minimax equilibrium strategies are characterized as Nash equilibrium strategies of a family of parametric bi-matrix games with crisp payoffs, where ‘crisp’ means ‘non-fuzzy’. Moreover, numerical examples are presented to illustrate utility of the obtained results.
{"title":"ON CHARACTERIZATION OF EQUILIBRIUM STRATEGY FOR MATRIX GAMES WITH L-R FUZZY PAYOFFS","authors":"Masamichi Kon","doi":"10.15807/jorsj.64.158","DOIUrl":"https://doi.org/10.15807/jorsj.64.158","url":null,"abstract":"In this paper, we consider fuzzy matrix games, namely, two-person zero-sum games with fuzzy payoffs. For such games, we define three kinds of concepts of minimax equilibrium strategies based on fuzzy max order, and their properties are investigated. Then, these minimax equilibrium strategies are characterized as Nash equilibrium strategies of a family of parametric bi-matrix games with crisp payoffs, where ‘crisp’ means ‘non-fuzzy’. Moreover, numerical examples are presented to illustrate utility of the obtained results.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48740976","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 develops a bi-objective model for determining the location and shape of two finite-size facilities. The objectives are to minimize both the closest and barrier distances. The former represents the accessibility of customers, whereas the latter represents the interference to travelers. The total closest and barrier distances are derived for two rectangular facilities in a rectangular city where the distance is measured as the rectilinear distance. The analytical expressions for the total closest and barrier distances demonstrate how the location and shape of the facilities affect the distances. A numerical example shows that there exists a tradeoff between the closest and barrier distances. The tradeoff curve provides planners with alternatives for the location and shape of the facilities. The Pareto optimal location and shape of the facilities are then obtained.
{"title":"BI-OBJECTIVE LOCATION MODEL OF TWO RECTANGULAR FACILITIES","authors":"M. Miyagawa","doi":"10.15807/jorsj.64.175","DOIUrl":"https://doi.org/10.15807/jorsj.64.175","url":null,"abstract":"This paper develops a bi-objective model for determining the location and shape of two finite-size facilities. The objectives are to minimize both the closest and barrier distances. The former represents the accessibility of customers, whereas the latter represents the interference to travelers. The total closest and barrier distances are derived for two rectangular facilities in a rectangular city where the distance is measured as the rectilinear distance. The analytical expressions for the total closest and barrier distances demonstrate how the location and shape of the facilities affect the distances. A numerical example shows that there exists a tradeoff between the closest and barrier distances. The tradeoff curve provides planners with alternatives for the location and shape of the facilities. The Pareto optimal location and shape of the facilities are then obtained.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41969934","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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