Variable selection is the process of finding variables relevant to a given dataset in model construction. One of the techniques for variable selection is exponentially evaluating many models with a goodness-of-fit (GOF) measure, for example, Akaike information criterion (AIC). The model with the lowest GOF value is considered as the best model. We proposed a mixed integer nonlinear programming approach to AIC minimization for linear regression and showed that the approach outperformed existing approaches in terms of computational time [13]. In this study, we apply the approach in [13] to AIC minimization for logistic regression and explain that a few of the techniques developed previously [13], for example, relaxation and a branching rule, can be used for the AIC minimization. The proposed approach requires solving relaxation problems, which are unconstrained convex problems. We apply an iterative method with an effective initial guess to solve these problems. We implement the proposed approach via SCIP, which is a noncommercial optimization software and a branch-and-bound framework. We compare the proposed approach with a piecewise linear approximation approach developed by Sato and others [16]. The results of computational experiments show that the proposed approach finds the model with the lowest AIC value if the number of candidates for variables is 45 or lower.
{"title":"APPLICATION OF A MIXED INTEGER NONLINEAR PROGRAMMING APPROACH TO VARIABLE SELECTION IN LOGISTIC REGRESSION","authors":"K. Kimura","doi":"10.15807/JORSJ.62.15","DOIUrl":"https://doi.org/10.15807/JORSJ.62.15","url":null,"abstract":"Variable selection is the process of finding variables relevant to a given dataset in model construction. One of the techniques for variable selection is exponentially evaluating many models with a goodness-of-fit (GOF) measure, for example, Akaike information criterion (AIC). The model with the lowest GOF value is considered as the best model. We proposed a mixed integer nonlinear programming approach to AIC minimization for linear regression and showed that the approach outperformed existing approaches in terms of computational time [13]. In this study, we apply the approach in [13] to AIC minimization for logistic regression and explain that a few of the techniques developed previously [13], for example, relaxation and a branching rule, can be used for the AIC minimization. The proposed approach requires solving relaxation problems, which are unconstrained convex problems. We apply an iterative method with an effective initial guess to solve these problems. We implement the proposed approach via SCIP, which is a noncommercial optimization software and a branch-and-bound framework. We compare the proposed approach with a piecewise linear approximation approach developed by Sato and others [16]. The results of computational experiments show that the proposed approach finds the model with the lowest AIC value if the number of candidates for variables is 45 or lower.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49561130","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 concerns a minimum maximal flow (MMF) problem, which finds a minimum maximal flow in a given network. The problem is known to be NP-hard. We show that the MMF problem can be formulated as a mixed integer programming (MIP) problem and we propose to find the minimum maximal flow by solving the MIP problem. By performing computational experiments, we observe that the proposed approach is efficient to the MMF problem even for relatively large instances, where the number of edges is up to 15,000, and that the growth rate of running time of our approach is slower than the rates of previous works when the sizes of the instances grow.
{"title":"A MIXED INTEGER PROGRAMMING APPROACH FOR THE MINIMUM MAXIMAL FLOW","authors":"Kuan Lu, S. Mizuno, Jianming Shi","doi":"10.15807/JORSJ.61.261","DOIUrl":"https://doi.org/10.15807/JORSJ.61.261","url":null,"abstract":"This paper concerns a minimum maximal flow (MMF) problem, which finds a minimum maximal flow in a given network. The problem is known to be NP-hard. We show that the MMF problem can be formulated as a mixed integer programming (MIP) problem and we propose to find the minimum maximal flow by solving the MIP problem. By performing computational experiments, we observe that the proposed approach is efficient to the MMF problem even for relatively large instances, where the number of edges is up to 15,000, and that the growth rate of running time of our approach is slower than the rates of previous works when the sizes of the instances grow.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.15807/JORSJ.61.261","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43719278","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 examining the spacing of intersections that connect different levels of roads in a hierarchical network. An analytical expression for the average travel time is obtained for a grid road network with two road types: minor and major roads. The travel time is defined as the sum of the free travel time and the delay at intersections. The analytical expression gives basic properties of the tradeoff between the travel time on minor and major roads. The optimal pattern of intersections that minimizes the average travel time is then obtained. The result demonstrates how the road length, the intersection delay, the travel speed, and the size of the city affect the optimal pattern. The model is also applied to the road network of Tokyo. The proposed model explicitly considers the tradeoff between the accessibility to higher level roads and the delay at intersections, and is useful for hierarchical road network design.
{"title":"SPACING OF INTERSECTIONS IN HIERARCHICAL ROAD NETWORKS","authors":"M. Miyagawa","doi":"10.15807/JORSJ.61.272","DOIUrl":"https://doi.org/10.15807/JORSJ.61.272","url":null,"abstract":"This paper presents an analytical model for examining the spacing of intersections that connect different levels of roads in a hierarchical network. An analytical expression for the average travel time is obtained for a grid road network with two road types: minor and major roads. The travel time is defined as the sum of the free travel time and the delay at intersections. The analytical expression gives basic properties of the tradeoff between the travel time on minor and major roads. The optimal pattern of intersections that minimizes the average travel time is then obtained. The result demonstrates how the road length, the intersection delay, the travel speed, and the size of the city affect the optimal pattern. The model is also applied to the road network of Tokyo. The proposed model explicitly considers the tradeoff between the accessibility to higher level roads and the delay at intersections, and is useful for hierarchical road network design.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.15807/JORSJ.61.272","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43080477","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}
Although there is a growing interest of applying regime switching models to portfolio optimization, it has never been quite easy as yet to obtain analytical solutions under practical conditions such as self-financing constraints and short sales constraints. In this paper, we extend the linear rebalancing rule proposed in Moallemi and Sağlam [17] to regime switching models and provide a multi-period dynamic investment strategy that is comprised of a linear combination of factors with regime dependent coefficients. Under plausible mathematical assumptions, the problem to determine optimal coefficients maximizing a mean-variance utility penalized for transaction costs subject to self-financing and short sales constraints can be formulated as a quadratic programming which is easily solved numerically. To suppress an exponential increase of a number of optimization variables caused by regime switches, we propose a sample space reduction method. From numerical experiments under a practical setting, we confirm that our approach achieves sufficiently reasonable performances, even when sample space reduction is applied for longer investment horizon. The results also show superior performance of our approach to that of the optimal strategy without concerning transaction costs.
{"title":"LINEAR REBALANCING STRATEGY FOR MULTI-PERIOD DYNAMIC PORTFOLIO OPTIMIZATION UNDER REGIME SWITCHES","authors":"Takahiro Komatsu, Naoki Makimoto","doi":"10.15807/JORSJ.61.239","DOIUrl":"https://doi.org/10.15807/JORSJ.61.239","url":null,"abstract":"Although there is a growing interest of applying regime switching models to portfolio optimization, it has never been quite easy as yet to obtain analytical solutions under practical conditions such as self-financing constraints and short sales constraints. In this paper, we extend the linear rebalancing rule proposed in Moallemi and Sağlam [17] to regime switching models and provide a multi-period dynamic investment strategy that is comprised of a linear combination of factors with regime dependent coefficients. Under plausible mathematical assumptions, the problem to determine optimal coefficients maximizing a mean-variance utility penalized for transaction costs subject to self-financing and short sales constraints can be formulated as a quadratic programming which is easily solved numerically. To suppress an exponential increase of a number of optimization variables caused by regime switches, we propose a sample space reduction method. From numerical experiments under a practical setting, we confirm that our approach achieves sufficiently reasonable performances, even when sample space reduction is applied for longer investment horizon. The results also show superior performance of our approach to that of the optimal strategy without concerning transaction costs.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42306887","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}
Multimodular functions, primarily used in the literature of queueing theory, discrete-event systems, and operations research, constitute a fundamental function class in discrete convex analysis. The objective of this paper is to clarify the properties of multimodular functions with respect to fundamental operations such as permutation and scaling of variables, projection (partial minimization) and convolution. It is shown, in particular, that the class of multimodular functions is stable under projection under a certain natural condition on the variables to be minimized, and the convolution of two multimodular functions is not necessarily multimodular, even in the special case of the convolution of a multimodular function with a separable convex function.
{"title":"ON FUNDAMENTAL OPERATIONS FOR MULTIMODULAR FUNCTIONS","authors":"Satoko Moriguchi, K. Murota","doi":"10.15807/JORSJ.62.53","DOIUrl":"https://doi.org/10.15807/JORSJ.62.53","url":null,"abstract":"Multimodular functions, primarily used in the literature of queueing theory, discrete-event systems, and operations research, constitute a fundamental function class in discrete convex analysis. The objective of this paper is to clarify the properties of multimodular functions with respect to fundamental operations such as permutation and scaling of variables, projection (partial minimization) and convolution. It is shown, in particular, that the class of multimodular functions is stable under projection under a certain natural condition on the variables to be minimized, and the convolution of two multimodular functions is not necessarily multimodular, even in the special case of the convolution of a multimodular function with a separable convex function.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":"41 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.15807/JORSJ.62.53","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41301398","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}
Optimal contribution selection (OCS) is a mathematical optimization problem that aims to maximize the total benefit from selecting a group of individuals under a constraint on genetic diversity. We are specifically focused on OCS as applied to forest tree breeding, when selected individuals will contribute equally to the gene pool. Since the diversity constraint in OCS can be described with a second-order cone, equal deployment in OCS can be mathematically modeled as mixed-integer second-order cone programming (MI-SOCP). If we apply a general solver for MI-SOCP, non-linearity embedded in OCS requires a heavy computation cost. To address this problem, we propose an implementation of lifted polyhedral programming (LPP) relaxation and a cone-decomposition method (CDM) to generate effective linear approximations for OCS. In particular, CDM successively solves OCS problems much faster than generic approaches for MI-SOCP. The approach of CDM is not limited to OCS, so that we can also apply the approach to other MI-SOCP problems.
{"title":"POLYHEDRAL-BASED METHODS FOR MIXED-INTEGER SOCP IN TREE BREEDING","authors":"Sena Safarina, T. Mullin, M. Yamashita","doi":"10.15807/jorsj.62.133","DOIUrl":"https://doi.org/10.15807/jorsj.62.133","url":null,"abstract":"Optimal contribution selection (OCS) is a mathematical optimization problem that aims to maximize the total benefit from selecting a group of individuals under a constraint on genetic diversity. We are specifically focused on OCS as applied to forest tree breeding, when selected individuals will contribute equally to the gene pool. Since the diversity constraint in OCS can be described with a second-order cone, equal deployment in OCS can be mathematically modeled as mixed-integer second-order cone programming (MI-SOCP). If we apply a general solver for MI-SOCP, non-linearity embedded in OCS requires a heavy computation cost. To address this problem, we propose an implementation of lifted polyhedral programming (LPP) relaxation and a cone-decomposition method (CDM) to generate effective linear approximations for OCS. In particular, CDM successively solves OCS problems much faster than generic approaches for MI-SOCP. The approach of CDM is not limited to OCS, so that we can also apply the approach to other MI-SOCP problems.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48099046","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 fuzzy linear programming problem with triangular fuzzy numbers in its objective functions or constraints has been discussed by many scholars based on using Zadeh’s decomposition theorem of fuzzy numbers and transforming it into some crisp linear programming problems. However, the existing methods and the results will be limited when the objective functions (or the constraint functions) of a fuzzy linear programming contain generalized fuzzy numbers. In this paper, we first investigate the approximate representation of the fully fuzzy constraints and the transformation theorem of the fully fuzzy linear programming problem by means of the definition of the extended LR-fuzzy numbers. At the same time, the fully fuzzy linear programming problem is solved by transforming it into a multi-objective linear programming problem under a new ordering of GLR-fuzzy numbers proposed in this paper. Finally, the results obtained are compared with the existing work, and some numerical examples are given.
{"title":"A STRAIGHTFORWARD APPROACH FOR SOLVING FULLY FUZZY LINEAR PROGRAMMING PROBLEM WITH LR-TYPE FUZZY NUMBERS","authors":"Z. Gong, Wencui Zhao, Kun Liu","doi":"10.15807/JORSJ.61.172","DOIUrl":"https://doi.org/10.15807/JORSJ.61.172","url":null,"abstract":"The fuzzy linear programming problem with triangular fuzzy numbers in its objective functions or constraints has been discussed by many scholars based on using Zadeh’s decomposition theorem of fuzzy numbers and transforming it into some crisp linear programming problems. However, the existing methods and the results will be limited when the objective functions (or the constraint functions) of a fuzzy linear programming contain generalized fuzzy numbers. In this paper, we first investigate the approximate representation of the fully fuzzy constraints and the transformation theorem of the fully fuzzy linear programming problem by means of the definition of the extended LR-fuzzy numbers. At the same time, the fully fuzzy linear programming problem is solved by transforming it into a multi-objective linear programming problem under a new ordering of GLR-fuzzy numbers proposed in this paper. Finally, the results obtained are compared with the existing work, and some numerical examples are given.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":"61 1","pages":"172-185"},"PeriodicalIF":0.0,"publicationDate":"2018-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.15807/JORSJ.61.172","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47541322","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 the inventory problem of a firm facing disruption probability in its supply chain which consists of multiple suppliers and multiple demand nodes. The firm wishes to minimize its total expected cost in a finite time horizon setting. In order to manage the supply chain disruption, we introduce flexibility into the supply chain network of our inventory management problem. The problem is formulated as a Markov decision process, and a state-dependent optimal threshold policy is derived. We show that the expected cost function is monotonic in the convex ordering of the demand distribution and that the optimal policy can be characterized with the ratio of the ordering cost and the disruption probability of supply. We also numerically demonstrate that the flexibility of the supply chain network reduces the total expected cost.
{"title":"DYNAMIC INVENTORY CONTROL MODEL WITH FLEXIBLE SUPPLY NETWORK","authors":"Kimitoshi Sato, Naoya Takezawa","doi":"10.15807/JORSJ.61.217","DOIUrl":"https://doi.org/10.15807/JORSJ.61.217","url":null,"abstract":"In this paper, we consider the inventory problem of a firm facing disruption probability in its supply chain which consists of multiple suppliers and multiple demand nodes. The firm wishes to minimize its total expected cost in a finite time horizon setting. In order to manage the supply chain disruption, we introduce flexibility into the supply chain network of our inventory management problem. The problem is formulated as a Markov decision process, and a state-dependent optimal threshold policy is derived. We show that the expected cost function is monotonic in the convex ordering of the demand distribution and that the optimal policy can be characterized with the ratio of the ordering cost and the disruption probability of supply. We also numerically demonstrate that the flexibility of the supply chain network reduces the total expected cost.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":"61 1","pages":"217-235"},"PeriodicalIF":0.0,"publicationDate":"2018-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.15807/JORSJ.61.217","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43592985","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}
While the algorithmic complexity is in general worse than the one of Tardos’ original algorithms, the authors, motivated by the practicality of such methods, recently proposed a simplex-based variant that is strongly polynomial if the coefficient matrix is totally unimodular and the auxiliary problems are nondegenerate. In this paper, we introduce a slight modification that circumvents the determination of the largest sub-determinant while keeping the same theoretical performance. Assuming that the coefficient matrix is integer-valued and the auxiliary problems are non-degenerate, the proposed algorithm is polynomial in the dimension of the input data and the largest absolute value of a sub-determinant of the coefficient matrix.
{"title":"An enhanced primal-simplex based tardos' algorithm for linear optimization","authors":"S. Mizuno, Noriyoshi Sukegawa, A. Deza","doi":"10.15807/JORSJ.61.186","DOIUrl":"https://doi.org/10.15807/JORSJ.61.186","url":null,"abstract":"While the algorithmic complexity is in general worse than the one of Tardos’ original algorithms, the authors, motivated by the practicality of such methods, recently proposed a simplex-based variant that is strongly polynomial if the coefficient matrix is totally unimodular and the auxiliary problems are nondegenerate. In this paper, we introduce a slight modification that circumvents the determination of the largest sub-determinant while keeping the same theoretical performance. Assuming that the coefficient matrix is integer-valued and the auxiliary problems are non-degenerate, the proposed algorithm is polynomial in the dimension of the input data and the largest absolute value of a sub-determinant of the coefficient matrix.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":"61 1","pages":"186-196"},"PeriodicalIF":0.0,"publicationDate":"2018-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.15807/JORSJ.61.186","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47478634","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}
Than Nguyen Hau, Naonori Kakimura, K. Kawarabayashi, Yusuke Kobayashi, Tatsuya Matsuoka, Yu Yokoi
Deploying caches on a network is an effective way to reduce the amount of data transmitted in a network. Recently, in an academic backbone network such as SINET (the Science Information Network) in Japan, the amount of transmitted data has signi(cid:12)cantly increased. It is desired to design an efficient mechanism to allocate caches in an optimal way. In this paper, we begin by formulating a discrete optimization model to (cid:12)nd a cache allocation that minimizes the total transmission cost. We then design two efficient algorithms to solve our proposed model. The (cid:12)rst one makes use of the fact that a backbone network has small treewidth. The algorithm runs in polynomial time when the number of items is (cid:12)xed and a graph has a bounded treewidth. The other one reduces the problem to the minimum-cost (cid:13)ow problem under the practical assumption that each item has at most one copy. This yields a polynomial-time combinatorial algorithm. Our numerical experiments on the real SINET network show that our algorithms can solve the cache placement problem efficiently in practice.
{"title":"Optimal cache placement for an academic backbone network","authors":"Than Nguyen Hau, Naonori Kakimura, K. Kawarabayashi, Yusuke Kobayashi, Tatsuya Matsuoka, Yu Yokoi","doi":"10.15807/JORSJ.61.197","DOIUrl":"https://doi.org/10.15807/JORSJ.61.197","url":null,"abstract":"Deploying caches on a network is an effective way to reduce the amount of data transmitted in a network. Recently, in an academic backbone network such as SINET (the Science Information Network) in Japan, the amount of transmitted data has signi(cid:12)cantly increased. It is desired to design an efficient mechanism to allocate caches in an optimal way. In this paper, we begin by formulating a discrete optimization model to (cid:12)nd a cache allocation that minimizes the total transmission cost. We then design two efficient algorithms to solve our proposed model. The (cid:12)rst one makes use of the fact that a backbone network has small treewidth. The algorithm runs in polynomial time when the number of items is (cid:12)xed and a graph has a bounded treewidth. The other one reduces the problem to the minimum-cost (cid:13)ow problem under the practical assumption that each item has at most one copy. This yields a polynomial-time combinatorial algorithm. Our numerical experiments on the real SINET network show that our algorithms can solve the cache placement problem efficiently in practice.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":"61 1","pages":"197-216"},"PeriodicalIF":0.0,"publicationDate":"2018-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.15807/JORSJ.61.197","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46202238","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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