We consider a multiagent network model consisting of nodes and edges as cities and their links to neighbors, respectively. Each network node has an agent and priced goods and the agent can buy or sell goods in the neighborhood. Though every node may not have an equal price, we show the prices will reach an equilibrium by iterating buy and sell operations. First, we present a protocol model in which each buying agent makes a bid to the lowest priced goods in the neighborhood; and each selling agent selects the highest bid, if any. Second, we derive a sufficient condition which stabilizes price in our model. We also show the equilibrium price can be derived from the total funds and the total goods for any network. This is a special case of the Fisher’s quantity equation, thus we can confirm the correctness of our model. We then examine the best bidding strategy is available to our protocol. Third, we analyze stabilization time for path and cycle networks. Finally, we perform simulation experiments for estimating the stabilization time, the number of bidders and the effects of spreading funds. Our model is suitable for investigating the effects of network topologies on price stabilization.
{"title":"A PRICE STABILIZATION MODEL IN NETWORKS","authors":"Jun Kiniwa, K. Kikuta, H. Sandoh","doi":"10.15807/JORSJ.60.479","DOIUrl":"https://doi.org/10.15807/JORSJ.60.479","url":null,"abstract":"We consider a multiagent network model consisting of nodes and edges as cities and their links to neighbors, respectively. Each network node has an agent and priced goods and the agent can buy or sell goods in the neighborhood. Though every node may not have an equal price, we show the prices will reach an equilibrium by iterating buy and sell operations. First, we present a protocol model in which each buying agent makes a bid to the lowest priced goods in the neighborhood; and each selling agent selects the highest bid, if any. Second, we derive a sufficient condition which stabilizes price in our model. We also show the equilibrium price can be derived from the total funds and the total goods for any network. This is a special case of the Fisher’s quantity equation, thus we can confirm the correctness of our model. We then examine the best bidding strategy is available to our protocol. Third, we analyze stabilization time for path and cycle networks. Finally, we perform simulation experiments for estimating the stabilization time, the number of bidders and the effects of spreading funds. Our model is suitable for investigating the effects of network topologies on price stabilization.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":"60 1","pages":"479-495"},"PeriodicalIF":0.0,"publicationDate":"2017-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.15807/JORSJ.60.479","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49078289","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}
Pairs trading strategy has a history of at least 30 years in the stock market and is one of the most common trading strategies used today due to its understandability. Recently, Yamamoto and Hibiki [13] studied optimal pairs trading strategy using a new approach under actual fund management conditions, such as transaction costs, discrete rebalance intervals, finite investment horizons and so on. However, this approach cannot solve the problem of multiple pairs because this problem is formulated as a large scale simulation based non-continuous optimization problem. In this research, we formulate a model to solve an optimal pairs trading strategy problem using multiple pairs under actual fund management conditions. Furthermore, we propose a heuristic algorithm based on a derivative free optimization (DFO) method for solving this problem efficiently.
{"title":"OPTIMAL MULTIPLE PAIRS TRADING STRATEGYUSING DERIVATIVE FREE OPTIMIZATIONUNDER ACTUAL INVESTMENT MANAGEMENT CONDITIONS","authors":"R. Yamamoto, Norio Hibiki","doi":"10.15807/JORSJ.60.244","DOIUrl":"https://doi.org/10.15807/JORSJ.60.244","url":null,"abstract":"Pairs trading strategy has a history of at least 30 years in the stock market and is one of the most common trading strategies used today due to its understandability. Recently, Yamamoto and Hibiki [13] studied optimal pairs trading strategy using a new approach under actual fund management conditions, such as transaction costs, discrete rebalance intervals, finite investment horizons and so on. However, this approach cannot solve the problem of multiple pairs because this problem is formulated as a large scale simulation based non-continuous optimization problem. In this research, we formulate a model to solve an optimal pairs trading strategy problem using multiple pairs under actual fund management conditions. Furthermore, we propose a heuristic algorithm based on a derivative free optimization (DFO) method for solving this problem efficiently.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":"60 1","pages":"244-261"},"PeriodicalIF":0.0,"publicationDate":"2017-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.15807/JORSJ.60.244","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45538848","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}
Ryuta Tamura, Ken Kobayashi, Yuichi Takano, Ryuhei Miyashiro, K. Nakata, Tomomi Matsui
This paper proposes a method for eliminating multicollinearity from linear regression models. Specifically, we select the best subset of explanatory variables subject to the upper bound on the condition number of the correlation matrix of selected variables. We first develop a cutting plane algorithm that, to approximate the condition number constraint, iteratively appends valid inequalities to the mixed integer quadratic optimization problem. We also devise a mixed integer semidefinite optimization formulation for best subset selection under the condition number constraint. Computational results demonstrate that our cutting plane algorithm frequently provides solutions of better quality than those obtained using local search algorithms for subset selection. Additionally, subset selection by means of our optimization formulation succeeds when the number of candidate explanatory variables is small.
{"title":"BEST SUBSET SELECTION FOR ELIMINATING MULTICOLLINEARITY","authors":"Ryuta Tamura, Ken Kobayashi, Yuichi Takano, Ryuhei Miyashiro, K. Nakata, Tomomi Matsui","doi":"10.15807/JORSJ.60.321","DOIUrl":"https://doi.org/10.15807/JORSJ.60.321","url":null,"abstract":"This paper proposes a method for eliminating multicollinearity from linear regression models. Specifically, we select the best subset of explanatory variables subject to the upper bound on the condition number of the correlation matrix of selected variables. We first develop a cutting plane algorithm that, to approximate the condition number constraint, iteratively appends valid inequalities to the mixed integer quadratic optimization problem. We also devise a mixed integer semidefinite optimization formulation for best subset selection under the condition number constraint. Computational results demonstrate that our cutting plane algorithm frequently provides solutions of better quality than those obtained using local search algorithms for subset selection. Additionally, subset selection by means of our optimization formulation succeeds when the number of candidate explanatory variables is small.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":"60 1","pages":"321-336"},"PeriodicalIF":0.0,"publicationDate":"2017-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.15807/JORSJ.60.321","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46711867","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 constrained nonlinear optimization, the squared slack variables can be used to transform a problem with inequality constraints into a problem containing only equality constraints. This reformulation is usually not considered in the modern literature, mainly because of possible numerical instabilities. However, this argument only concerns the development of algorithms, and nothing stops us in using the strategy to understand the theory behind these optimization problems. In this note, we clarify the relation between the Karush-Kuhn-Tucker points of the original and the reformulated problems. In particular, we stress that the second-order sufficient condition is the key to establish their equivalence.
{"title":"A NOTE ON THE SQUARED SLACK VARIABLES TECHNIQUE FOR NONLINEAR OPTIMIZATION","authors":"E. H. Fukuda, M. Fukushima","doi":"10.15807/JORSJ.60.262","DOIUrl":"https://doi.org/10.15807/JORSJ.60.262","url":null,"abstract":"In constrained nonlinear optimization, the squared slack variables can be used to transform a problem with inequality constraints into a problem containing only equality constraints. This reformulation is usually not considered in the modern literature, mainly because of possible numerical instabilities. However, this argument only concerns the development of algorithms, and nothing stops us in using the strategy to understand the theory behind these optimization problems. In this note, we clarify the relation between the Karush-Kuhn-Tucker points of the original and the reformulated problems. In particular, we stress that the second-order sufficient condition is the key to establish their equivalence.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":"60 1","pages":"262-270"},"PeriodicalIF":0.0,"publicationDate":"2017-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.15807/JORSJ.60.262","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48255663","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":"EDITORIAL INTRODUCTION A SPECIAL ISSUE, PART 2, ON THE 60TH ANNIVERSARY OF THE OPERATIONS RESEARCH SOCIETY OF JAPAN","authors":"S. Mizuno, T. Takine","doi":"10.15807/jorsj.61.1","DOIUrl":"https://doi.org/10.15807/jorsj.61.1","url":null,"abstract":"","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":"61 1","pages":"1-1"},"PeriodicalIF":0.0,"publicationDate":"2017-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.15807/jorsj.61.1","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49379056","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 Different strategies can be used to find a straight cable buried underground. The original problem considered by Faber et al. focused on a telephone company that wishes to dig a trench to locate a straight cable. The cable is known to pass within a given distance, a, from a marker erected above the putative location of the cable. Faber et al. showed that the shortest simply connected curve guaranteed to find the cable is a U-shaped curve whose length is about 18% less than that of a circular trench of radius a. This problem can be regarded as minimizing the maximum length that a trench digger must dig. In reality, once the cable is found, digging can stop. So far, however, no attempt has been made to evaluate the trench shape on characteristics other than the maximum trench length. In this paper, we present geometric probability models to analytically derive the distribution of trench length and calculate the expected value and variance for both the short-length (U-shaped) trench and a circular trench. Our main result is that the expected digging length is about 5% less for the circular trench than for the U-shaped trench.
{"title":"Geometric probability models to analyze strategies for finding a buried cable","authors":"Ken-ichi Tanaka, Kana Shiina","doi":"10.15807/JORSJ.60.400","DOIUrl":"https://doi.org/10.15807/JORSJ.60.400","url":null,"abstract":"Abstract Different strategies can be used to find a straight cable buried underground. The original problem considered by Faber et al. focused on a telephone company that wishes to dig a trench to locate a straight cable. The cable is known to pass within a given distance, a, from a marker erected above the putative location of the cable. Faber et al. showed that the shortest simply connected curve guaranteed to find the cable is a U-shaped curve whose length is about 18% less than that of a circular trench of radius a. This problem can be regarded as minimizing the maximum length that a trench digger must dig. In reality, once the cable is found, digging can stop. So far, however, no attempt has been made to evaluate the trench shape on characteristics other than the maximum trench length. In this paper, we present geometric probability models to analytically derive the distribution of trench length and calculate the expected value and variance for both the short-length (U-shaped) trench and a circular trench. Our main result is that the expected digging length is about 5% less for the circular trench than for the U-shaped trench.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":"60 1","pages":"400-417"},"PeriodicalIF":0.0,"publicationDate":"2017-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.15807/JORSJ.60.400","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47032206","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 authors analyse a search game involving an immobile hider and a searcher in which play takes place in discrete time on a network comprising a cycle together with a node 0 adjacent to a specified set of nodes in the cycle. The hider chooses a node of the cycle. Unaware of the hider’s choice, the searcher starts at the node 0 and, at each subsequent time instant, moves from the node he occupies to an adjacent node and decides whether to search it. Play terminates when the searcher is at the node chosen by the hider and searches there. The searcher incurs a cost of one in moving from a node to an adjacent one and a search cost depending on whether or not the node is in the specified set. The searcher wants to minimize the costs of finding the hider and the hider to maximize them. We obtain upper bounds for the value of this game for the cases when the specified set has no adjacent nodes and when it is an interval. We show that these upper bounds are the value of the game in a number of cases.
{"title":"SEARCH GAMES ON A BROKEN WHEEL WITH TRAVELING AND SEARCH COSTS","authors":"V. Baston, K. Kikuta","doi":"10.15807/JORSJ.60.379","DOIUrl":"https://doi.org/10.15807/JORSJ.60.379","url":null,"abstract":"The authors analyse a search game involving an immobile hider and a searcher in which play takes place in discrete time on a network comprising a cycle together with a node 0 adjacent to a specified set of nodes in the cycle. The hider chooses a node of the cycle. Unaware of the hider’s choice, the searcher starts at the node 0 and, at each subsequent time instant, moves from the node he occupies to an adjacent node and decides whether to search it. Play terminates when the searcher is at the node chosen by the hider and searches there. The searcher incurs a cost of one in moving from a node to an adjacent one and a search cost depending on whether or not the node is in the specified set. The searcher wants to minimize the costs of finding the hider and the hider to maximize them. We obtain upper bounds for the value of this game for the cases when the specified set has no adjacent nodes and when it is an interval. We show that these upper bounds are the value of the game in a number of cases.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":"60 1","pages":"379-392"},"PeriodicalIF":0.0,"publicationDate":"2017-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.15807/JORSJ.60.379","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44496421","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 deals with a two-person zero-sum (TPZS) attrition game on a network in which attackers depart from a start node and attempt to reach a destination node while defenders deploy to intercept the attackers. Both players incur some attrition due to con(cid:13)ict between them, but the payoff of the game is the number of surviving attackers reaching the destination. We generate a system of models categorized according to various scenarios of the player’s information acquisition (IA) about his opponent and derive linear programming formulations for the equilibria of the models. Comparing the equilibria, we evaluate the values of the situations around the IA in a comprehensive manner.
{"title":"EFFECTS OF A PLAYER'S AWARENESS OF INFORMATION ACQUISITION AND ABILITY TO CHANGE STRATEGY IN ATTRITION GAMES","authors":"Ryusuke Hohzaki, Makoto Tanaka","doi":"10.15807/JORSJ.60.353","DOIUrl":"https://doi.org/10.15807/JORSJ.60.353","url":null,"abstract":"This paper deals with a two-person zero-sum (TPZS) attrition game on a network in which attackers depart from a start node and attempt to reach a destination node while defenders deploy to intercept the attackers. Both players incur some attrition due to con(cid:13)ict between them, but the payoff of the game is the number of surviving attackers reaching the destination. We generate a system of models categorized according to various scenarios of the player’s information acquisition (IA) about his opponent and derive linear programming formulations for the equilibria of the models. Comparing the equilibria, we evaluate the values of the situations around the IA in a comprehensive manner.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":"60 1","pages":"353-378"},"PeriodicalIF":0.0,"publicationDate":"2017-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.15807/JORSJ.60.353","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44423683","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}
Theorems of alternatives are useful mathematical tools in optimization. Their objects are pairs of linear systems. Folding a paper with a crease defines a linear inequality in R. So one gets convex polygons by folding a paper many times. This paper provides a new perspective of duality to origami mathematics. We show that Gale’s theorem of alternatives is useful for the study of twist fold.
{"title":"An application of a theorem of alternatives to origami","authors":"H. Kawasaki","doi":"10.15807/jorsj.60.393","DOIUrl":"https://doi.org/10.15807/jorsj.60.393","url":null,"abstract":"Theorems of alternatives are useful mathematical tools in optimization. Their objects are pairs of linear systems. Folding a paper with a crease defines a linear inequality in R. So one gets convex polygons by folding a paper many times. This paper provides a new perspective of duality to origami mathematics. We show that Gale’s theorem of alternatives is useful for the study of twist fold.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":"60 1","pages":"393-399"},"PeriodicalIF":0.0,"publicationDate":"2017-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.15807/jorsj.60.393","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48467542","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":"HERGLOTZ-BOCHNER REPRESENTATION THEOREM VIA THEORY OF DISTRIBUTIONS","authors":"T. Maruyama","doi":"10.15807/JORSJ.60.122","DOIUrl":"https://doi.org/10.15807/JORSJ.60.122","url":null,"abstract":"","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":"60 1","pages":"122-135"},"PeriodicalIF":0.0,"publicationDate":"2017-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.15807/JORSJ.60.122","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42107881","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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