This special issue on Mathematical Decision Making under Uncertainty was planed by the official research group “Stochastic Model and its Application (SMA)” in Operations Research Society of Japan and the research group “Dynamic Programming (DP)” in Kyushu District in Japan. SMA is well-known as “DP Bukai” in Japanese which has over 40 years history and so is one of the most historical research groups in Operations Research Society of Japan. SMA and DP have collaborated for many years. Our research interest is in such areas as Stochastic Optimization, Dynamic Programming, Markov Decision Process, Sequential Statistical Decision, Optimal Stopping, Game Theory, Fuzzy Theory, Financial Engineering, Operations Research in Sports and so on. Workshop on Mathematical Models of Decision Making under Uncertainty, which has been organized by our two research groups every year, was held in Research Institute of Mathematical Sciences, Kyoto University, on November 11-13, 2015. Invited sessions are organized by our research groups at both 20th Conference of the International Federation of Operational Research Societies held in Barcelona, on June 13-18, 2014, and at 27th European Conference on Operational Research held in Glasgow, on July 12-15, 2015. Based on not only the research results presented at these three nice occasions but also the latest achievements by non-participants of the conference, we planned to edit the special issue on Mathematical Decision Making under Uncertainty. We received many well-prepared and high quality submissions by February 27, 2016, and spent almost one year to complete our editing task. In accordance with the journal’s review discipline, each submission was reviewed by two referees without conflict to the authors. We regret to mention that we had to reject some good papers because of our tight review schedule. The guest editors are pleased to publish this special issue on the most recent research results in mathematical decision making. Finally, we thank the former editor-in-chief, Dr. Shinji Mizuno, and the present editor-in-chief, Dr. Tetsuya Takine, for their helpful support and comments.
{"title":"PREFACE TO THE SPECIAL ISSUE ON MATHEMATICAL DECISION MAKING UNDER UNCERTAINTY","authors":"K. Ano, Yukihiro Maruyama","doi":"10.15807/jorsj.60.43","DOIUrl":"https://doi.org/10.15807/jorsj.60.43","url":null,"abstract":"This special issue on Mathematical Decision Making under Uncertainty was planed by the official research group “Stochastic Model and its Application (SMA)” in Operations Research Society of Japan and the research group “Dynamic Programming (DP)” in Kyushu District in Japan. SMA is well-known as “DP Bukai” in Japanese which has over 40 years history and so is one of the most historical research groups in Operations Research Society of Japan. SMA and DP have collaborated for many years. Our research interest is in such areas as Stochastic Optimization, Dynamic Programming, Markov Decision Process, Sequential Statistical Decision, Optimal Stopping, Game Theory, Fuzzy Theory, Financial Engineering, Operations Research in Sports and so on. Workshop on Mathematical Models of Decision Making under Uncertainty, which has been organized by our two research groups every year, was held in Research Institute of Mathematical Sciences, Kyoto University, on November 11-13, 2015. Invited sessions are organized by our research groups at both 20th Conference of the International Federation of Operational Research Societies held in Barcelona, on June 13-18, 2014, and at 27th European Conference on Operational Research held in Glasgow, on July 12-15, 2015. Based on not only the research results presented at these three nice occasions but also the latest achievements by non-participants of the conference, we planned to edit the special issue on Mathematical Decision Making under Uncertainty. We received many well-prepared and high quality submissions by February 27, 2016, and spent almost one year to complete our editing task. In accordance with the journal’s review discipline, each submission was reviewed by two referees without conflict to the authors. We regret to mention that we had to reject some good papers because of our tight review schedule. The guest editors are pleased to publish this special issue on the most recent research results in mathematical decision making. Finally, we thank the former editor-in-chief, Dr. Shinji Mizuno, and the present editor-in-chief, Dr. Tetsuya Takine, for their helpful support and comments.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.15807/jorsj.60.43","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49199286","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}
Recently, Iwamoto, Kimura, and Ueno proposed dynamic dualization to present dual problems for unconstrained optimization problems whose objective function is a sum of squares. The aim of this paper is to show that dynamic dualization works well for unconstrained problems whose objective function is a sum of convex functions. Further we give another way to get dual problems, which is based on the infimal convolution. In both approaches we make clear the assumption for duality to hold.
{"title":"DYNAMIC DUALIZATION IN A GENERAL SETTING","authors":"H. Kawasaki","doi":"10.15807/JORSJ.60.44","DOIUrl":"https://doi.org/10.15807/JORSJ.60.44","url":null,"abstract":"Recently, Iwamoto, Kimura, and Ueno proposed dynamic dualization to present dual problems for unconstrained optimization problems whose objective function is a sum of squares. The aim of this paper is to show that dynamic dualization works well for unconstrained problems whose objective function is a sum of convex functions. Further we give another way to get dual problems, which is based on the infimal convolution. In both approaches we make clear the assumption for duality to hold.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.15807/JORSJ.60.44","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41744160","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 security games which would be found around our lives. In a facility represented by a network, several types of invaders/attackers conflict with security guards/defenders who have also several security teams. The attacker chooses an invasion path to move along. He incurs some attrition by the conflict on arcs but surviving attackers give damage to the facility on his invasion route while the defender tries to minimize the damage by intercepting the attacker by a limited number of guards. The defender takes a randomized plan with respect to the adoption of each security team and the deployment of guards. Since the attacker know the defender’s randomized plan before his decision making, the security problem is modeled by a Stackelberg game with the superiority of the attacker on information acquisition to the defender. There has been no research on the security game with multiple types of players modeled on a network, which explicitly takes account attrition on players. By some numerical examples, we investigate the best configuration of staff numbers in security teams and some characteristics of optimal defense to mitigate the damage caused by the attackers.
{"title":"SECURITY GAMES TAKING ACCOUNT OF INVASION ROUTES AND ATTRITION","authors":"Ryusuke Hohzaki, Ginjiro Sakai","doi":"10.15807/JORSJ.60.156","DOIUrl":"https://doi.org/10.15807/JORSJ.60.156","url":null,"abstract":"This paper deals with security games which would be found around our lives. In a facility represented by a network, several types of invaders/attackers conflict with security guards/defenders who have also several security teams. The attacker chooses an invasion path to move along. He incurs some attrition by the conflict on arcs but surviving attackers give damage to the facility on his invasion route while the defender tries to minimize the damage by intercepting the attacker by a limited number of guards. The defender takes a randomized plan with respect to the adoption of each security team and the deployment of guards. Since the attacker know the defender’s randomized plan before his decision making, the security problem is modeled by a Stackelberg game with the superiority of the attacker on information acquisition to the defender. There has been no research on the security game with multiple types of players modeled on a network, which explicitly takes account attrition on players. By some numerical examples, we investigate the best configuration of staff numbers in security teams and some characteristics of optimal defense to mitigate the damage caused by the attackers.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.15807/JORSJ.60.156","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47042792","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 particle survival model, which was originally proposed to analyze the dynamics of species’ coexistence, has surprisingly found to be related to a non-homogeneous Poisson process. It is also well known that successive record values of independent and identically distributed sequences have the spatial distribution of such processes. In this paper, we show that the particle survival model and the record value process are indeed equivalent. Further, we study their application to determine the optimal strategy for placing selling orders on stock exchange limit order books. Our approach considers the limit orders as particles, and assumes that the other traders have zero intelligence.
{"title":"EQUIVALENCE OF PARTICLE SURVIVAL MODEL AND RECORD VALUE PROCESS, AND ITS NEW APPLICATION TO LIMIT ORDER BOOKS","authors":"H. Toyoizumi","doi":"10.15807/JORSJ.60.101","DOIUrl":"https://doi.org/10.15807/JORSJ.60.101","url":null,"abstract":"The particle survival model, which was originally proposed to analyze the dynamics of species’ coexistence, has surprisingly found to be related to a non-homogeneous Poisson process. It is also well known that successive record values of independent and identically distributed sequences have the spatial distribution of such processes. In this paper, we show that the particle survival model and the record value process are indeed equivalent. Further, we study their application to determine the optimal strategy for placing selling orders on stock exchange limit order books. Our approach considers the limit orders as particles, and assumes that the other traders have zero intelligence.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.15807/JORSJ.60.101","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43171678","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 fuzzy sets on a metric, vector, or normed space. It is not assumed that the fuzzy sets have compact supports. In the present paper, a fuzzy distance and a fuzzy norm are proposed in order to measure the difference between two fuzzy sets, and their fundamental properties are investigated. Their definitions are based on Zadeh’s extension principle. Although they are different from the classical ones based on the Hausdorff metric, they are suitable for data containing uncertainty or vagueness. The obtained results can be expected to be useful for analyzing such data when the data are represented as fuzzy sets.
{"title":"FUZZY DISTANCE AND FUZZY NORM","authors":"Masamichi Kon","doi":"10.15807/JORSJ.60.66","DOIUrl":"https://doi.org/10.15807/JORSJ.60.66","url":null,"abstract":"We consider fuzzy sets on a metric, vector, or normed space. It is not assumed that the fuzzy sets have compact supports. In the present paper, a fuzzy distance and a fuzzy norm are proposed in order to measure the difference between two fuzzy sets, and their fundamental properties are investigated. Their definitions are based on Zadeh’s extension principle. Although they are different from the classical ones based on the Hausdorff metric, they are suitable for data containing uncertainty or vagueness. The obtained results can be expected to be useful for analyzing such data when the data are represented as fuzzy sets.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.15807/JORSJ.60.66","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44816436","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}
It is shown that the Fibonacci sequence is optimal for two quadratic programming problems (maximization and minimization) under semi-Fibonacci constraints. The two conditional (primal) problems have their unconditional (dual) problems. The optimal solution is characterized by the Fibonacci number. Both pairs of primal and dual problems are mutually derived through three methods — dynamic, plus-minus and inequality —.
{"title":"QUADRATIC OPTIMIZATION UNDER SEMI-FIBONACCI CONSTRAINT (II)","authors":"Y. Kimura, Seiichi Iwamoto","doi":"10.15807/JORSJ.60.78","DOIUrl":"https://doi.org/10.15807/JORSJ.60.78","url":null,"abstract":"It is shown that the Fibonacci sequence is optimal for two quadratic programming problems (maximization and minimization) under semi-Fibonacci constraints. The two conditional (primal) problems have their unconditional (dual) problems. The optimal solution is characterized by the Fibonacci number. Both pairs of primal and dual problems are mutually derived through three methods — dynamic, plus-minus and inequality —.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.15807/JORSJ.60.78","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47907790","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 studies the relation between a given nondeterministic discrete decision process (ndddp) and a nondeterministic sequential decision process (nd-sdp), which is a finite nondeterministic automaton with a cost function, and its subclasses (nd-msdp, nd-pmsdp, nd-smsdp). We show super-strong representation theorems for nd-sdp and its subclasses, for which the functional equations of nondeterministic dynamic programming are obtainable. The super-strong representation theorems provide necessary and sufficient conditions for the existence of the nd-sdp and its subclasses with the same set of feasible policies and the same cost value for every feasible policy as the given process nd-ddp.
{"title":"SUPER-STRONG REPRESENTATION THEOREMS FOR NONDETERMINISTIC SEQUENTIAL DECISION PROCESSES","authors":"Yukihiro Maruyama","doi":"10.15807/JORSJ.60.136","DOIUrl":"https://doi.org/10.15807/JORSJ.60.136","url":null,"abstract":"This paper studies the relation between a given nondeterministic discrete decision process (ndddp) and a nondeterministic sequential decision process (nd-sdp), which is a finite nondeterministic automaton with a cost function, and its subclasses (nd-msdp, nd-pmsdp, nd-smsdp). We show super-strong representation theorems for nd-sdp and its subclasses, for which the functional equations of nondeterministic dynamic programming are obtainable. The super-strong representation theorems provide necessary and sufficient conditions for the existence of the nd-sdp and its subclasses with the same set of feasible policies and the same cost value for every feasible policy as the given process nd-ddp.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.15807/JORSJ.60.136","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49295242","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}
Project risk is an uncertain event that causes positive or negative effects on the project objectives in relation to the cost, time, quality and so on to complete the project. Project risk management is the set of processes of identifying, analyzing and responding to project risks. For example, the project risk management includes the process of eliminating the project risks from the project to complete any activities in the project by the specified day. In terms of not only the risk but also the time, many researches have been done. Especially, as for the time, there are many researches on CPM and PERT, which use mathematical techniques. However, few researchers discuss the effectiveness of project risk responses to deal with project risks for making a success of the project. In this paper, we propose a new mathematical model of the project risk responses. And, with our proposing model, we show how to calculate the effectiveness of project risk responses quantitatively. Moreover, we can decide quantitatively which project risk response should be executed by the consequences of the above calculation.
{"title":"THE MATHEMATICAL MODEL OF PROJECT RISK RESPONSES IN PROJECT RISK MANAGEMENT","authors":"H. Fukuda, H. Kuwano","doi":"10.15807/JORSJ.60.192","DOIUrl":"https://doi.org/10.15807/JORSJ.60.192","url":null,"abstract":"Project risk is an uncertain event that causes positive or negative effects on the project objectives in relation to the cost, time, quality and so on to complete the project. Project risk management is the set of processes of identifying, analyzing and responding to project risks. For example, the project risk management includes the process of eliminating the project risks from the project to complete any activities in the project by the specified day. In terms of not only the risk but also the time, many researches have been done. Especially, as for the time, there are many researches on CPM and PERT, which use mathematical techniques. However, few researchers discuss the effectiveness of project risk responses to deal with project risks for making a success of the project. In this paper, we propose a new mathematical model of the project risk responses. And, with our proposing model, we show how to calculate the effectiveness of project risk responses quantitatively. Moreover, we can decide quantitatively which project risk response should be executed by the consequences of the above calculation.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.15807/JORSJ.60.192","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49598442","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 pricing decision of a retailer who experiences peak demand for a product during a given time interval and wishes to stabilize the demand by adjusting the sales price. The stabilization of demand brings about desirable outcomes such as a reduction in the need for capacity investment and improves the production efficiency in the supply chain. We establish a continuous-time model to analyze the effect of dynamic pricing on peak demand. We find that a closed-form optimal pricing policy minimizes the difference between the actual demand and target level. It is shown that the dynamic pricing not only reduces peak demand but also mitigates fluctuations in the peak demand. Using electricity consumption data as a case study, we show that the proposed pricing policy is effective for reducing the mean peak demand compared to a constant pricing policy.
{"title":"CONTINUOUS-TIME DYNAMIC PRICING FOR STABILIZING STOCHASTIC DEMAND","authors":"Kimitoshi Sato, K. Sawaki","doi":"10.15807/JORSJ.60.178","DOIUrl":"https://doi.org/10.15807/JORSJ.60.178","url":null,"abstract":"In this paper, we consider the pricing decision of a retailer who experiences peak demand for a product during a given time interval and wishes to stabilize the demand by adjusting the sales price. The stabilization of demand brings about desirable outcomes such as a reduction in the need for capacity investment and improves the production efficiency in the supply chain. We establish a continuous-time model to analyze the effect of dynamic pricing on peak demand. We find that a closed-form optimal pricing policy minimizes the difference between the actual demand and target level. It is shown that the dynamic pricing not only reduces peak demand but also mitigates fluctuations in the peak demand. Using electricity consumption data as a case study, we show that the proposed pricing policy is effective for reducing the mean peak demand compared to a constant pricing policy.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.15807/JORSJ.60.178","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48028570","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}
Recently, a seating position can be often selected when a plane or bullet train ticket is reserved. Specially, for theater and stadium, it is important to decide how to assign reservations to seats. This paper proposes a dynamic model where seats’ resources are located at a single line with considering seats position that have already been assigned. An analysis has been conducted and the results show that, 1) optimal policy for an arriving request is to allocate it to one side of the edges of the adjacent vacancies, 2) if all of the resources are vacant at beginning time for booking, then the model corresponds to a single-leg model with multiple seat bookings and single fare class in Lee and Hersh (1993), 3) it is not necessarily optimal that a request is allocated to the less adjacent seats’ vacancy. Finally, this paper proposes an algorithm to solve the optimal policy using above results and conducts numerical examples.
{"title":"A DYNAMIC MODEL WITH RESOURCES PLACED ON SINGLE LINE IN REVENUE MANAGEMENT","authors":"Yu Ogasawara","doi":"10.15807/JORSJ.60.91","DOIUrl":"https://doi.org/10.15807/JORSJ.60.91","url":null,"abstract":"Recently, a seating position can be often selected when a plane or bullet train ticket is reserved. Specially, for theater and stadium, it is important to decide how to assign reservations to seats. This paper proposes a dynamic model where seats’ resources are located at a single line with considering seats position that have already been assigned. An analysis has been conducted and the results show that, 1) optimal policy for an arriving request is to allocate it to one side of the edges of the adjacent vacancies, 2) if all of the resources are vacant at beginning time for booking, then the model corresponds to a single-leg model with multiple seat bookings and single fare class in Lee and Hersh (1993), 3) it is not necessarily optimal that a request is allocated to the less adjacent seats’ vacancy. Finally, this paper proposes an algorithm to solve the optimal policy using above results and conducts numerical examples.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.15807/JORSJ.60.91","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45765946","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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