{"title":"Optimal multivariate financial decision making","authors":"C. Bernard, L. Aquino, S. Vanduffel","doi":"10.2139/ssrn.3931992","DOIUrl":"https://doi.org/10.2139/ssrn.3931992","url":null,"abstract":"","PeriodicalId":11868,"journal":{"name":"Eur. J. Oper. Res.","volume":"25 1","pages":"468-483"},"PeriodicalIF":0.0,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74406532","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}
Pub Date : 2022-08-26DOI: 10.48550/arXiv.2208.12570
M. Goerigk, Michael Hartisch
With dramatic improvements in optimization software, the solution of large-scale problems that seemed intractable decades ago are now a routine task. This puts even more real-world applications into the reach of optimizers. At the same time, solving optimization problems often turns out to be one of the smaller difficulties when putting solutions into practice. One major barrier is that the optimization software can be perceived as a black box, which may produce solutions of high quality, but can create completely different solutions when circumstances change leading to low acceptance of optimized solutions. Such issues of interpretability and explainability have seen significant attention in other areas, such as machine learning, but less so in optimization. In this paper we propose an optimization framework that inherently comes with an easily interpretable optimization rule, that explains under which circumstances certain solutions are chosen. Focusing on decision trees to represent interpretable optimization rules, we propose integer programming formulations as well as a heuristic method that ensure applicability of our approach even for large-scale problems. Computational experiments using random and real-world data indicate that the costs of inherent interpretability can be very small.
{"title":"A Framework for Inherently Interpretable Optimization Models","authors":"M. Goerigk, Michael Hartisch","doi":"10.48550/arXiv.2208.12570","DOIUrl":"https://doi.org/10.48550/arXiv.2208.12570","url":null,"abstract":"With dramatic improvements in optimization software, the solution of large-scale problems that seemed intractable decades ago are now a routine task. This puts even more real-world applications into the reach of optimizers. At the same time, solving optimization problems often turns out to be one of the smaller difficulties when putting solutions into practice. One major barrier is that the optimization software can be perceived as a black box, which may produce solutions of high quality, but can create completely different solutions when circumstances change leading to low acceptance of optimized solutions. Such issues of interpretability and explainability have seen significant attention in other areas, such as machine learning, but less so in optimization. In this paper we propose an optimization framework that inherently comes with an easily interpretable optimization rule, that explains under which circumstances certain solutions are chosen. Focusing on decision trees to represent interpretable optimization rules, we propose integer programming formulations as well as a heuristic method that ensure applicability of our approach even for large-scale problems. Computational experiments using random and real-world data indicate that the costs of inherent interpretability can be very small.","PeriodicalId":11868,"journal":{"name":"Eur. J. Oper. Res.","volume":"43 1","pages":"1312-1324"},"PeriodicalIF":0.0,"publicationDate":"2022-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73825920","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}
Pub Date : 2022-08-19DOI: 10.48550/arXiv.2208.09253
Ankur Sinha, A. Das, Guneshwar Anand, S. Jayaswal
In this article, we discuss an exact algorithm for solving mixed integer concave minimization problems. A piecewise inner-approximation of the concave function is achieved using an auxiliary linear program that leads to a bilevel program, which provides a lower bound to the original problem. The bilevel program is reduced to a single level formulation with the help of Karush-Kuhn-Tucker (KKT) conditions. Incorporating the KKT conditions lead to complementary slackness conditions that are linearized using BigM, for which we identify a tight value for general problems. Multiple bilevel programs, when solved over iterations, guarantee convergence to the exact optimum of the original problem. Though the algorithm is general and can be applied to any optimization problem with concave function(s), in this paper, we solve two common classes of operations and supply chain problems; namely, the concave knapsack problem, and the concave production-transportation problem. The computational experiments indicate that our proposed approach outperforms the customized methods that have been used in the literature to solve the two classes of problems by an order of magnitude in most of the test cases.
{"title":"A General Purpose Exact Solution Method for Mixed Integer Concave Minimization Problems","authors":"Ankur Sinha, A. Das, Guneshwar Anand, S. Jayaswal","doi":"10.48550/arXiv.2208.09253","DOIUrl":"https://doi.org/10.48550/arXiv.2208.09253","url":null,"abstract":"In this article, we discuss an exact algorithm for solving mixed integer concave minimization problems. A piecewise inner-approximation of the concave function is achieved using an auxiliary linear program that leads to a bilevel program, which provides a lower bound to the original problem. The bilevel program is reduced to a single level formulation with the help of Karush-Kuhn-Tucker (KKT) conditions. Incorporating the KKT conditions lead to complementary slackness conditions that are linearized using BigM, for which we identify a tight value for general problems. Multiple bilevel programs, when solved over iterations, guarantee convergence to the exact optimum of the original problem. Though the algorithm is general and can be applied to any optimization problem with concave function(s), in this paper, we solve two common classes of operations and supply chain problems; namely, the concave knapsack problem, and the concave production-transportation problem. The computational experiments indicate that our proposed approach outperforms the customized methods that have been used in the literature to solve the two classes of problems by an order of magnitude in most of the test cases.","PeriodicalId":11868,"journal":{"name":"Eur. J. Oper. Res.","volume":"70 1","pages":"977-992"},"PeriodicalIF":0.0,"publicationDate":"2022-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83755689","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":"Bowley vs. Pareto optima in reinsurance contracting","authors":"T. Boonen, Mario Ghossoub","doi":"10.2139/ssrn.3979049","DOIUrl":"https://doi.org/10.2139/ssrn.3979049","url":null,"abstract":"","PeriodicalId":11868,"journal":{"name":"Eur. J. Oper. Res.","volume":"3 1","pages":"382-391"},"PeriodicalIF":0.0,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90622147","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":"Project scheduling problem with fuzzy activity durations: A novel operational law based solution framework","authors":"Mingxuan Zhao, Jian Zhou, Ke Wang, A. Pantelous","doi":"10.2139/ssrn.4170706","DOIUrl":"https://doi.org/10.2139/ssrn.4170706","url":null,"abstract":"","PeriodicalId":11868,"journal":{"name":"Eur. J. Oper. Res.","volume":"374 1","pages":"519-534"},"PeriodicalIF":0.0,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76610310","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":"Scheduling shared passenger and freight transport on a fixed infrastructure","authors":"Lena Hörsting, Catherine Cleophas","doi":"10.2139/ssrn.3886691","DOIUrl":"https://doi.org/10.2139/ssrn.3886691","url":null,"abstract":"","PeriodicalId":11868,"journal":{"name":"Eur. J. Oper. Res.","volume":"16 1","pages":"1158-1169"},"PeriodicalIF":0.0,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87116986","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}
Pub Date : 2022-05-20DOI: 10.48550/arXiv.2205.10017
Matthew Darlington, K. Glazebrook, D. Leslie, Robert Shone, R. Szechtman
In this paper we consider a stochastic game for modelling the interactions between smugglers and a patroller along a border. The problem we examine involves a group of cooperating smugglers making regular attempts to bring small amounts of illicit goods across a border. A single patroller has the goal of preventing the smugglers from doing so, but must pay a cost to travel from one location to another. We model the problem as a two-player stochastic game and look to find the Nash equilibrium to gain insight to real world problems. Our framework extends the literature by assuming that the smugglers choose a continuous quantity of contraband, complicating the analysis of the game. We discuss a number of properties of Nash equilibria, including the aggregation of smugglers, the discount factors of the players, and the equivalence to a zero-sum game. Additionally, we present algorithms to find Nash equilibria that are more computationally efficient than existing methods. We also consider certain assumptions on the parameters of the model that give interesting equilibrium strategies for the players.
{"title":"A stochastic game framework for patrolling a border","authors":"Matthew Darlington, K. Glazebrook, D. Leslie, Robert Shone, R. Szechtman","doi":"10.48550/arXiv.2205.10017","DOIUrl":"https://doi.org/10.48550/arXiv.2205.10017","url":null,"abstract":"In this paper we consider a stochastic game for modelling the interactions between smugglers and a patroller along a border. The problem we examine involves a group of cooperating smugglers making regular attempts to bring small amounts of illicit goods across a border. A single patroller has the goal of preventing the smugglers from doing so, but must pay a cost to travel from one location to another. We model the problem as a two-player stochastic game and look to find the Nash equilibrium to gain insight to real world problems. Our framework extends the literature by assuming that the smugglers choose a continuous quantity of contraband, complicating the analysis of the game. We discuss a number of properties of Nash equilibria, including the aggregation of smugglers, the discount factors of the players, and the equivalence to a zero-sum game. Additionally, we present algorithms to find Nash equilibria that are more computationally efficient than existing methods. We also consider certain assumptions on the parameters of the model that give interesting equilibrium strategies for the players.","PeriodicalId":11868,"journal":{"name":"Eur. J. Oper. Res.","volume":"28 1","pages":"1146-1158"},"PeriodicalIF":0.0,"publicationDate":"2022-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90300812","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":"Unrestricted maximum likelihood estimation of multivariate realized volatility models","authors":"Jan P. Vogler, Vasyl Golosnoy","doi":"10.2139/ssrn.4077801","DOIUrl":"https://doi.org/10.2139/ssrn.4077801","url":null,"abstract":"","PeriodicalId":11868,"journal":{"name":"Eur. J. Oper. Res.","volume":"80 1","pages":"1063-1074"},"PeriodicalIF":0.0,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88599831","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}
Pub Date : 2022-05-01DOI: 10.1016/j.ejor.2022.05.017
M. Kapelko, A. Lansink, J. Zofío
{"title":"Endogenous dynamic inefficiency and optimal resource allocation: An application to the European Dietetic Food Industry","authors":"M. Kapelko, A. Lansink, J. Zofío","doi":"10.1016/j.ejor.2022.05.017","DOIUrl":"https://doi.org/10.1016/j.ejor.2022.05.017","url":null,"abstract":"","PeriodicalId":11868,"journal":{"name":"Eur. J. Oper. Res.","volume":"13 1","pages":"1444-1457"},"PeriodicalIF":0.0,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79918096","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}
Pub Date : 2022-04-01DOI: 10.1016/j.ejor.2022.03.051
Gudbrand Lien, S. Kumbhakar, A. Mishra, J. Hardaker
{"title":"Does risk management affect productivity of organic rice farmers in India? Evidence from a semiparametric production model","authors":"Gudbrand Lien, S. Kumbhakar, A. Mishra, J. Hardaker","doi":"10.1016/j.ejor.2022.03.051","DOIUrl":"https://doi.org/10.1016/j.ejor.2022.03.051","url":null,"abstract":"","PeriodicalId":11868,"journal":{"name":"Eur. J. Oper. Res.","volume":"1 1","pages":"1392-1402"},"PeriodicalIF":0.0,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91135085","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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