An Estimation of Distribution Algorithm for Mixed-Variable Newsvendor Problems
As one of the classical problems in the economic market, the newsvendor problem aims to make maximal profit by determining the optimal order quantity of products. However, the previous newsvendor models assume that the selling price of a product is a predefined constant and only regard the order qua...
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| Veröffentlicht in: | IEEE transactions on evolutionary computation Jg. 24; H. 3; S. 479 - 493 |
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01.06.2020
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| Abstract | As one of the classical problems in the economic market, the newsvendor problem aims to make maximal profit by determining the optimal order quantity of products. However, the previous newsvendor models assume that the selling price of a product is a predefined constant and only regard the order quantity as a decision variable, which may result in an unreasonable investment decision. In this article, a new newsvendor model is first proposed, which involves of both order quantity and selling price as decision variables. In this way, the newsvendor problem is reformulated as a mixed-variable nonlinear programming problem, rather than an integer linear programming problem as in previous investigations. In order to solve the mixed-variable newsvendor problem, a histogram model-based estimation of distribution algorithm (EDA) called <inline-formula> <tex-math notation="LaTeX">{\mathrm{ EDA}}_{mvn} </tex-math></inline-formula> is developed, in which an adaptive-width histogram model is used to deal with the continuous variables and a learning-based histogram model is applied to deal with the discrete variables. The performance of <inline-formula> <tex-math notation="LaTeX">{\mathrm{ EDA}}_{mvn} </tex-math></inline-formula> was assessed on a test suite with eight representative instances generated by the orthogonal experiment design method and a real-world instance generated from real market data of Alibaba. The experimental results show that, <inline-formula> <tex-math notation="LaTeX">{\mathrm{ EDA}}_{mvn} </tex-math></inline-formula> outperforms not only the state-of-the-art mixed-variable evolutionary algorithms, but also a commercial software, i.e., Lingo. |
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| AbstractList | As one of the classical problems in the economic market, the newsvendor problem aims to make maximal profit by determining the optimal order quantity of products. However, the previous newsvendor models assume that the selling price of a product is a predefined constant and only regard the order quantity as a decision variable, which may result in an unreasonable investment decision. In this article, a new newsvendor model is first proposed, which involves of both order quantity and selling price as decision variables. In this way, the newsvendor problem is reformulated as a mixed-variable nonlinear programming problem, rather than an integer linear programming problem as in previous investigations. In order to solve the mixed-variable newsvendor problem, a histogram model-based estimation of distribution algorithm (EDA) called <inline-formula> <tex-math notation="LaTeX">{\mathrm{ EDA}}_{mvn} </tex-math></inline-formula> is developed, in which an adaptive-width histogram model is used to deal with the continuous variables and a learning-based histogram model is applied to deal with the discrete variables. The performance of <inline-formula> <tex-math notation="LaTeX">{\mathrm{ EDA}}_{mvn} </tex-math></inline-formula> was assessed on a test suite with eight representative instances generated by the orthogonal experiment design method and a real-world instance generated from real market data of Alibaba. The experimental results show that, <inline-formula> <tex-math notation="LaTeX">{\mathrm{ EDA}}_{mvn} </tex-math></inline-formula> outperforms not only the state-of-the-art mixed-variable evolutionary algorithms, but also a commercial software, i.e., Lingo. As one of the classical problems in the economic market, the newsvendor problem aims to make maximal profit by determining the optimal order quantity of products. However, the previous newsvendor models assume that the selling price of a product is a predefined constant and only regard the order quantity as a decision variable, which may result in an unreasonable investment decision. In this article, a new newsvendor model is first proposed, which involves of both order quantity and selling price as decision variables. In this way, the newsvendor problem is reformulated as a mixed-variable nonlinear programming problem, rather than an integer linear programming problem as in previous investigations. In order to solve the mixed-variable newsvendor problem, a histogram model-based estimation of distribution algorithm (EDA) called [Formula Omitted] is developed, in which an adaptive-width histogram model is used to deal with the continuous variables and a learning-based histogram model is applied to deal with the discrete variables. The performance of [Formula Omitted] was assessed on a test suite with eight representative instances generated by the orthogonal experiment design method and a real-world instance generated from real market data of Alibaba. The experimental results show that, [Formula Omitted] outperforms not only the state-of-the-art mixed-variable evolutionary algorithms, but also a commercial software, i.e., Lingo. |
| Author | Tang, Ke Li, Yixuan Zhou, Aimin Wang, Feng |
| Author_xml | – sequence: 1 givenname: Feng surname: Wang fullname: Wang, Feng email: fengwang@whu.edu.cn organization: School of Computer Science, Wuhan University, Hubei, China – sequence: 2 givenname: Yixuan surname: Li fullname: Li, Yixuan email: liyixuan@whu.edu.cn organization: School of Computer Science, Wuhan University, Hubei, China – sequence: 3 givenname: Aimin orcidid: 0000-0002-4768-5946 surname: Zhou fullname: Zhou, Aimin email: amzhou@cs.ecnu.edu.cn organization: School of Computer Science and Technology, East China Normal University, Shanghai, China – sequence: 4 givenname: Ke orcidid: 0000-0002-6236-2002 surname: Tang fullname: Tang, Ke email: tangk3@sustech.edu.cn organization: Department of Computer Science and Engineering, Shenzhen Key Laboratory of Computational Intelligence, Southern University of Science and Technology, Shenzhen, China |
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| SubjectTerms | Adaptation models Biological system modeling Computational modeling Continuity (mathematics) Design of experiments Economics Estimation of distribution algorithm (EDA) Evolutionary algorithms histogram model Histograms Integer programming Investment Linear programming Mathematical model mixed-variable optimization problem newsvendor problem Nonlinear programming Order quantity orthogonal experiment design Variables |
| Title | An Estimation of Distribution Algorithm for Mixed-Variable Newsvendor Problems |
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