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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Bibliographic Details
Published in:IEEE transactions on evolutionary computation Vol. 24; no. 3; pp. 479 - 493
Main Authors: Wang, Feng, Li, Yixuan, Zhou, Aimin, Tang, Ke
Format: Journal Article
Language:English
Published: New York IEEE 01.06.2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
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
ISSN:1089-778X, 1941-0026
Online Access:Get full text
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Summary: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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ISSN:1089-778X
1941-0026
DOI:10.1109/TEVC.2019.2932624