1. NCCU Academic Hub
  2. Publications
  3. College of Commerce
  4. Theses
  5. Item

Publications-Theses

Article View/Open

Publication Export

Google ScholarTM

NCCU Library

Citation Infomation

Related Publications in TAIR

題名 多變量配適深度學習與最佳化決策
Deep Learning for Multivariate Distribution Fitting and Optimal Decision Making
作者 汪君儫
Wang, Chun-Hao
貢獻者 周彥君<br>莊皓鈞
Chou, Yen-Chun<br>Chuang, Hao-Chun
汪君儫
Wang, Chun-Hao
關鍵詞 混合密度網路
高斯混合模型
深度學習
線性規劃
報童問題
Mixture Density Network
Gaussian Mixture Model
Deep Learning
Linear Programming
Newsvendor problem
日期 2023
上傳時間 16-Aug-2023 13:31:55 (UTC+8)
摘要 本研究旨在運用基於高斯混合模型 (Gaussian Mixture Model, GMM) 的多變量混合密度網路 (Mixture Density Networks, MDN) 並結合線性整數規劃解決實務和理論上常見的問題：具隨機性的多品項調配最佳化。多品項調配最佳化是企業在資源有限之情況下，需要分配資源給多個品項以最大化利潤或最小化成本，其中每個品項的參數有各自的隨機分布。為了展示模型效果，本研究選定一個具代表性的問題作為分析標的：資源限制下的多品項報童問題，並分別探討考慮風險中立與規避的情況，以鮮食品項的銷售資料進行實證分析。本研究貢獻在於應用GMM理論和深度學習配適大量銷售資料以估計任何多品項的真實分布，以及計算效率高的線性整數規劃模型能夠確保有最佳解，亦能彈性增加限制式以符合實務情境。
This research aims to utilize Gaussian Mixture Model (GMM) based Multivariate Mixture Density Networks (MDN) and combine them with linear integer programming to solve a common practical and theoretical problem: stochastic multi-item allocation optimization. Multi-item allocation optimization involves allocating resources to multiple items in order to maximize profit or minimize cost, under the constraint of limited resources, where each item’s parameters have their own stochastic distribution. To demonstrate the effectiveness of the model, this study selects a representative problem for analysis: the multi-item newsvendor problem under resource constraints, making decision under risk neutral and risk averse. Empirical analysis is conducted using sales data of fresh food items. The contributions of this research lie in applying GMM theory and deep learning to fit a large amount of sales data to estimate unknown distribution of multi-item, as well as developing a computationally efficient linear integer programming model that ensures the optimal solution while allowing flexibility to add constraints to match practical scenarios.
參考文獻 Bandi, H., Bertsimas, D., & Mazumder, R. (2019). Learning a mixture of gaussians via mixed-integer optimization. INFORMS Journal on Optimization, 1(3), 221-240.
     Bishop, C. M. (1994). Mixture density networks. Technical Report. Aston University, Birmingham. (Unpublished)
     Chen, J., & Tan, X. (2009). Inference for multivariate normal mixtures. Journal of Multivariate Analysis, 100(7), 1367-1383.
     Guillaumes, A. B. (2017). Mixture density networks for distribution and uncertainty estimation (Doctoral dissertation, Universitat Politècnica de Catalunya. Facultat d`Informàtica de Barcelona).
     Hartigan, J. A., & Hartigan, P. M. (1985). The dip test of unimodality. The Annals of Statistics, 70-84.
     Huber, J., Müller, S., Fleischmann, M., & Stuckenschmidt, H. (2019). A data-driven newsvendor problem: From data to decision. European Journal of Operational Research. 278(3), 904-915.
     Jammernegg, W., & Kischka, P. (2012). Newsvendor problems with VaR and CVaR consideration. Handbook of newsvendor problems: models, extensions and applications, 197-216.
     Kruse, J. (2020). Technical report: Training mixture density networks with full covariance matrices. arXiv preprint arXiv: 2003.05739.
     Lotfi, S., & Zenios, S. A. (2018). Robust VaR and CVaR optimization under joint ambiguity in distributions, means, and covariances. European Journal of Operational Research, 269(2), 556-576.
     Murray, C. C., Gosavi, A., & Talukdar, D. (2012). The multi-product price-setting newsvendor with resource capacity constraints. International Journal of Production Economics, 138(1), 148-158.
     Özler, A., Tan, B., & Karaesmen, F. (2009). Multi-product newsvendor problem with value-at-risk considerations. International Journal of Production Economics, 117(2), 244-255.
     Peerlings, D. E., van den Brakel, J. A., Baştürk, N., & Puts, M. J. (2022). Multivariate Density Estimation by Neural Networks. IEEE Transactions on Neural Networks and Learning Systems, 1-12.
     Punia, S., Singh, S. P., & Madaan, J. K. (2020). From predictive to prescriptive analytics: A data-driven multi-item newsvendor model. Decision Support Systems, 136, 113340.
     Reynolds, D. A. (2009). Gaussian mixture models. Encyclopedia of biometrics, 741(659-663).
     Wang, J., & Taaffe, M. R. (2015). Multivariate mixtures of normal distributions: properties, random vector generation, fitting, and as models of market daily changes. INFORMS Journal on Computing, 27(2), 193-203.
     Wang, T., Cho, K., & Wen, M. (2019, August). Attention-based mixture density recurrent networks for history-based recommendation. In Proceedings of the 1st International Workshop on Deep Learning Practice for High-Dimensional Sparse Data (pp. 1-9).
     Williams, P. M. (1996). Using neural networks to model conditional multivariate densities. Neural computation, 8(4), 843-854.
描述 碩士
國立政治大學
資訊管理學系
110356003
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0110356003
資料類型 thesis
dc.contributor.advisor 周彥君<br>莊皓鈞zh_TW
dc.contributor.advisor Chou, Yen-Chun<br>Chuang, Hao-Chunen_US
dc.contributor.author (Authors) 汪君儫zh_TW
dc.contributor.author (Authors) Wang, Chun-Haoen_US
dc.creator (作者) 汪君儫zh_TW
dc.creator (作者) Wang, Chun-Haoen_US
dc.date (日期) 2023en_US
dc.date.accessioned 16-Aug-2023 13:31:55 (UTC+8)-
dc.date.available 16-Aug-2023 13:31:55 (UTC+8)-
dc.date.issued (上傳時間) 16-Aug-2023 13:31:55 (UTC+8)-
dc.identifier (Other Identifiers) G0110356003en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/146789-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 資訊管理學系zh_TW
dc.description (描述) 110356003zh_TW
dc.description.abstract (摘要) 本研究旨在運用基於高斯混合模型 (Gaussian Mixture Model, GMM) 的多變量混合密度網路 (Mixture Density Networks, MDN) 並結合線性整數規劃解決實務和理論上常見的問題：具隨機性的多品項調配最佳化。多品項調配最佳化是企業在資源有限之情況下，需要分配資源給多個品項以最大化利潤或最小化成本，其中每個品項的參數有各自的隨機分布。為了展示模型效果，本研究選定一個具代表性的問題作為分析標的：資源限制下的多品項報童問題，並分別探討考慮風險中立與規避的情況，以鮮食品項的銷售資料進行實證分析。本研究貢獻在於應用GMM理論和深度學習配適大量銷售資料以估計任何多品項的真實分布，以及計算效率高的線性整數規劃模型能夠確保有最佳解，亦能彈性增加限制式以符合實務情境。zh_TW
dc.description.abstract (摘要) This research aims to utilize Gaussian Mixture Model (GMM) based Multivariate Mixture Density Networks (MDN) and combine them with linear integer programming to solve a common practical and theoretical problem: stochastic multi-item allocation optimization. Multi-item allocation optimization involves allocating resources to multiple items in order to maximize profit or minimize cost, under the constraint of limited resources, where each item’s parameters have their own stochastic distribution. To demonstrate the effectiveness of the model, this study selects a representative problem for analysis: the multi-item newsvendor problem under resource constraints, making decision under risk neutral and risk averse. Empirical analysis is conducted using sales data of fresh food items. The contributions of this research lie in applying GMM theory and deep learning to fit a large amount of sales data to estimate unknown distribution of multi-item, as well as developing a computationally efficient linear integer programming model that ensures the optimal solution while allowing flexibility to add constraints to match practical scenarios.en_US
dc.description.tableofcontents 第一章 研究背景 1
     第二章 風險中立下的隨機性多品項最佳化 3
     第一節 線性規劃模型 3
     第二節 單變量MDN介紹 5
     第三章 多品項期望利潤最佳化分析 8
     第一節 資料與分布配適 8
     第二節 實驗結果分析 12
     第四章 風險規避下的隨機性多品項最佳化 14
     第一節 線性規劃模型 14
     第二節 實驗結果 15
     第五章 結論 24
     參考文獻 25		zh_TW
dc.format.extent 1750859 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0110356003en_US
dc.subject (關鍵詞) 混合密度網路zh_TW
dc.subject (關鍵詞) 高斯混合模型zh_TW
dc.subject (關鍵詞) 深度學習zh_TW
dc.subject (關鍵詞) 線性規劃zh_TW
dc.subject (關鍵詞) 報童問題zh_TW
dc.subject (關鍵詞) Mixture Density Networken_US
dc.subject (關鍵詞) Gaussian Mixture Modelen_US
dc.subject (關鍵詞) Deep Learningen_US
dc.subject (關鍵詞) Linear Programmingen_US
dc.subject (關鍵詞) Newsvendor problemen_US
dc.title (題名) 多變量配適深度學習與最佳化決策zh_TW
dc.title (題名) Deep Learning for Multivariate Distribution Fitting and Optimal Decision Makingen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) Bandi, H., Bertsimas, D., & Mazumder, R. (2019). Learning a mixture of gaussians via mixed-integer optimization. INFORMS Journal on Optimization, 1(3), 221-240.
     Bishop, C. M. (1994). Mixture density networks. Technical Report. Aston University, Birmingham. (Unpublished)
     Chen, J., & Tan, X. (2009). Inference for multivariate normal mixtures. Journal of Multivariate Analysis, 100(7), 1367-1383.
     Guillaumes, A. B. (2017). Mixture density networks for distribution and uncertainty estimation (Doctoral dissertation, Universitat Politècnica de Catalunya. Facultat d`Informàtica de Barcelona).
     Hartigan, J. A., & Hartigan, P. M. (1985). The dip test of unimodality. The Annals of Statistics, 70-84.
     Huber, J., Müller, S., Fleischmann, M., & Stuckenschmidt, H. (2019). A data-driven newsvendor problem: From data to decision. European Journal of Operational Research. 278(3), 904-915.
     Jammernegg, W., & Kischka, P. (2012). Newsvendor problems with VaR and CVaR consideration. Handbook of newsvendor problems: models, extensions and applications, 197-216.
     Kruse, J. (2020). Technical report: Training mixture density networks with full covariance matrices. arXiv preprint arXiv: 2003.05739.
     Lotfi, S., & Zenios, S. A. (2018). Robust VaR and CVaR optimization under joint ambiguity in distributions, means, and covariances. European Journal of Operational Research, 269(2), 556-576.
     Murray, C. C., Gosavi, A., & Talukdar, D. (2012). The multi-product price-setting newsvendor with resource capacity constraints. International Journal of Production Economics, 138(1), 148-158.
     Özler, A., Tan, B., & Karaesmen, F. (2009). Multi-product newsvendor problem with value-at-risk considerations. International Journal of Production Economics, 117(2), 244-255.
     Peerlings, D. E., van den Brakel, J. A., Baştürk, N., & Puts, M. J. (2022). Multivariate Density Estimation by Neural Networks. IEEE Transactions on Neural Networks and Learning Systems, 1-12.
     Punia, S., Singh, S. P., & Madaan, J. K. (2020). From predictive to prescriptive analytics: A data-driven multi-item newsvendor model. Decision Support Systems, 136, 113340.
     Reynolds, D. A. (2009). Gaussian mixture models. Encyclopedia of biometrics, 741(659-663).
     Wang, J., & Taaffe, M. R. (2015). Multivariate mixtures of normal distributions: properties, random vector generation, fitting, and as models of market daily changes. INFORMS Journal on Computing, 27(2), 193-203.
     Wang, T., Cho, K., & Wen, M. (2019, August). Attention-based mixture density recurrent networks for history-based recommendation. In Proceedings of the 1st International Workshop on Deep Learning Practice for High-Dimensional Sparse Data (pp. 1-9).
     Williams, P. M. (1996). Using neural networks to model conditional multivariate densities. Neural computation, 8(4), 843-854.		zh_TW