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.

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