班德氏分解是一種將原問題分解為主問題與子問題的方法，可以應用於大規模最優化、混整數規劃、隨機最優化等...問題中。典型BLP模型是一種可以預測消費者對產品喜好的效用函數。現在我們擁有一個透過均衡約束數學規劃將典型BLP離散選擇模型建構為混整數規劃的逆優化問題，由於這個模型的目的在於分析2001-2015 UK汽車市場的消費者喜好，模型會隨著消費者人數與產品數量被建構成一個大規模限制式問題。我們將在此研究中提出如何透過班德氏分解法去分解此問題。

Benders decomposition partitions original problem into master problem and subproblem. It can be applied to large scale optimization problem, mixed-integer programming, stochastic optimization, etc. The BLP type model is a utility function to predict consumer preferences for products. We change BLP-type discrete choice model into random-coefficients and mix-integer inverse optimization via mathematical programming with equilibrium constraints. The purpose of this model is to analyze consumer preferences of the UK vehicle market from 2001 to 2015. The model is constructed to a large scale constraints problem due to a large number of customers and products. In this study, the proposed algorithm provides a way of applying the Benders decomposition to solve this problem.

摘要
目錄
第一章 緒論-------------------------1
第二章 文獻回顧-------------------------2
第三章 原問題-------------------------9
第四章 方法-------------------------14
第五章 數學證明-------------------------39
第六章 結論-------------------------44
Reference-------------------------46

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