無母數逆最佳化方法與純特徵需求函數預測最優產品特徵組合的數值實驗

Experiment of a nonparametric inverse optimization method to predict optimal product characteristic combination with pure characteristics demand function

李軍毅(Chun-Yi Lee)

指導教授 ： 李雨青

國立清華大學/工學院/工業工程與工程管理學系/碩士(2019年)

摘要

目前具有隨機係數的離散選擇模型已廣泛應用於研究各種異質消費者偏好的產品市場。我們利用逆最佳化的方式建立一個具均衡限制式的數學最佳化模型，並延伸Fox等人在2011年所提出的無母數方法估計純特徵需求模型中的隨機係數。在本實驗中我們採用非線性規劃求解器Gurobi來求解我們重組改寫的均衡限制數學規劃模型並提出將估計問題轉化為求解全域最佳化問題的推導過程。我們利用西元2001年至2015年的英國汽車市場總體的銷售數據進行數值實驗，以評估該模型的有效性和計算效率。在此研究中我們使用兩種皆延伸自Fox等人在2011年提出的估計量來達到無母數假設的目的。我們從個人電腦得到的數值實驗結果中發現，其中一種方法在目前可執行的問題規模下能夠從研究者生成的市場總體數據訓練出有效的隨機係數以預測出訓練資料外產品的市佔率。我們在未來的目標是在Gurobi Cloud上進行真實世界規模問題的數值實驗，並在真實規模下找出此模型有效性與計算效率間的平衡點。

關鍵字

純特徵需求函數 ； 隨機係數 ； 無母數預測 ； 數學規劃 ； 最佳特徵組合

並列摘要

Discrete choice model with random coefficients have widely applied in discriminating heterogeneous preferences over consumers in various product market. We build constrained optimization models of mathematical program with equilibrium constraints (MPEC) to estimate the random coefficients in the pure characteristics demand model with the nonparametric method proposed by Fox et al. (2011). We adopt combinatorial reformulation of MPEC and propose a procedure to transform the estimation problem into global optimization problem solved by nonlinear programing solver Gurobi. We conduct the numerical experiments to realize the effectiveness and efficiency of the model with the aggregate data collected from UK vehicle market during 2001 to 2015. Inspired by research conducted by Fox et al. (2011), we use two approaches of generating grid points estimator to discretize distribution. We observe that one of them can predict market share solidly in synthetic data from numerical results obtained on our local single machine. We aim to carry out these experiments on Gurobi Cloud with real-world problem size data and to find an appropriate number of grid points for such problem size in the future.

並列關鍵字

pure characteristics demand ； random coefficient ； nonparametric estimation ； mathematical program with equilibrium constraints ； optimal characteristic combination

參考文獻

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Berry, S., & Pakes, A. (2007). The pure characteristics demand model. International Economic Review, 48(4), 1193-1225.