資料包絡分析法 (Data Envelopment Analysis; DEA) 為一項被廣泛地用來衡量各決策方案(Decision Making Units; DMU) 相對績效的有效工具。而在傳統的DEA方法中限制資料為已知，因此無法有效地被應用在衡量方案的未來績效上，導致使用者無法保證利用傳統DEA 預測出的績效之準確性。在此研究中，我們發展一序列統計漸進抽樣法 (Sequential Statistical Approximation)，以有效地抽樣方式來估計隨機DEA 模型中的未知數，並保證方案的真實績效會落於一信賴區間內。數值實驗中，證明了提出的新方法優於傳統的抽樣方式，在相同的樣本數下，能更準確地預估方案的相對績效。而在實證研究中，我們以一無人搬運車系統 ( Automated Guided Vehicle System; AGVS) 為例子，衡量由不同水準的車數與車載量兩因子組成的方案績效，判斷出相對有效的設計方案以提供給決策者參考。

Data Envelopment Analysis (DEA) is widely used as a tool to measure the eciency of a set of decision making units(DMUs). Traditional DEA requires observations to be deterministic while many of them are stochastic in practice and this results that eciencies are stochastic as well. In that case, conclusions based on traditional DEA could be misleading because the realized level of stochastic data is sensitive to eciency scores. In this paper, we develop a sequential sampling method to find optimal sample sizes of each DMU to estimate random inputs or outputs in a cost eective way. The
gap of estimated eciency scores between true ones are guaranteed to fall in a small interval. Furthermore, the quality of eciency scores and the feasibility of solutions
are assured by statistical theories. We illustrate the proposed method by performing an Automated Guided Vehicle System (AGVS) to identify eective alternatives with two input factors: the number of vehicles and the load capacity of single vehicle. The eciency interval and the sample size of each DMU are obtained to observe their scores. The numerical results present the viability and the eectiveness of our proposed method.

1 Introduction 1
1.1 Problem Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Research Objectives and Framework . . . . . . . . . . . . . . . . . . . . . . 3
2 Literature Review 6
2.1 Traditional Data Envelopment Analysis . . . . . . . . . . . . . . . . . . . . . 6
2.2 Stochastic Data Envelopment Analysis . . . . . . . . . . . . . . . . . . . . . 6
3 Problem Denition 8
4 Solution Methodology 11
4.1 The Mainframe of SSA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
4.2 Notation Simplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
4.3 Feasibility Condence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.4 Optimality Gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.5 Sampling Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
5 Numerical Example 18
5.1 Problem Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
5.2 Comparison with Sample Average Allocation . . . . . . . . . . . . . . . . . . 19
6 Empirical Study 25
7 Conclusions 28
Appendix 29

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