次序試驗(OofA)研究物件添加的順序對於實驗結果的影響。在研究此類型實驗時，一個常用的分析方法是利用成對順序模型(PWO)。而在設計的選擇上，儘管包含所有可能排序的全次序設計是最佳的，實務上我們經常無法對每一種排序進行實驗。在本論文中，我們提出一個基於William設計且滿足多個平衡性質的部分次序設計，並展示其於單機排程問題中找出最佳排序的應用。此外，我們介紹一種基於成對順序模型的分數演算法，用於決定次序問題中的最佳執行排序。模擬的結果顯示該演算法能在短時間內提供一個相當接近最佳解的排序。

Order-of-addition (OofA) experiments are to study the addition order of components and the response. A popular way to analyze such experiments is by using pair-wise ordering (PWO) models. The full design that includes all possible orderings is optimal but impractical due to its large run size. In this paper, we propose a fractional OofA design based on William’s design that satisfies several balance criteria and present its application in single-machine scheduling where the goal is to find the best ordering of tasks. Additionally, we introduce the score method based on the PWO model that determines an ordering of the tasks. Simulation results suggest that the method is capable of providing an ordering with its cost value close to the optimal value.

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