未知偏好函式下之互動式多目標派工方法

Abstract

本研究提出了一種用於具有未知偏好函數的多標準派工決策問題（Multi-Criteria Decision-Making）的互動式重心法（Interactive Centroid Method, ICM）。在製造過程中的各種問題中，派工問題是最需要解決的問題之一，因為產品和機器的不同組合會導致每個指標的性能不同。然而，大多數研究只關注優化總完成時間或總能耗，而不是同時考慮其他製造目標。因此，不僅難以提出有效的協調戰略，而且難以實施研究成果到現實產業界。 在這項研究中，我們建立了一個與決策者交互的互動方法。其目標是在偏好函式未知的情況下，協助決策者實現同時最小化完工時間、最小化總產量損失和最小化總能耗的目標並且讓最終方案能夠使決策者的效用值最大化。而通過決策者的每次選擇，互動式重心法會學習未知的偏好函式並且移除較不偏好的範圍。最後，決策者可以在大約10次比較中獲得近乎最優的方案。另外，我們還通過和逼近理想解排序法（Technique for Order Preference by Similarity to Ideal Solution , TOPSIS）與分段線性觀點理論法（Piecewise Linear Prospect Theory Method, PLP）進行比較，研究也針對線性與二次偏好函式進行驗證，結果顯示互動式重心法不僅能夠處理連續標準問題，而且能夠在合理的交互次數和計算時間內找到近乎最優的解決方案。

This study presents an interactive centroid method (ICM) for multi-criteria decision-making (MCDM) in dispatching problems with unknown preference functions. Among various problems in manufacturing, dispatching problem is one of the most needed issue since different combination of products and machines will lead to different performance in each criterion. However, most of the research only focuses on optimizing total completion time or total power consumption instead of considering in other manufacturing objectives at the same time. Hence, it’s not only hard to come up with an efficient coordinated strategy but also hard to implement the research outcome to the industry. In this research, we construct an interactive approach to interact with decision makers. The objective is to assist decision makers to reach the goal of minimizing the makespan, total yield loss, and total power consumption at the same time meanwhile optimize the utility value of final solution under the condition of unknown preference function. Through each selection by decision makers, ICM learns the unknown preference function and shrinks down the least preferred criteria space. Afterwards, decision makers can obtain the near-optimal solution in approximately 10 comparisons. We also verify ICM by comparing different performance with Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) as well as Piecewise Linear Prospect Theory (PLP) under linear and quadratic preference functions, and the result shows that ICM is not only capable to deal with the continuous criteria problems but also able to find the near-optimal solution in reasonable number of interactive times and computing time.