考量加工時間不確定之加權分位數排程方法初探

Abstract

本研究旨在針對少量多樣生產環境下的非等效平行機台排程問題，建立一加工時間分位數預測模型，以及基於加工時間分位數的隨機性排程模型。產品於機台上的加工時間為排程問題的重要參數，除了其預測值的精準度會影響排程效能，了解加工時間的不確定性亦為決策的關鍵要素。然而，由於此生產模式具有產品多樣性高、生產批量小，以及加工時間不確定性高等特性，導致1.歷史數據觀察數不足、2.產品機台組合更複雜、3.加工時間無一固定的機率分佈，以上皆為少量多樣生產系統難以有效預測加工時間的因素，而傳統以加工時間期望值為基礎的排程方法亦無法有效捕捉生產過程的變異，使排程決策的優化更加艱難。為了克服這些問題，本研究利用集成學習方法預測不同產品機台組合的加工時間分位數，並將其納入排程最佳化模型中，提出加權分位數排程方法。與傳統的期望值方法相比，分位數方法能更全面地反映加工時間的分布範圍，有助於在不確定性高的環境下提升排程決策的穩健性。透過多次模擬實驗，本研究驗證了分位數排程方法在最小化最大完工時間上的優勢，也探討其在機台平均完工時間與產品平均完工時間的表現，並分析不同分位數權重配置對排程結果的影響。本研究不僅突破了加工時間需假設為特定機率分布的限制，也提供了一種提升生產系統穩健性的隨機性排程方法，對於動態生產環境下的決策應用具有潛在貢獻。

This study aims to address the unrelated parallel machine scheduling problem in a high-mix, low-volume (HMLV) production environment by developing a processing time quantile prediction model and a stochastic scheduling model based on processing time quantiles. Processing time on machines is a crucial parameter for scheduling problems, as both its prediction accuracy and consideration of its uncertainty are key factors in decision-making. However, due to the high diversity of products, small batch sizes, and significant processing time variability in HMLV production, effective processing time prediction is hindered by factors such as (1) insufficient historical data, (2) complex product-machine combinations, and (3) a lack of a fixed probability distribution for processing times. As a result, scheduling methods based on expected processing times fail to capture uncertain factors in production systems appropriately, making scheduling optimization more challenging. To address these issues, this study employs ensemble learning methods to predict processing time quantiles for various product-machine combinations, incorporating these quantiles into the scheduling optimization model and proposing a weighted quantile scheduling approach. Compared to traditional expected value methods, the quantile-based approach offers a more comprehensive reflection of processing time distribution, improving the robustness of scheduling decisions in highly uncertain environments. Through multiple simulation experiments, this study validates the advantages of the quantile scheduling method in minimizing makespan and explores its performance in terms of average machine completion time and average product completion time. The effects of different quantile weighting configurations on scheduling outcomes are also analyzed. This study not only breaks the assumption of specific probability distributions for processing times but also presents a stochastic scheduling approach that enhances the robustness of production systems, demonstrating potential contributions to decision-making in dynamic production environments.