考量成本結構下運用貝式逐樣法於存貨監控機制之研究

Abstract

全球性的新冠疫情，揭櫫了現代供應鏈背後的複雜和脆弱。這些斷鏈事件促使企業重新思考其存貨控制的策略。傳統的存貨控制方法，如 Shewhart 管制圖及其貝氏的變形，在動態、成本敏感的環境下往往不敷使用。因此，本論文探討了一種創新的存貨控制方法，即利用貝氏逐樣法，將成本結構嵌入存貨管制圖中。

傳統的存貨管制圖通常假設了靜態的環境，且未能充分考慮存貨相關成本。例如 Shewhart 管制圖依賴預設的管制上下限來確定需求是否落在可接受範圍內，但並未考慮缺貨或庫存過剩的成本影響。同樣地，現有的貝氏管制圖雖然改進了 Shewhart 模型，透過後驗分佈來捕捉需求變化，但仍缺乏對成本的整合。為了解決這些限制，基於貝氏逐樣法，考慮與成本相關的參數，我們提出了一種新型的管制圖。我們首先用動態規劃重述問題，然後利用成本函數的分段線性近似來求解問題。

透過在各種需求情景和成本結構下的數值模擬，我們全面地評估我們所提出的成本貝氏管制圖。在市場需求穩定的情況下，我們的管制圖維持了略高的存貨水準。至於在市場需求增長的情境下，無論需求成長的幅度大小，我們提出的方法都能達到最低的總成本。研究的結果顯示，將成本結構整合到控制圖中特別有益於存貨管理。成本貝氏管制圖在缺貨成本超過存貨過剩成本的情況下呈現顯著的成本優勢。

我們的研究結果表明，將成本結構納入存貨管制圖中，能大幅提高存貨管制圖的效能。我們所提出的貝氏逐樣方法為存貨管理提供了一個既靈活且具有成本效益的解決方案。企業若透過根據特定成本結構制定公司的存貨管制圖，可以最大化存貨管理的效率，更好地管理現代供應鏈的複雜性。

Recent global events, such as the COVID-19 pandemic, have highlighted the complexities and vulnerabilities of modern supply chains. These disruptions have prompted companies to rethink their inventory control strategies. Traditional control methods, such as Shewhart control charts and various Bayesian approaches, have their merits but often fall short in dynamic and cost-sensitive environments. This thesis explores an innovative approach to inventory control by embedding cost structures into control charts using Bayesian sequential analysis.

Traditional inventory control charts, while helpful, often assume a static environment and do not adequately consider the costs. The Shewhart control chart, for instance, relies on preset control limits to determine whether demands are within acceptable ranges. However, it does not account for the cost implications of stockouts or overstocking. Similarly, existing Bayesian control charts improve on the Shewhart model by using posterior distributions to capture demand changes, but they still lack comprehensive cost integration. To address these limitations, we propose a novel control chart that integrates cost-related parameters. Our methodology is grounded in the Bayesian sequential analysis. We first express the problem in dynamic programming. Then, we utilize a piecewise linear approximation to solve the formulation.

We evaluated our Cost-Bayesian control chart through numerical simulations under various demand scenarios and cost structures. Under stable market demand conditions, the proposed control chart maintains slightly higher stock levels. In scenarios with increasing market demand, the proposed method achieves the lowest total cost, regardless of the growth magnitude. The results show that integrating cost structures into the control chart is particularly beneficial. The Cost-Bayesian control chart shows significant cost advantages in the case where stockout costs exceed overstock costs.

The findings of our study suggest that incorporating cost structures into inventory control charts greatly enhances their performance. The proposed Bayesian sequential approach offers a flexible and cost-effective solution for inventory management. By tailoring inventory control charts to specific cost structures, companies can achieve optimal performance and better manage the complexities of modern supply chains.