本研究考慮景氣不確定下，單一製造商的產能擴充決策分析。我們假設需求隨著景氣而變動，相較於過往的文獻，大多假設市場景氣是可以觀測得知，而我們是假設決策者對於市場景氣的認知是未知且無法觀測。本研究會以最大化利潤為目標，進行產能擴充決策。其中，我們提出一個能描述市場景氣波動之產能擴充決策的部分可觀察式馬可夫決策過程(partially observable Markov decision process,POMDP)模型，用於景氣狀態不確定下之情境；製造商能藉由當期顧客實際需求量作觀測函數，利用觀測函數去更新後期對於市場景氣狀態的置信度，使製造商在進行產能擴充時，有一定的信心程度得知市場景氣樣貌，大幅降低需求的不確定性，最終將決策過程以動態規劃最優化模型進行求解。進行數值求解後，求得製造商在不同狀態下各期的最佳產能擴充決策。本研究發現，無論市場景氣狀態的變動如何，當機台擴充數量達到臨界值時，製造商偏向不擴充機台數，藉此節省成本支出，以提高期望利潤。此外，在雙景氣變動的考量下，本研究提出一個近似動態規劃方法來求解對於景氣不確定時的決策問題；多景氣變動的考量下，利用短視近利(myopic)決策求解多景氣不確定時的決策問題，並驗證該策略能近似於最佳解。

This research addresses the decision analysis of capacity expansion for a single manufacturer considering economic uncertainty. Unlike most existing literature that assumes market conditions can be observed, we assume that decision-makers have limited knowledge and cannot directly observe the state of the market. The objective of this study is to maximize profit through capacity expansion decisions. We propose a partially observable Markov decision process (POMDP) model that captures the market’s volatility and enables decision-making under uncertain economic conditions. The manufacturer utilizes the actual customer demand as an observation function to update its belief about the state of the market, reducing demand uncertainty when making capacity expansion decisions. The optimal decision process is then solved using dynamic programming. The numerical analysis provides the manufacturer’s optimal capacity expansion decisions for different states. Our findings suggest that regardless of changes in market conditions, the manufacturer tends to refrain from expanding the number of production units once the expansion quantity reaches a critical value, thus saving costs and increasing expected profits. Additionally, under considerations of dual economic fluctuations, we propose an approximate dynamic programming method to solve decision problems under economic uncertainty. Furthermore, for multiple economic fluctuations, we employ a myopic decision strategy to approximate the optimal solution for decision problems under uncertain economic conditions and validate its effectiveness.

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