多產品流線型環境中考慮隨機良率的製造與預防性保養整合規劃問題

Abstract

生產規劃問題和預防性保養計劃問題在學術研究中被視為獨立的主題，而常被分開研究。然而在現實情況下，保養活動和生產活動的影響經常互相關聯。保養機臺會使生產效能降低，並可能導致供不應求。忽視保養還可能導致生產設備持續惡化，增加生產過程中的不確定性並降低生產效率。因此，涉及生產規劃和預防性保養計劃的整合決策過程是一個需要關注的議題。 在這項研究中，我們考慮一個決策者同時決定生產計劃和預防性保養計劃的問題。在每個週期決策者決定生產數量以及是否進行維護，以最小化總成本。我們將此問題以動態規劃模型描述，並證明此問題的確定性版本為NP-困難。 我們提出了兩個演算法，根據每個週期的狀態，在週期的開頭決定計劃。我們透過兩個啟發式規則，即設置良率閾值和比較保養決策的成本，來決定保養計畫，之後通過求解線性規劃模型來獲得生產計劃。我們通過數值實驗評估算法的性能和在不同情境下的有效性。

Production planning and preventive maintenance planning are typically treated as separate subjects in academic studies. However, in real-world scenarios, maintenance activities can significantly impact production capacity, potentially resulting in a shortage of supply to meet demand. Neglecting maintenance can also lead to a continuous deterioration of production equipment, causing uncertainty and inefficiency in the production process. Consequently, the integrated decision-making process involving both production planning and preventive maintenance planning becomes a critical and practical challenge that requires attention. In this study, we consider a problem where the decision maker determines both production plan and preventive maintenance plan. The production quantity and whether to conduct maintenance are decided every period, aiming to minimize the total cost. We formulate the problem with dynamic programming model, then show the deterministic version of our problem to be NP-hard. We propose two algorithms, where planning is conducted at the beginning of each period given observed states. The maintenance plan is decided by two heuristic ideas, setting a yield rate threshold and comparing costs of decisions. After that, the production plan may be obtained through solving linear programming model. We evaluate the algorithms performance and their effectiveness under different scenarios through numerical experiments.