多階段流水線生產環境中考量部分維護之生產與預防性保養最佳化問題

Abstract

本研究探討在流水線生產系統中具備部分維護機制的多階段整合生產與維護問題。在此情境下，機器狀態會隨時間惡化導致良率下降，且產生的瑕疵品無法重新加工，需要透過預防性維修恢復機器效能。系統提供多種維護等級，每種等級能帶來不同程度的良率提升，同時也伴隨不同程度的產能損失。每個生產階段皆假設具有已知的最大產能，並會因選擇的維護等級而減少。本研究假設該生產系統僅生產單一產品，且生產需要依序經過多個生產階段。每一期的需求為確定且事先已知，若未能滿足需求則會產生短缺成本。本研究的目標是找出一個整合的生產與維護排程以最小化總成本，其中包含生產成本、庫存成本與短缺成本。 在本研究中，我們以非線性整數規劃模型（NLIP）來構建此問題。由於NLIP 模型求解較耗時，我們設計了一套啟發式演算法，能在可接受的計算時間內提供近似最適佳解。該演算法包含三個階段。第一階段透過向後搜尋（backward search），為每個生階段獨立產生維護排程。接著在第二階段中，利用線性規劃模型決定生產計畫。第三階段則調整維護時間，以增強整體維護排程中各階段之間的一致性。透過數值實驗，我們展示了所提演算法的有效性，並證明該演算法的結構具備平行化的潛力，可進一步提升運算效率。最後，我們在隨機環境下進行額外實驗，進一步驗證所提演算法在處理不確定性時仍能維持有效性與效率。

This research addresses a multi-stage integrated production and maintenance problem with partial maintenance in a flow shop production system. In this setting, machine conditions deteriorate over time, leading to a decline in yield rate, and any defective items produced cannot be reworked. To restore the machine performance, preventive maintenance can be performed. Multiple maintenance levels are available, each offering a different degree of yield improvement, but also incurring varying levels of capacity loss. Each production stage is assumed to have a known maximum processing capacity, which is reduced depending on the chosen maintenance level. We assume the production system only produces a single type of product, which must be processed sequentially across multiple stages. A deterministic demand is specified for every period in advance, and any unfulfilled demand incurs a shortage cost. The objective of this research is to determine an integrated production and maintenance schedule that minimizes the total cost, which comprises production cost, inventory cost, and shortage cost. In this study, we formulate the problem with nonlinear integer programming model. Since the NLIP model is time-consuming, we develop a heuristic algorithm which is able to provide near-optimal solution in an acceptable computation time. The proposed algorithm consists of three phases. In first phase, maintenance schedule for each stage is generated independently by backward search process. After that, the production plan can be obtained by linear programming model in second phase. In the third phase, perform maintenance timing shifting to enhance inter-stage dependencies of the overall schedule. Through numerical experiment, we illustrate the effectiveness of our proposed algorithm, and further indicate its inherent structure is able to implement parallelization which provide more efficiency. Finally, we conduct an additional experiment under a stochastic environment, which further confirms the efficiency of the proposed algorithm in handling uncertainty.