Modeling and Analysis of Final-Order Problems with Repairable Spare Parts

在商品供應鏈中，上游零部件供應或生產廠商通常會與使用其零部件的客戶簽訂一個訂單合同。為了向其客戶提供更好的服務，合同中通常包括對所提供零部件維護與修理的約定。然而，隨著科技的革新，供應或生產廠商可能致力於研發下一代新產品，而停止生產某些既有的零部件。此時，這些零部件供應或生產商會向他的客戶提供一個最後訂購該零部件的機會。在這篇論文中，我們從一個客戶的角度出發，探討當為其提供零部件的供應或生產商將停止生產某個特定零部件時，如何決定最後一筆訂單的數量，也就是所謂的最後訂單問題。我們假設在給定的一段時間內，供應或生產廠商依然會對客戶使用過程中壞掉的零部件提供維修，且維修率，即單位時間內能夠維修處理的零部件數目固定，但每次維修的成功率是一個小於100%的確定值，即在修理過程中可能出現維修不成功而需報廢的情況。我們應用瑪律柯夫鏈對上述問題進行建模，而後結合C#、MATLAB、EXCEL等程式語言與軟體分析求解，特別的，我們通過一「實際服務水準」指標ASL替客戶評估所需的最後訂單數量。事實上，模型中一些資料的回歸分析也可為我們提供其他衡量指標，並且簡化計算過程。最後，我們以案例示範如何依據所建立的瑪律柯夫鏈模型，透過陣列模擬，為客戶決定最後訂單的數量。案例分析結果顯示，我們所提出的方法確可幫助客戶，依他們實際情況，決定最後一筆訂單的最佳採購數量。Original equipment manufacturers of advanced products often offer service contracts for system support to their customers, for which spare parts are needed. In order to provide better service to their customers, these suppliers need to ensure the availability of spare parts in repairing and maintenance operations. However, manufactures of spare parts may stop their productions at certain future time because of technology innovation, and their customers are usually offered opportunities to place final orders for these spare parts. In this paper, we consider a manufacturer of complex spare parts offering service contracts for its customers and committing to repair failed spare parts throughout a fixed service period. A customer would instead face the problem of how many spare parts to order, which we may address as a problem of determining the optimal number of final order. The spare parts that we consider are repairable with a fixed repair rate in terms of number of parts per unit time. However, for each part under repair, the chance of being successfully repaired may not be 100%. A transient Markov model is established to deal with the problem, and programming language C# combing with software packages MATLAB and EXCEL is employed to perform the simulation. An index ASL representing the actual service level is adopted to describe the performance of the selected final order. A regression analysis that results in another index for us to carry out more efficient computation is proposed as well. Finally, simulation results of the model are discussed. It is found that the proposed model can indeed help a customer to place an optimal order when facing a final order problem.Acknowledgements i Abstract ii 中文摘要 iii Contents iii List of Figures v List of Tables vi List of Symbols vii Chapter 1: Introduction 1 1.1. Background and Motivation 1 1.2. Research Purpose 2 1.3. Literature Review 2 Chapter 2: Model, Assumptions and Definitions 5 2.1. Background Knowledge 5 2.1.1. Reliability and Maintainability Theory 5 2.1.2. Absorbing Markov Chain 6 2.1.3. Regression Theory 7 2.2. The Basic Model and Definitions 8 2.3. Assumptions and Extensions 12 Chapter 3: Markov Analysis 14 3.1. From CTMC to DTMC 14 3.2. Time to Absorbing State 15 3.3. Actual Service Level 17 Chapter 4: Numerical Results 20 4.1. Simulation Combining C# and Matlab 20 4.2. Managerial Insights 24 4.3. Regression Approach 26 Chapter 5: Conclusions and Future Work 28 5.1. Conclusions 28 5.2. Future Work 29 References 30 Appendix 3