中斷式幾何良率分配及交期限制下二階段生產系統投料決策之研究

Abstract

本研究探討一個新的多次投料問題，此問題為一有交期限制的二階段生產系統，其製程良率服從中斷式幾何分配。我們建立遞迴數學模式代表此問題並以動態規劃求解。本研究也提出界定最佳解範圍的定理，幫助求解此問題。然而利用動態規劃求解大規模問題可能存在求解效率議題。因此本研究提出一個簡化動態規劃網路的演算法，利用將數個分支結合為一個的手法，將原本的網路轉變為較簡單的網路。在大量的實驗中，結果顯示本研究提出之簡化演算法可幫助現場人員有效率地求解大規模及高良率情境下之多次投料問題。

This research examines a new multiple lot-sizing problem, which is in the context of a two-stage production system with a due-date-based demand and the process yields are both governed by interrupted geometric (IG) distributions. We model this problem as a recursive formula and solve it by dynamic programming. This research also develops lemmas for solving this problem. However, there may still be many computational efforts in solving this DP problem. An efficient algorithm for resolving the computational issue is proposed. This algorithm is designed to reduce the DP network into a much simpler one—through combining a group of DP branches into a single one. Extensive experiments have been carried out. Results indicate that the reduction algorithm is quite helpful to practitioners in dealing with large-scale cases with high-yield.