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

Multiple lot-sizing decisions in a two-stage production with an interrupted geometric yield and non-rigid demand

黃亮銓(Liang-Chuan Huang)

指導教授 ： 巫木誠

國立交通大學/管理學院/工業工程與管理系所/碩士(2009年)

https://doi.org/10.6842/NCTU.2009.00275

摘要

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。

關鍵字

批量 ； 中斷式幾何分配 ； 動態規劃 ； 兩階段系統 ； 生產/存貨系統

並列摘要

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.

並列關鍵字

lot-sizing ； interrupted geometric distribution ； dynamic programming ； two-stage system ； production/inventory system

參考文獻

Anily S (1995). Single machine lot sizing with uniform yields and rigid demands: robustness of the optimal solution. IIE Transactions 27: 625-633.

Anily S, Beja A and Mendel A (2002). Optimal lot sizes with geometric production yield and rigid demand. Operations Research 5: 424-432.

Barad M and Braha D (1996). Control limits for multi-stage manufacturing processes with binomial yield (single and multiple production runs). Journal of the Operational Research Society 47: 98-112.

Beja A (1977). Optimal reject allowance with constant marginal production efficiency. Naval Research Logistics Quarterly 24: 21-33.

Ben-Zvi T and Grosfeld-Nir A (2007). Serial production systems with random yield and rigid demand: a heuristic. Operations Research Letters 35: 235-244.