多次投料問題在中斷式幾何分配下之研究

Multiple Lot Sizing Decisions with Interrupted Geometric Yield

蘇泰盛(Tai-Sheng Su)

指導教授 ： 許錫美

國立交通大學/管理學院/工業工程與管理系所/博士(2009年)

https://doi.org/10.6842/NCTU.2009.00083

摘要

本論文探討有交期限制的多次投料問題：首先探討生產週期時間具不確定性，單階段生產系統的多次投料問題；隨之探討二階段生產系統的多次投料問題。二階段生產系統在每個生產階段之後，皆設有檢驗站，在每個投料時點，藉由每個階段的良品在製品數量與未滿足的需求量，須同時決定各階段的投料量。本研究假設各階段產出的良品個數服從中斷式幾何分配，成本函數考慮設置成本、變動成本、成品存貨持有成本及缺貨成本四項。以最小生產成本為目標，提出最佳投料量的特性，基於此特性，來設計動態規劃演算法，以求解各階段的最佳投料量。針對二階段生產系統的多次投料問題，在需求量較大時，我們提出一個啟發式演算法，可以有效地求得滿意解。最後，藉由數值範例來觀察決策參數的特性與最佳投料量的特性。

關鍵字

批量 ； 中斷式幾何分配 ； 動態規劃 ； 生產/存貨系統

並列摘要

In this study, we examine two issues of multiple lot-sizing problem with interrupted geometric yield and non-rigid demand. Firstly, we investigate a single-stage multiple lot-sizing problem with variable production lead-time. Secnodly, we investigate a two-stage multiple lot-sizing problem with simultaneously determining the optimal lot sizes for the two production stages in each period. The following cost items are considered in these problems: setup cost, variable production cost, inventory holding cost, and shortage cost. These problems are formulated as a dynamic program (DP), respectively, and some lemmas are proposed to confine their solution spaces. We propose a heuristic solution method to solve the two-stage multiple lot-sizing problem for reducing the computational time. Finally, numerical examples are illustrated to shown the efficiences of the proposed heuristic method.

並列關鍵字

Lot-sizing ； Interrupted geometric distribution ； Dynamic programming ； Production/Inventory system

參考文獻

[1] Anily, S., “Single machine lot sizing with uniform yields and rigid demands: robustness of the optimal solution,” IIE Transactions, 27, 625-633, 1995.

[2] Anily, S., A. Beja, and A. Mendel, “Optimal lot sizes with geometric production yield and rigid demand,” Operations Research, 5(3), 424-432, 2002.

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

[4] Beja, A., “Optimal Reject Allowance with Constant Marginal Production Efficiency,” Naval Research Logistics Quarterly, 24, 21-33, 1977.

[5] Ben-Zvi, T. and A. Grosfeld-Nir, “Serial production systems with random yield and rigid demand: a heuristic,” Operations Research Letters, 35, 235-244, 2007.