A Multiple Lot-Sizing Decision for Two-Stage Systems with Interrupted Geometric Yield and Non-Rigid Demand

二階段生產系統在中斷式幾何分配和有交期限制下的多次投料問題

10.29977/JCIIE.200907.0001

許錫美(Hsi-Mei Hsu)；蘇泰盛(Tai-Sheng Su)；巫木誠(Muh-Cherng Wu)；黃亮銓(Liang-Chuan Huang)

批量 ； 中斷式幾何分配 ； 動態規劃 ； 二階段系統 ； 生產／存貨系統 ； lot-sizing ； interrupted geometric distribution ； dynamic programming ； two-stage system ； production/inventory system

工業工程學刊

26卷4期（2009 / 07 / 01）

229 - 244

英文

本研究探討二階段生產系統的多次投料問題。己知顧客訂購數量、交期、及各階段產出良品的個數屬中斷式幾何分配，以最小化生產總成本爲目標，在訂單確認後及交期前的每個投料時點，如何決定各階段的最佳投料量。生產總成本包含：每次生產各階段的設置成本、變動成本、成品的存貨成本及缺貨成本。本研究將該問題建構成動態規劃問題，提出四個定理以縮小求解搜尋空間。當需求量很大時，動態規劃的手法求解精確最佳解相當耗時，因此本研究提出一個啟發式演算法，快速求得近似最佳解。當需求量較小時，因利用動態規劃求精確最佳解的時間不長，因此仍建議使用該法求精確最佳解。由多個案例中，驗證該啟發式演算法在需求量很大時有極好的績效。

In this paper, we investigate a multiple-lot-sizing-production-to-order problem for a two-stage system with interrupted geometric yield and non-rigid demand. Given a due date for an order, we simultaneously determine the optimal lot sizes for the two production stages in each period. This problem is formulated as a dynamic program (DP), and four lemmas are proposed to confine its solution space. Solving the DP for large-scale cases is computationally extensive. We propose a heuristic solution method for the DP in order to obtain a satisfactory solution efficiently. Numerical tests indicate that the heuristic method yields results with satisfactory accuracy in cases with large initial demand. However, while in cases with low initial demand, we would suggest the use of DP method to solve the problem because its required computational efforts are acceptable in practice and the results obtained from the heuristic method become far less accurate.

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