決定批量是生產管理的一項重要決策，但現有的批量方法皆忽視批量問題中的需求模糊性。因此，本研究乃以經濟批量排程問題(economic lot scheduling problem ; ELSP)為範圍，即針對單一生產設備的幾種產品去調整其生產計劃，討論在模糊需求環境下批量方法的研究。
經濟批量排程問題的模式主要分為三類：(1)兩種基本解法：獨立解法(The Independent Solution ; IS)與共同週期法(The Common Cycle Approaches ; CC) ; (2)基本週期法(basic period ; BP) ; (3)延伸基本週期法(extended basic period ; EBP)。本研究的方法主要是將各個模式中之需求量透過三角模糊數來表示，並利用模糊數學的各種運算，將模糊需求代入經濟批量排程問題的各個模式中。由於所運算出的數學模式非常龐大，且模式中又含有限制式的因子，因此，將再加入遺傳演算法做最佳解的搜尋。經實驗分析後得知，模糊需求ELSP之平均總成本與傳統ELSP模式中之平均總成本相差無幾。
藉由本研究所設計出之運作模式，不僅考慮了現實環境中需求的不確定性因素，由於利用遺傳演算法做為搜尋的機制，也加快了獲得整體最佳解的速度，與避免落入區域最佳解的機會，提供決策者做決策的一項依據。在研究過程中亦發現許多值得未來繼續探討的問題與研究機會，並於文末提出建議。

Determining the lot sizes for products is an important strategy. Conventionally lot-sizing models often ignore future fuzziness or uncertainty in the lot sizing problems. This thesis considers the economic lot-size scheduling problem (ELSP) that concerns production planning in multi-product, single machine, and discusses fuzzy demands.
The economic lot-size scheduling problem is divided to three parts: (1) Two basic approaches ─ Independent Solution (IS) and Common Cycle (CC) approaches,(2) The Basic Period (BP) approach, and (3) The Extended Basic Period (EBP) approach. The thesis uses triangular fuzzy number and fuzzy mathematic in order to put the fuzzy demand into the economic lot-size scheduling problem models. Due to the complexity of the mathematical model and constraint, a genetic algorithm (GA) approach is developed to search for the optimal solution. After the data analyses, we found that the average total cost of the ELSP between the fuzzy and nonfuzzy models is almost equal.
According to the result and approach of this thesis, we were able to consider the uncertain demand factor and quickly find the optimal solution. It may provide important reference to industrial makers.

目錄
中文摘要……………………………………………………………………I
英文摘要……………………………………………………………………II
致謝…………………………………………………………………………III
目錄…………………………………………………………………………IV
表目錄………………………………………………………………………VII
圖目錄………………………………………………………………………VIII
第一章 緒論1
1.1研究背景與動機1
1.2研究目的2
1.3研究方法與步驟3
1.4研究工具3
1.5論文架構4
第二章 文獻探討5
2.1存貨模式的種類與演進5
2.1.1單階批量與排程問題(single-level lot sizing problem)6
2.1.2多階批量與排程問題(multi-level lot sizing problem)8
2.2經濟批量排程問題之背景(economic lot scheduling problem ; LSP)11
2.2.1經濟批量排程問題之定義11
2.2.2經濟批量排程問題模式12
2.3模糊理論18
2.3.1模糊理論簡介18
2.3.2三角模糊數18
2.3.3解模糊19
2.4遺傳演算法21
2.4.1編碼與解碼22
2.4.2初始母體22
2.4.3適應函數22
3.4.4複製22
2.4.5交配23
2.4.6突變23
2.4.7終止條件23
第三章 模糊需求單階ELSP模式中的二種基本解法24
3.1模糊需求之獨立解法(The Independent Solution ; IS)26
3.2模糊需求之共同週期法(The Common Cycle Approaches ; CC)30
3.3模糊需求共同週期法模式上之推論37
第四章 以基本週期法與延伸基本週期法求解模糊需求單階ELSP44
4.1基本週期(basic period ; BP)法44
4.1.1模糊需求之基本週期法44
4.1.2遺傳算法求解模糊需求之基本週期法58
4.2延伸基本週期(extended basic period ; EBP)法64
4.2.1模糊需求之延伸基本週期法64
4.2.2遺傳算法求解模糊需求之延伸基本週期法79
第五章 數據實證86
5.1基本參數設定之探討86
5.2數據實證探討87
5.2.1不同機器利用率下之探討87
5.2.2六個文獻中比較之例子92
5.3本章小節100
第六章 結論與未來研究方向101
6.1結論101
6.2未來研究方向101
參考文獻103
附錄一 ELSP模式範例說明110
附錄二 公式推導117
2.2(a)：獨立解法推導過程117
2.2(b)：共同週期法推導過程118
2.2(c)：延伸基本週期法推導過程119
3.1(a)：IS法之重心求解120
3.2(a)：模糊數學之運算123
3.2(b)：CC法目標式之重心求解123
3.2(c)：CC法限制式之重心求解130
3.3(a)：Lemma 1推導過程132
3.3(b)：模糊需求之解模糊135
4.1(a)：模糊數學之運算136
4.1(b)：BP法目標式之重心求解137
4.1(c)：BP法限制式之重心求解143
4.2(a)：模糊數學之運算145
4.2(b)：EBP法目標式之重心求解145
4.2(c)：EBP法限制式之重心求解152
附錄三：實證結果圖表154

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