Optimize0530v 3

May 31, 20190 likes44 views

本文讨论了一个专业母婴用品公司的年度生产计划，以最大化总利润为目标，建立了线性规划数学模型。模型中考虑了多项约束条件，包括最低和最高需求、生产能力以及采购资金限制，并利用贰虫肠别濒进行求解。最终得出的利润比前一年有所增加，显示了优化生产计划的重要性。

大綱
? 文章資訊
? 企業概況與目標
? 生產計劃線性模型建立
? 目標函數
? 限制式
? 模型結果
? EXCEL求解

文章資訊
? 遼寧工程技術大學學報(自然科學版)
第29 卷第2 期、2010 年4 月
? 作者：
陳金鳳（上海交通大學軟體學院）
? 求解方法：
EXCEL（線性模型）

企業概況與目標
? 該企業為一間集設計、製造、銷售為一體的專業母嬰用品公司
? 背景:
利潤高的產品得不到最大生產，資金使用在效益不高的產品上，導致淨
利潤創新低
? 目標:
建立年度生產計畫的總利潤最大化的線性規劃數學模型

生產計劃線性模型建立
假設:
?定價不變
?必須滿足銷售預測需求
?月度採購資金不能超過去年同期
?工人工作不加班
?裝配車間能力不足可隨時獲得補充
目標:
利潤最大化

生產計劃線性模型建立
? 目標函式 – 營收
營收
月份項目
??? 為第 i 個月產品 j 的產量
?? 為產品 j 的平均銷售價格
??
??
??
利潤
補充
變數???共有8(項目)*12(月)=96個
=> 最佳化每個項目在每個月要生產多少
MAX ? = ?
?=1
12
?
?=1
8
?? ??? ? ?

生產計劃線性模型建立
? 目標函式 - 成本
成本
??? × (採購成本??+運輸成本)
+ 1,600(每人每月薪資) × 30(人數) × 12(月)
+ 其他成本120,000(元/月) × 12(月)
??
??
??
利潤
MAX ? = ?
?=1
12
?
?=1
8
?? ??? ? ?

生產計劃線性模型建立
? 限制式
1.最低需求約束：各種產品月產量最低限制
2.最高需求約束：各種產品月產量最高限制
??? ≥ ??? ? = 1,2, … , 12; ? = 1,2, … , 10
; ??? 為第i個月產品j的最低產量
??? ≥ ??? ? = 1,2, … , 12; ? = 1,2, … , 10
; ???為第i個月產品j的最高產量

生產計劃線性模型建立
? 限制式
3. 生產能力約束：生產人員的月總工時有最大限制
4. 採購資金約束：每個月的採購資金有最高額限制
5. 非負限制
?
?=1
10
??? ?? ≤ 30 人 × 2,000(??/人)
??為產品j的平均耗費工時數
?
?=1
12
?
?=1
8
??? ?? ≤ ??
?? 為產品j的平均採購成本, ??為第i月的採購資金上限
??? ≥ 0 ? = 1,2, … , 12; ? = 1,2, … , 10

? MAX Z 為 1,091,422.86元
? 與前一年比較，用同樣採購金
額，多出淨利416,167.46元
模型結果

EXCEL求解
? =MAX(目標式)
? =COUNT(變數)
在此有96個
? 限制式
=變數<=限制
在此有206個
96 ×2+1+12+1

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2. 大綱 ? 文章資訊 ? 企業概況與目標 ? 生產計劃線性模型建立 ? 目標函數 ? 限制式 ? 模型結果 ? EXCEL求解

3. 文章資訊 ? 遼寧工程技術大學學報(自然科學版) 第29 卷第2 期、2010 年4 月 ? 作者：陳金鳳（上海交通大學軟體學院） ? 求解方法： EXCEL（線性模型）

4. 企業概況與目標 ? 該企業為一間集設計、製造、銷售為一體的專業母嬰用品公司 ? 背景: 利潤高的產品得不到最大生產，資金使用在效益不高的產品上，導致淨利潤創新低 ? 目標: 建立年度生產計畫的總利潤最大化的線性規劃數學模型

5. 生產計劃線性模型建立假設: ?定價不變 ?必須滿足銷售預測需求 ?月度採購資金不能超過去年同期 ?工人工作不加班 ?裝配車間能力不足可隨時獲得補充目標: 利潤最大化

6. 生產計劃線性模型建立 ? 目標函式 – 營收營收月份項目 ??? 為第 i 個月產品 j 的產量 ?? 為產品 j 的平均銷售價格 ?? ?? ?? 利潤補充變數???共有8(項目)*12(月)=96個 => 最佳化每個項目在每個月要生產多少 MAX ? = ? ?=1 12 ? ?=1 8 ?? ??? ? ?

7. 生產計劃線性模型建立 ? 目標函式 - 成本成本 ??? × (採購成本??+運輸成本) + 1,600(每人每月薪資) × 30(人數) × 12(月) + 其他成本120,000(元/月) × 12(月) ?? ?? ?? 利潤 MAX ? = ? ?=1 12 ? ?=1 8 ?? ??? ? ?

8. 生產計劃線性模型建立 ? 限制式 1.最低需求約束：各種產品月產量最低限制 2.最高需求約束：各種產品月產量最高限制 ??? ≥ ??? ? = 1,2, … , 12; ? = 1,2, … , 10 ; ??? 為第i個月產品j的最低產量 ??? ≥ ??? ? = 1,2, … , 12; ? = 1,2, … , 10 ; ???為第i個月產品j的最高產量

9. 生產計劃線性模型建立 ? 限制式 3. 生產能力約束：生產人員的月總工時有最大限制 4. 採購資金約束：每個月的採購資金有最高額限制 5. 非負限制 ? ?=1 10 ??? ?? ≤ 30 人 × 2,000(??/人) ??為產品j的平均耗費工時數 ? ?=1 12 ? ?=1 8 ??? ?? ≤ ?? ?? 為產品j的平均採購成本, ??為第i月的採購資金上限 ??? ≥ 0 ? = 1,2, … , 12; ? = 1,2, … , 10

10. ? MAX Z 為 1,091,422.86元 ? 與前一年比較，用同樣採購金額，多出淨利416,167.46元模型結果

11. EXCEL求解 ? =MAX(目標式) ? =COUNT(變數) 在此有96個 ? 限制式 =變數<=限制在此有206個 96 ×2+1+12+1

12. 決策分析 ? 靈敏性分析（敏感度報告）

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