1 Introduction 管理科學簡介 Chapter 1. 2 1.1 什麼是管理科學 (What is Management...

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Introduction管理科學簡介

Chapter 1

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1.1 什麼是管理科學 (What is Management Science)?

管理科學是解決問題的科學方法可以適用於管理者作最佳決策

管理科學的目標是在內部與外部的限制下，以所得的資源獲得最大的效用

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管理科學求解過程包含下列基本步驟- 分析與建立企業現狀的數學模型- 求解數學模型 - 依據此模型來溝通 / 執行結果

1.1 什麼是管理科學 ?

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管理科學方法Management Science Approach

提供管理部門以數量為基礎來作為營運決策的一種科學方法 (Philip McCord Morse).

以不妨礙常識 (Common Sense) 的方法來應用邏輯 (Logic) 與數學 (Mathematics) (Gene Woolsey)

運用 (US army pamphlet 660-3):– 統計推論 (Statistical inference)– 數學規劃 (Mathematical programming)– 機率模型 (Probabilistic models)– 網路與電腦科學 (Network and computer science)

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管理科學應用Management Science Applications

漢堡王生產漢堡 ( 線性規劃 Linear Programming to best blend cuts of meat to minimize costs)

美國航空人員排班 ( 整數規劃 Integer Programming model to determine an optimal flight schedule.

新立旅遊資訊系統 ( 最短路徑法 Shortest Route Algorithm to developed an onboard car navigation system.

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管理科學應用Management Science Applications

美國州立 10 號公路 ( 專案排程 Project Scheduling Techniques to rebuild Interstate 10 damaged in the 1994 earthquake in the Los Angeles area)

芬蘭環境政策規劃 ( 決策分析 Decision Analysis approach was the basis for the development of a comprehensive framework for planning environmental policy in Finland.

迪斯奈樂園景點設計 ( 等候線模型 Queuing models lead to the development of ‘waiting line entertainment’ in order to improve customer satisfaction.

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1.3 數學模型建立Mathematical Modeling

許多需要管理決策之問題可透過計量或管理分析之程序來解決

管理科學依賴數學模式化受限的數學模式 (constrained mathematical

model) 包含– 目標函數 (An objective function)– 一個或數個限制式 (One or more constraints)

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Desks (D) Chairs (C) Molded steel (M)

– Net profit ( 淨利 ) is $50 per desk $30 per chair $6 per pound of molded steel

sold

– Raw material required 7 pounds of per desk 3 pounds of per chair 1.5 pounds per one pound of

molded steel produced.– Raw material available

2000 pounds

1.3 數學模型建立Mathematical Modeling

範例 Example NewOffice Furniture produces three products

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目標 (Objective): 在原料與其他限制下，決定三種產品產量使得總利潤最大

最大化 (Maximize) 50D + 30C + 6 M 總利潤受限於 (Subject to) 7D + 3C + 1.5M 2000 ( 原鋼

料 ) D 100 ( 合約 )

C500 ( 椅子 )D, C, M 0 ( 非負 Non-negativity)D and C are integers ( 整數 )

1.3 數學模型Mathematical Modeling

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數學模型的分類Classification of Mathematical Models

由模型目的分類– 最佳化模型 Optimization models– 預測模型 Prediction models

由確定性程度分類– 確定性模型 Deterministic models– 機率或隨機性模型 Probabilistic (stochastic) models

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管理科學程序Management Science Process

管理科學是一種採用科學方法來提供管理者關鍵資訊以用於決策的一種原理

管理科學四個程序步驟– 定義問題– 數學模型化– 模型求解– 結果溝通執行

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管理科學程序Management Science Process

Problem definition

Mathematical modeling

Solution of the model

Communication/implementationof results

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1.6 試算表使用 Using Spreadsheets in Management Science Models

試算表 (Spreadsheet) 已成為管理科學模型化一個強而有利的工具

試算表重要性– 以試算表格式呈現給模型建立者– 試算表中易使用統計與數學工具使資料容易分析

– 資料與資訊容易以圖形方式呈現– 試算表事實上以是”企業的語言”

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基本 Excel 函數與運算Basic Excel functions and operators

算術運算 (Arithmetic Operations)– Addition of cells A1and B1:– Subtracting cell B1 from A1:– Multiplication of cell A1 by B1:– Division of cell A1 by B1:– Cell A1xraised to the power in cell B1:

= A1 + B1

= A1 - B1

= A1 * B1

= A1 / B1

= A1^ B1

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相對與絕對位址 (Relative and absolute addresses)– All row and column references are considered relative unless

preceded by a “$” sign– When copied, ‘relative addresses’ change relative to the original

cell position.

Example: Cell E5

Cell G9

=A1+B$3+$C4+$D$6

= C5+D$3+$C8+$D$6


Excel試算表

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F4 鑑 (F4 key)– Pressing F4 will automatically put a $ sign in highlighted

portions of formulas.– Specific operations:

Press the F4 key once: The sign “$” appears in front of all rows and columns of the highlighted area of the formula.

Press the F4 key twice: The “$” sign appears in front of only the row references of the highlighted area of the formula.

Press the F4 key third time: The “$” sign appears in front of only the column references of the highlighted area of the formula.

Press the F4 key forth time: All the “$” signs are eliminated.


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算術函數 (Arithmetic functions)– Sum =SUM(A1:A3)

Returns the sum A1+A2+A3– Average =Average(A1:A3)

Returns the arithmetic average of cells A1, A2, A3– SUMPRODUCT =SUMPRODUCT(A1:A3,B1:B3)

Returns the sum of products A1B1+A2B2+A3B3– ABS =ABS(A3)

Returns the absolute value of the entry in cell A3.


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算術函數 (Arithmetic functions – continued )– SQRT =SQRT(A3)

Returns A3– MAX =MAX(A1:A9)

Returns the Maximum of the entries in cells A1 through A9.– MIN =MIN(A1:A9)

Returns the Minimum of the entries in cells A1 through A9.


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統計函數 Statistical functions– RAND() =RAND()

Generate a random number between 0 and 1 from a uniform distribution.– Probabilities and variable values under the normal distribution

NORMDIST NORMINV=NORMDIST(25,20,3,TRUE) =NORMINV(.55,20,3)Returns P(X<25) when = 20 Returns x0,, such that P(X<x0)=.55 and = 3 when = 20 and = 3

NORMSDIST NORMSMINV=NORMSDIST(1.78) =NORMSINV(.55)Returns P(Z<1.78) Returns z0, such that P(Z<z0)=.55


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統計函數 Statistical functions– Probabilities and variable values under the t- distribution

TDIST TINV=TDIST(1.5,12,1) =TINV(.05,15)Returns P(t>1.5) when =12 Returns t0,, such that

P(t<-t0)=.025 and P(t>t0)=.025

when =15.Note: =TDIST(1.5,12,2) returns P(t<-1.5) + P(t>1.5)when =12.


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統計函數 Statistical functions – 其他機率分配 Other probability distributions

– Poisson =POISSON(7,5,TRUE) Returns P(X<7) for Poisson with = 5.Note: false returns the probability density P(X = 7)

– EXPONDIST =EXPONDIST(40,1/20,TRUE) Returns P(X<40) for the exponential distribution with 1/=20Note: false returns the probability density f(40)=20exp(-20(40))


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條件型函數 (Conditional functions)– IF =IF(A4>4,B1+B2, B1 – B2)

Returns B1+B2 if A4>4, and B1 – B2 if A4

– SUMIF =SUMIF(F1:F12, “>60”,G1:G12) Returns G1+G2+…+G12 only if F1+F2+…+F12>60


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– VLOOKUP =VLOOKUP(6.6,A1:E6,4) If the values in column A of a given table [A1:E6] are sorted (in an

ascending order), VLOOKUP finds the largest value in column A that is less than or equal to 6.6, identifies the row it belongs to, and returns the value in the fourth column that correspond to this row.

Note: If the values in column A are not sorted, =VLOOKUP(6.6,A1:E6,4,FALSE) finds the value 6.6 in column A, identifies the row it belongs to, and returns the value in the fourth column that corresponds to this row.


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統計 Statistical/ 最佳化 Optimization– Data Analysis [Selected from the Tools menu]. Useful entries:

Descriptive Statistics Regression Exponential Smoothing Anova


1 Introduction 管理科學簡介 Chapter 1. 2 1.1 什麼是管理科學 (What is Management...

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