Transcript Ch01 - Introduction

Chapter 1
Introduction
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1.1 What Is Management Science?
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Management Science is the discipline that adapts the
scientific approach for problem solving to help managers
make informed decisions.
The goal of management science is to recommend the
course of action that is expected to yield the best
outcome with what is available.
1.1 What Is Management Science?
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The basic steps in the management science problem
solving process involves
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Analyzing business situations and building mathematical
models to describe them;
Solving the mathematical models;
Communicating/implementing recommendations based on the
models and their solutions.
The Management Science Approach
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A scientific method of providing executive departments with a
quantitative basis for decisions regarding operations (Philip
McCord Morse).
Logic and common sense are basic components in supporting
the decision making process.
The use of techniques such as (US army pamphlet 660-3):
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Statistical inference
Mathematical programming
Probabilistic models
Network and computer science
Management Science Applications
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Linear Programming was used by Burger King to find how
to best blend cuts of meat to minimize costs.
Integer Linear Programming model was used by American Air
Lines to determine an optimal flight schedule.
The Shortest Route Algorithm was implemented by the Sony
Corporation to developed an onboard car navigation
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Management Science Applications
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Project Scheduling Techniques were used by a contractor to
rebuild Interstate 10 damaged in the 1994 earthquake in the Los
Angeles area.
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Decision Analysis approach was the basis for the development of
a comprehensive framework for planning environmental policy in
Finland.
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Queuing models are incorporated into the overall design plans for
Disneyland and Disney World, which lead to the development of
‘waiting line entertainment’ in order to improve customer
satisfaction.
1.3 Mathematical Modeling
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Many managerial decision situations lend themselves to
quantitative analyses.
A constrained mathematical model consists of
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An objective
One or more constraints
1.3 Mathematical Modeling
Example
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NewOffice Furniture produces three products
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$50 per desk
$30 per chair
$6 per pound of molded steel
sold
Raw material required
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Net profit is
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Desks (D)
Chairs (C)
Molded steel (M)
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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 Mathematical Modeling
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Objective: Determine production mix that maximizes the
profit under the raw material constraint and other
production requirements (detailed next).
Maximize 50D + 30C + 6 M
Subject to 7D + 3C + 1.5M 2000 (raw steel)
D
100 (contract )
C
500 (cushions available)
D, C, M 0
(Non-negativity)
D and C are integers
Classification of Mathematical Models
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Classification by the model purpose
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Classification by the degree of certainty of the data in the
model
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Optimization models
Prediction models
Deterministic models
Probabilistic (stochastic) models
The Management Science Process
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Management Science is a discipline that adopts the
scientific method to provide management with key
information needed in making informed decisions.
The team concept calls for the formation of (consulting)
teams consisting of members who come from various
areas of expertise.
The Management Science Process
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The four-step management science process (for details
click on each button)
Problem definition
Mathematical modeling
Solution of the model
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Communication/implementation
of results
1.6 Using Spreadsheets in Management
Science Models
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Spreadsheets have become a powerful tool in
management science modeling.
Several reasons for the popularity of spreadsheets:
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Data are submitted to the modeler in spreadsheets
Data can be analyzed easily using statistical and mathematical
tools readily available in the spreadsheet.
Data and information can easily be displayed using graphical
tools.
Basic Excel functions and operators
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Arithmetic Operations
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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
Basic Excel functions and operators
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Relative and absolute addresses
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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 =A1+B$3+$C4+$D$6
Cell G9 = C5+D$3+$C8+$D$6
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Basic Excel functions and operators
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The F4 key
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Pressing F4 will automatically put a $ sign in highlighted
portions of formulas.
Specific operations:
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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.
Basic Excel functions and operators
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Arithmetic functions
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Sum
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=SUMPRODUCT(A1:A3,B1:B3)
Returns the sum of products A1B1+A2B2+A3B3
ABS
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=Average(A1:A3)
Returns the arithmetic average of cells A1, A2, A3
SUMPRODUCT
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Returns the sum A1+A2+A3
Average
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=SUM(A1:A3)
=ABS(A3)
Returns the absolute value of the entry in cell A3.
Basic Excel functions and operators
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Arithmetic functions – continued
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SQRT
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=MAX(A1:A9)
Returns the Maximum of the entries in cells A1 through A9.
MIN
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Returns A3
MAX
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=SQRT(A3)
=MIN(A1:A9)
Returns the Minimum of the entries in cells A1 through A9.
Basic Excel functions and operators
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Statistical functions
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RAND()
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Generate a random number between 0 and 1 from a uniform distribution.
Probabilities and variable values under the normal distribution
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=RAND()
NORMDIST
=NORMDIST(25,20,3,TRUE)
Returns P(X<25) when m = 20
and s = 3
NORMSDIST
=NORMSDIST(1.78)
Returns P(Z<1.78)
NORMINV
=NORMINV(.55,20,3)
Returns x0,, such that P(X<x0)=.55
when m = 20 and s = 3
NORMSMINV
=NORMSINV(.55)
Returns z0, such that P(Z<z0)=.55
Basic Excel functions and operators
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Statistical functions
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Probabilities and variable values under the t- distribution
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TDIST
=TDIST(1.5,12,1)
Returns P(t>1.5) when n=12
Note:
=TDIST(1.5,12,2)
returns P(t<-1.5) + P(t>1.5)
when n=12.
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TINV
=TINV(.05,15)
Returns t0,, such that
P(t<-t0)=.025 and P(t>t0)=.025
when n=15.
Basic Excel functions and operators
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Statistical functions – Other probability distributions
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Poisson
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Returns P(X<7) for Poisson with l = 5.
Note: false returns the probability density P(X = 7)
EXPONDIST
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=POISSON(7,5,TRUE)
=EXPONDIST(40,1/20,TRUE)
Returns P(X<40) for the exponential distribution with 1/m=20
Note: false returns the probability density f(40)=20exp(-20(40))
Basic Excel functions and operators
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Conditional functions:
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IF
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Returns B1+B2 if A4>4, and B1 – B2 if A4
SUMIF
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=IF(A4>4,B1+B2, B1 – B2)
=SUMIF(F1:F12, “>60”,G1:G12)
Returns G1+G2+…+G12 only if F1+F2+…+F12>60
Basic Excel functions and operators
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VLOOKUP
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=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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Basic Excel functions and operators
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Statistical/Optimization
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Data Analysis [Selected from the Tools menu]. Useful entries:
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Descriptive Statistics
Regression
Exponential Smoothing
Anova
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