1. Chapter 1
Introduction

2. 1.1 What Is Management Science?
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.

3. 1.1 What Is Management Science?
The basic steps in the management science problem solving process involves
Analyzing business situations and building mathematical models to describe them;
Solving the mathematical models;
Communicating/implementing recommendations based on the models and their solutions.

4. The Management Science Approach
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):
Statistical inference
Mathematical programming
Probabilistic models
Network and computer science

5. Management Science Applications
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
system.

6. Management Science Applications
Project Scheduling Techniques were used by a contractor to rebuild Interstate 10 damaged in the 1994 earthquake in the Los Angeles area.
Decision Analysis approach was the basis for the development of a comprehensive framework for planning environmental policy in Finland.
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.

7. 1.3 Mathematical Modeling
Many managerial decision situations lend themselves to quantitative analyses.
A constrained mathematical model consists of
An objective
One or more constraints

8. 1.3 Mathematical Modeling
Example
NewOffice Furniture produces three products
Desks (D)
Chairs (C)
Molded steel (M)
Net profit 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

9. 1.3 Mathematical Modeling
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 £ (raw steel) D ³ 100 (contract ) C £ 500 (cushions available) D, C, M ³ 0 (Non-negativity) D and C are integers

10. Classification of Mathematical Models
Classification by the model purpose
Optimization models
Prediction models
Classification by the degree of certainty of the data in the model
Deterministic models
Probabilistic (stochastic) models

11. The Management Science Process
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.

12. The Management Science Process
The four-step management science process (for details click on each button)
Problem definition
Mathematical modeling
Solution of the model
Communication/implementation of results

13. 1.6 Using Spreadsheets in Management Science Models
Spreadsheets have become a powerful tool in management science modeling.
Several reasons for the popularity of spreadsheets:
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.

14. Basic Excel functions and operators
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

15. Basic Excel functions and operators
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
=A1+B$3+$C4+$D$6
Cell G9
= C5+D$3+$C8+$D$6

16. Basic Excel functions and operators
The 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.

17. Basic Excel functions and operators
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 A1·B1+A2·B2+A3·B3
ABS =ABS(A3)
Returns the absolute value of the entry in cell A3.

18. Basic Excel functions and operators
Arithmetic functions – continued
SQRT =SQRT(A3)
Returns ÖA3
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.

19. Basic Excel functions and operators
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 m = 20 Returns x0,, such that P(X<x0)=.55 and s = when m = 20 and s = 3
NORMSDIST NORMSMINV =NORMSDIST(1.78) =NORMSINV(.55) Returns P(Z<1.78) Returns z0, such that P(Z<z0)=.55

20. Basic Excel functions and operators
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 n=12 Returns t0,, such that P(t<-t0)=.025 and P(t>t0)= when n=15. Note: =TDIST(1.5,12,2) returns P(t<-1.5) + P(t>1.5) when n=12.

21. Basic Excel functions and operators
Statistical functions – Other probability distributions
Poisson =POISSON(7,5,TRUE)
Returns P(X<7) for Poisson with l = 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/m=20 Note: false returns the probability density f(40)=20exp(-20(40))

22. Basic Excel functions and operators
Conditional functions:
IF =IF(A4>4,B1+B2, B1 – B2)
Returns B1+B2 if A4>4, and B1 – B2 if A4£4.
SUMIF =SUMIF(F1:F12, “>60”,G1:G12)
Returns G1+G2+…+G12 only if F1+F2+…+F12>60

23. Basic Excel functions and operators
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.

24. Basic Excel functions and operators
Statistical/Optimization
Data Analysis [Selected from the Tools menu]. Useful entries:
Descriptive Statistics
Regression
Exponential Smoothing
Anova

25. Copyright 2002John Wiley & Sons, Inc. All rights reserved
Copyright 2002John Wiley & Sons, Inc. All rights reserved. Reproduction or translation of this work beyond that named in Section 117 of the United States Copyright Act without the express written consent of the copyright owner is unlawful. Requests for further information should be addressed to the Permissions Department, John Wiley & Sons, Inc. Adopters of the textbook are granted permission to make back-up copies for their own use only, to make copies for distribution to students of the course the textbook is used in, and to modify this material to best suit their instructional needs. Under no circumstances can copies be made for resale. The Publisher assumes no responsibility for errors, omissions, or damages, caused by the use of these programs or from the use of the information contained herein.