1

Introduction

Chapter 1

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

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.

1.1 What Is Management Science?

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 SonyCorporation 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

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

1.3 Mathematical Modeling

Example NewOffice Furniture produces three products

9

Objective: Determine production mix that maximizes the profit under the raw material constraint and other production requirements (detailed next).

Maximize 50D + 30C + 6 MSubject to 7D + 3C + 1.5M 2000 (raw steel)

D 100 (contract )C500 (cushions available)

D, C, M 0 (Non-negativity)D and C are integers

1.3 Mathematical Modeling

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/implementationof 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

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

Basic Excel functions and operators

16

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.

Basic Excel functions and operators

17

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.

Basic Excel functions and operators

18

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.

Basic Excel functions and operators

19

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

Basic Excel functions and operators

20

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.

Basic Excel functions and operators

21

Statistical functions – 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/=20

Note: false returns the probability density f(40)=20exp(-20(40))

Basic Excel functions and operators

22

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

Basic Excel functions and operators

23

– 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.

Basic Excel functions and operators

24

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

Descriptive Statistics Regression Exponential Smoothing Anova

Basic Excel functions and operators

25

Copyright 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.