Introduction1 [Compatibility Mode]

8/13/2019 Introduction1 [Compatibility Mode]

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INTRODUCTION TO MANAGEMENT

SCIENCE


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Introduction to Management

Science Models Air India operates a fleet of hundreds of different types of

aircraft and employs thousands of people as pilots, flight

attendants, ticket agents, ground crews, and service

personnel in its operations throughout the Country, Canada,

Central and South America, Euro e,Asia and Australia.

The complexity of operations requires Air India to be highly

mechanized and to utilize the latest mathematical tools,

information , and computer technology so that it can:


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Develop master flight schedules

Forecast demand for its routes

Determine an aircraft lease/ purchase plan Assign planes and crews to the routes

Set fares

urc ase ue Schedule airport ticket agents and service personnel.

Schedule maintenance crews.

Maintain service facilities.

Lease airport gates.

Design and monitor its frequent flyer program


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Factors impacting these decisions include:

Budget, equipment, and personnel restrictions Union agreements for personnel scheduling

Federal Aviation Administration guidelines

Safe distance/ turnaround time requirements

The flexibility to react in real time to complications due to

weather, congestion, and other causes.

These are but a few of complicated and interrelated problems

and constraints affecting Air Indias bottom-line profitability.

Proper planning and operations require more sophisticatedanalyses than merely making educated guesses. Accordingly,

Air India makes liberal use of management science models to

increase profits and customer satisfaction in a constrained

environment.


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What is Management Science

Management Science is the discipline that adapts the

scientific approach for problem solving to executive

decision making in order to accomplish the goal ofdoing the best you can with what youve got. It involves:

Analyzing and building mathematical models of complex

us ness s tuat ons Solving and refining the mathematical models typically

using spreadsheets and/ or other software programs to

gain insights into the business situations.Communicating/ implementing the resulting insights

and recommendations based on these models.


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Business and Management

Science Every enterprise has an objective to accomplish.

Companies that operate for profit want to provide productsor services to customers in order to make money for their

owners or stockholders.

provide services to patients at minimum cost.

In general , the goal of both for profit and non-profit

organizations is to optimize the use of available resources,

given all the internal and external constraints placed onthem.

Success is usually measured by how well they do.


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Thus an organization is always looking for ways to run more

efficiently, more effectively, and, in the case of profit

motivated businesses, more profitably.

In other words organization want to do the best they can

i h h h This is the realm in which

management science operates.


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Management Science Management Science, an approach to decision making based

on the scientific method, makes extensive use of quantitative

analysis.

In addition to management science, two other and widely

acce ted names are o erations research and decision science

Operations Research is assuming an increasing degree of

importance in theory and practice of management. Some of

the factors which are responsible for this development are:


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1. Decision problems of modern management are so complex

that only a systematic and scientifically based analysis can

yield realistic solutions.

2. Availability of different types of quantitative models for

solvin these com lex mana erial roblems

3. Availability of high speed computers has made it possible

both in terms of time and cost to apply quantitative models

to all real life problems in all types of organizational

problems such as business, industry, military, government,health and so on.


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Evolution of Operations Research Operations research is generally considered to have

originated during the world war II period, when teams were

formed to deal with strategic and tactical problems faced by

the military.

These teams which often consisted of eo le with diverse

specialties (e.g. mathematician, engineers, and behavioralscientist), were joined together to solve a common problem

through the utilization of the scientific method.


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Problem Solving and Decision Making

Problem Solving can be defined as the process of

identifying a difference between the actual and the desired

state of affairs and then taking action to resolve the

difference. Steps in problem solving:

1 Identif and define the roblem

2. Determine the set of alternative solutions.

3. Determine the criterion or criteria that will be used to

evaluate the alternatives.

4. Evaluate the alternatives

5. Choose an alternative


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6. Implement the selected alternative.

7. Evaluate the results to determine whether a satisfactorysolution has been obtained.

Decision Making is the term generally associated with

. ,

first step of decision making is to identify and define the

problem. Decision making ends with the choosing of an

alternative, which is the act of making the decision.


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Example of Decision Making For the moment assume that you are currently unemployed

and that you would like a position that will lead to a satisfying

career. Suppose that your job search has resulted in offers

from companies in Banglore, NCR, Delhi. Thus alternatives

for our decision roblem can be stated as follows:

1. Accept the position in Banglore.

2. Accept the position in NCR.

3. Accept the position in Delhi.

4. Accept the position in NCR.


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Alternative Starting Salary Potential for

Advancement

Job Location

Banglore 38, 500 Average Average

NCR 36,000 Excellent Good

e , oo oo

NCR 37,000 Average Excellent


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Decision making process may take two

basic form

Qualitative Analysis Quantitative Analysis

Qualitative analysis is based primarily on the managersjudgment and experience; it includes the managers intuitive

feel for the problem and is more than a art than a science


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Reasons for using Quantitative Analysis is

used in Decision Making

The problem is complex, and the manager cannot develop a

good solution without the aid of quantitative analysis.

The problem is especially important (e.g., a great deal of

money is involved), and the manager desires a through

anal sis before attem tin to make a decision

The problem is new, and the manager has no previous

experience from which to draw.

The problem is repetitive, and the manager saves time and

effort by relying on quantitative procedures to make routinedecision recommendations.


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Model Development Objective function

Constraints Non-Negative restriction


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Objective Function A mathematical expression that describes the problems

objectives is referred to as the objective function.

For example, the profit equation would be an

objective function of a firm attempting to maximize profit.10P x=


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Constraints Constraints are the set of restrictions on the objective

function.

For example, the production capacity constraint: 5 hours are

required to produce each unit and only 40 hours of

roduction time are available er week

5 4 0x


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Complete Mathematical Model

10Maximize P x objective function

Subject to

=

0 non - negative restrictionx


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Example Suppose, NewOffice furniture produces three products

desks, chairs, and molded steel (which it sells to other

manufacturers) and is trying to decide on the number of

desks (D), chairs (C), and pounds of molded steel (M) to

roduce durin a articular roduction run.

If new office nets a $50 profit on each desk produced, $30on each chair produced, and $6 per pound of molded steel

produced, the total profit for a production run can be

molded by the expression:

50D + 30C + 6M


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Similarly, if 7 pounds of raw steel are needed to manufacture

a desk, 3 pounds to manufacture a chair, and 1.5 pounds to

produce a pound of moulded steel, the amount of raw steel

used during the production run is moulded by the

ex ression:

7D+3C+1.5M

For example, if NewOffice has only 2000 pounds of raw steel

available for the production run, the functional constraint

that expresses the fact that it cannot use more than 2000pounds of raw steel is moulded by the inequality:

7 3 1.5 2000D C M+ +


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Other constraints are At least 100 desks must be produced to satisfy contract

commitments, and due to the availability of seat cushions, no

more than 500 chairs can be produced, these can be

expressed as follows:

and100D 500C

The the quantities of desks and chairs produced during the

production run must be integer valued (the amount of

molded steel must not be integer valued).


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Maximize (Total Profit)

Subject to

(Raw Steel)

(Contract)

50 30 6D C M+ +

7 3 1.5 2000D C M+ +

100D

(Cushions)(nonnegativity)

are integers

C 500, , 0D C M

,D C


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Classification of Mathematical

Models Optimization Models

Prediction Models

Deterministic Models

Stochastic Models


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Definitions: Operations research may be described as a scientific approach to

decision-making that involves the operations of organizational

system.

large complex organizations or activities. It provides top level

administrators with a quantitative basis for decisions that will

increase the effectiveness of such organizations in carrying out their

basic purposes.


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Features of OR/ MS Decision-making

Scientific Approach

Objective

Inter-disciplinary Team Approach


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The Team Concept Building a good mathematical model is an art that is at the

heart of the management science process.

The greater the knowledge of the project under study, the

more reliable the model is in assessing the true situation.

management science models.


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Team Member Expertise

Chemical Engineer Petroleum blending

requirements

Economist Forecasts of oil prices

Marketing Analyst Forecast of market demand for

gasoline

Financial Officer Analysis of cash flow

Accountant Cash flow / tax requirements

Production Manager Analysis of production

capabilitiesTransportation Specialist Distribution of refined oil

products

M th d l f O ti R h*


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Methodology of Operations Research*

The Seven Steps to a Good OR Analysis

Feedback loopsat all levels!

M th d l g f O ti R h*


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What are the objectives?

Is the proposed problemtoo narrow?

Is it too broad?

M th d l g f O ti R h*


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What data shouldbe collected?

How will data becollected?

How do differentcomponents of the

system interact witheach other?



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What kind of model shouldbe used?

Is the model accurate?

Is the model too complex?



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Do outputs match current

observations for current

inputs?

Are outputs reasonable?

erroneous?



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What if there are conflictingobjectives?

Inherently the most difficultstep.

This is where software toolswill help us!



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Must communicate

results in laymansterms.

System must be user



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Users must be trained on

the new system.

System must be observedover time to ensure it worksproperly.


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Operations Research Models in

Practice Allocation models

Inventory models

Waiting line (or Queuing) models

Network models

Simulation models Decision models


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Successful OR ApplicationsCompany Year Problem Techniques Used Annual Savings

Hewlett Packard 1998Designing buffers into production

lineQueuing models $280 million

Taco Bell 1998 Employee scheduling IP, Forecasting, Simulation $13 million

Proctor & Gamble 1997Redesign production & distributon

systemTransportation models $200 million

Delta Airlines 1994 Assigning planes to routes Integer Programming $100 million

AT&T 1993 Call center designQueuing models,

Simulation$750 million

Yellow Freight Systems,

Inc.1992 Design trucking network

Network models,

Forecasting, Simulation$17.3 million

San Francisco Police

Dept. 1989 Patrol Scheduling Linear Programming $11 million

Bethlehem Steel 1989 Design an Ingot Mold Stripper Integer Programming $8 million

North American Van

Lines1988 Assigning loads to drivers Network modeling $2.5 million

Citgo Petroleum 1987 Refinery operations & distributionLinear Programming,

Forecasting$70 million

United Airlines 1986 Scheduling reservation personnel LP, Queuing, Forecasting $6 million

Dairyman's Creamery 1985 Optimal production levels Linear Programming $48,000

Phillips Petroleum 1983 Equipment replacement Network modeling $90,000


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Model Construction


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,

,

, ,

$ $

$ $

() () () ()


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,

4 100x lb. of steel=

,

20 5

4 100

Z $ x x

x

=

=


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20 5

4 100

max imize Z $ x x

subject to

x

=

=

( )x

, , () ,

, , () ,

xx


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, x

4 1 0 0

1 0 0

4

2 5

x

x

x u n i t s

=

=

=

x

20 5Z $ x x = 20(25) - 5(25)

= $375

=


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BreakEven Analysis The purpose of break-even analysis is to determine the

number of units of a product (i.e., the volume) to sell or

produce that will equate total revenue with total cost.

The point where total revenue equals total cost is called the

break-even oint and at this oint rofit is zero

The break even point gives a manager a point of reference indetermining how many units will be needed to ensure a

profit.

C t f B k E A l i


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Components of Break-Even Analysis

. (.. ) . . (.. ) .

.

.


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. ,

. ,

vv c

vc v

. .

f vc v c=

fc

.

.

v p

p


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f v

f v

Z v p ( c v c )

Z v p c v c

= +

=

, .

$10,000 $

, , 00 ,

$10,000 + (00) () $ 13, 200

fcvc

f vT C c v c= +


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$ 23 00 ,

(00) (23) $ ,200

$ ,200 $ 13,200 $ ,000

v p

f vZ v p ( c v c )= +

, $ ,000


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0 2 3 1 0 0 0 0 8

0 2 3 1 0 0 0 0 81 5 1 0 0 0 0

6 6 6 7

f vZ v p c v c

v ( ) , v ( )

v , vv ,

v . p a i r s o f j e a n s

=

=

=

=

=


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In other words, if the company produces and sells 666.7 pairs

of jeans, the profit (and loss) will be zero and the companywill break even.

This gives a company a point of reference from which to

determine how many pairs of jeans it needs to produce andsell in order to gain a profit.

For example, a sales volume of 800 pairs of denim jeans will

result in the following monthly profit

8 0 0 2 3 1 0 0 0 0 8 0 0 8

f vZ v p c v c

$ ( ) ( ) , ( ) ( )

= $ 2 ,0 0 0

=

=


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0

f v

v f

v f

f

Z v p c v c

v ( p c ) c

v ( p c ) c

c

=

=

=

v

p c

For our example

1 0 0 0 0

2 3 8

f

v

cv

p c,

= 6 6 6 . 7 p a i r s o f j e a n s

=

=

Graphical Solution


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Graphical Solution


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Sensitivity Analysis When we developed this model, we assumed that our

parameters, fixed and variable cost and price were constant.

In reality such parameters are frequently uncertain and canrarely be assumed to be constant, and changes in any of the

arameters can effect the model solution

The study of changes in any of the parameters is calledsensitivity analysis i.e. seeing how sensitive the model is to

changes.


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Change in Price The first thing we analyze the price. We will increase the

price of denim jeans from $23 to $30.

f

v

cv

p c=

As expected, this increases the total revenue, and it therefore

reduces the break even point from 666.7 to 454.5 pairs of

jeans.

3 0 8

,

= 4 5 4 . 5 p a i r s o f j e a n s

=


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Sensitivity Analysis with a change in price


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Change in Variable Cost Suppose the stitching on the denim jeans is changed to make

the jeans more attractive and stronger. This change results in

an increase in variable costs of $ 4 per pair of jeans, thusraising the variable cost per unit, , to $ 12 per pair. This

chan e (in conjunction with our revious rice chan e to $vc

30) results in a new break even volume:

1 0 0 0 03 0 1 2

f

v

cv

p c

,

= 5 5 5 . 5 p a i r s o f j e a n s

=

=


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Sensitivity Analysis with a change in variable cost


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Change in Fixed Cost Next lets consider an increase in advertising expenditures to

offset the potential loss in sales resulting from a price

increase. Increase in advertising expenditure increase thefixed cost.

If the com an increases its monthl advertisin bud et b

3, 000, then the total fixed cost, , becomes $ 13,000

1 3 0 0 0

3 0 1 2

f

v

cv

p c

,

= 7 2 2 . 2 p a i r s o f j e a n s

=

=

fc


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Sensitivity Analysis with a change in fixed cost

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Introduction1 [Compatibility Mode]