ORDUDE #2-Introduction

8/14/2019 ORDUDE #2-Introduction

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Dual Degree Management UNP

LecturerGesit Thabrani

Introduction toOperations Research


OperationsOperationsResearchResearch

OR#2


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Learning Objectives

1. Describe the operations research approach2. Understand the application of operations

research in a real situation

3. Describe the use of modeling in operationsresearch4. Perform a break-even analysis

After completing this chapter, students will be able to:After completing this chapter, students will be able to:


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Outline

1. Introduction

2. What Is Operations Research?3. The Operations Research Approach4. How to Develop a Operations

Research Model5. Implementation Not Just the FinalStep


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Introduction

Mathematical tools have been used forthousands of years

Operations Research can be applied to

a wide variety of problems Its not enough to just know the

mathematics of a technique

One must understand the specificapplicability of the technique, itslimitations, and its assumptions


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Introduction

Operations Research (also referred to asmanagement science, quantitative methods,

quantitative analysis, and decision

sciences) is part of the fundamentalcurriculum of most programs in business


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Meaningful

Information

Operations

Research

Operations ResearchOperations Researchis the application of a scientific

approach to solving management problems in orderto help managers make better decisions wherebyraw data are processed and manipulated resulting inmeaningful information

Raw Data

What is Operations Research?


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What is Operations Research?

Operations research techniques can be applied to

solve problems in different types of organizations,including services, government, military, businessand industry, and health care.

Operations research is more than just a collection

of techniques. Operations research also involves the philosophy

of approaching a problem in a logical manner (i.e.,a scientific approach).

The logical, consistent, and systematic approachto problem solving can be as useful (and valuable)as the knowledge of the mechanics of the

mathematical techniques themselves.


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Dual Degree Management UNPImplementing the Results

Analyzing the Results

Testing the Solution

Developing a Solution

Acquiring Input Data

Developing a Model

Operations Research Approach

Defining the Problem

Figure 1.1


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Defining the Problem

Need to develop a clear and concise

statement that gives direction and meaningto the following steps This may be the most important and difficult

step

It is essential to go beyond symptoms andidentify true causes

May be necessary to concentrate on only a few

of the problems selecting the right problemsis very important

Specific and measurable objectives may haveto be developed


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Developing a ModelQuantitative analysis models are realistic,

solvable, and understandable mathematicalrepresentations of a situation

$ Advertising

$

Sa

les


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Developing a Model

Models generally contain variables(controllable and uncontrollable) andparameters

Controllable variables are generally thedecision variables and are generallyunknown

Parameters are known quantities that

are a part of the problem


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Acquiring Input Data

Input data must be accurate GIGO rule

Data may come from a variety of sources such ascompany reports, company documents, interviews,on-site direct measurement, or statistical sampling

GarbageIn

Process

GarbageOut


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Developing a Solution

The best (optimal) solution to a problem

is found by manipulating the modelvariables until a solution is found that ispractical and can be implemented

Common techniques are SolvingSolvingequations Trial and errorTrial and error trying various approaches

and picking the best result Complete enumerationComplete enumeration trying all possible

values Using an algorithmalgorithm a series of repeating

steps to reach a solution


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Testing the Solution

Both input data and the model should be

tested for accuracy before analysis andimplementation New data can be collected to test the model

Results should be logical, consistent, andrepresent the real situation


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Analyzing the Results

Determine the implications of the solution

Implementing results often requires changein an organization

The impact of actions or changes needs tobe studied and understood before

implementation

Sensitivity analysisSensitivity analysisdetermines how muchthe results of the analysis will change ifthe model or input data changes Sensitive models should be very thoroughly

tested


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Implementing the Results

Implementation incorporates the solution

into the company Implementation can be very difficult

People can resist changes

Many quantitative analysis efforts have failedbecause a good, workable solution was notproperly implemented

Changes occur over time, so even

successful implementations must bemonitored to determine if modifications arenecessary


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Implementing the Results

ExampleResponding to complaints of slow

elevator service in a large office building,the OR team initially perceived the situationas a waiting-line problem that might requirethe use of mathematical queuing analysis orsimulation. After studying the behavior of

the people voicing the complaint, thepsychologist on the team suggestedinstalling full-length mirrors at the entranceto the elevators. Miraculously thecomplaints disappeared, as people werekept occupied watching themselves andothers while waiting for the elevator


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How To Develop a Operations

Research Model

An important part of the operationsresearch approach

Lets look at a simple mathematicalmodel of profit

Profit = Revenue Expenses


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Research Model

Expenses can be represented as the sum of fixed andvariable costs and variable costs are the product of

unit costs times the number of units

Profit = Revenue (Fixed cost + Variable cost)

Profit = (Selling price per unit)(number of units

sold) [Fixed cost + (Variable costs perunit)(Number of units sold)]

Profit = sX [f+ vX]

Profit = sXf vXwhere

s = selling price per unit v = variable cost per unitf= fixed cost X= number of units sold


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Research Model

Expenses can be represented as the sum of fixed andvariable costs and variable costs are the product of

unit costs times the number of units

Profit = Revenue (Fixed cost + Variable cost)

Profit = (Selling price per unit)(number of units

sold) [Fixed cost + (Variable costs perunit)(Number of units sold)]

Profit = sX [f+ vX]

Profit = sXf vXwhere

s = selling price per unit v = variable cost per unitf= fixed cost X= number of units sold

The parametersof this modelaref, v, ands as these are theinputs inherent in the model

The decision variableof

interest isX


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Pritchetts Precious Time Pieces

Profits =sXf vX

The company buys, sells, and repairs old clocks.Rebuilt springs sell for $10 per unit. Fixed cost of

equipment to build springs is $1,000. Variable costfor spring material is $5 per unit.

s = 10 f= 1,000 v = 5

Number of spring sets sold =X

If sales = 0, profits =$1,000$1,000If sales = 1,000, profits = [(10)(1,000) 1,000 (5)(1,000)]

= $4,000


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0 =sXf vX, or 0 = (s v)Xf

Companies are often interested in their breakbreak--evenevenpointpoint(BEP). The BEP is the number of units sold

that will result in $0 profit.

Solving forX, we havef= (s v)X

X=f

s

v

BEP =Fixed cost

(Selling price per unit) (Variable cost per unit)


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0 =sXf vX, or 0 = (s v)Xf

Companies are often interested in their breakbreak--evenevenpointpoint(BEP). The BEP is the number of units sold

that will result in $0 profit.

Solving forX, we havef= (s v)X

X=f

s

v

BEP =Fixed cost

(Selling price per unit) (Variable cost per unit)

BEP for Pritchetts Precious Time Pieces

BEP = $1,000/($10 $5) = 200 units

Sales of less than 200 units of rebuilt springswill result in a loss

Sales of over 200 units of rebuilt springs willresult in a profit


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Models Categorized by Risk

Mathematical models that do not involverisk are called deterministicmodels We know all the values used in the model

with complete certainty

Mathematical models that involve risk,chance, or uncertainty are calledprobabilisticmodels

Values used in the model are estimatesbased on probabilities

ORDUDE #2-Introduction

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