1 Introduction to Or

832019 1 Introduction to Or

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Operations Research

An Introduction



Introduction

bull What is Operations Research

(Management Science)

A Scientific Approach of applying

advanced analytical methods to help

make better decisions

It is concerned with the development

and application of quantitative analyses

to the solution of problems faced by the

managers



Management decision making

bull An emerging retail giant has to decide on size and location of itsproposed grocery Malls

bull A portfolio manager is debating on the amount of investment to bemade on various instruments

bull A marketing media planner has to decide how manyadvertisements to be given in different media slots

bull The head of a large Chinese telecom component manufacturer isplanning to expand his market beyond Asia in a big scale He iscontemplating on the appropriate production-storage-distribution

architecture

bull A project head of IT company has to assign his software executivesto various team leads

bull An BPO firm manager is planning to restructure the routing of callsacross the various levels of employees

bull A logistics manager of a beverage company is wondering whatshould be the ideal dispatch plan for the various products from

plants to demand points



Motivation amp Overview

bull Managerial Decision making process

ndash Finding the best ldquosolutionrdquo for a problem ndash Within the limitations posed by environment

resources etchellip

Alternatives

ObjectiveProblem How to find best

CONSTRAINTS



Decision Making situations

bull Production Decisions

Product Mix Decisions

Location Decisions

Routing Decisions





bull Marketing Decisions

bull


Routing Decisions

Location Decisions






bull Financial Decisions


Routing Decisions

Location Decisions



Decision Making situationsbull Production Decisions



bull HR Decisionsbull etc Etc


Routing Decisions

Location Decisions







bull HR Decisions

bull etc Etc


Routing Decisions

Location Decisions

What is common in all these



Decision Problems

bull Objective(s)

bull Decision(s)

bull Constraint(s)

Example

Maximise Utility

Which Marbles to pick

Capacity of Container

How to DECIDE

Quantitative Approach

Qualitative Approach



bull Managers tend touse a qualitativeapproach toproblem solving

1The problem is

fairly simple2The problem is

familiar

3The costsinvolved are notgreat

bull Managers tend touse a quantitative

approach toproblem solving

1The problem iscomplex

2The problem is notfamiliar

3The costs involvedare substantial

4Enough time isavailable to analyzethe problem

Problem Solving



bull Directs attention to the essence of an

analysis to solve a specific problembull Improves planning which helps prevent future

problems

bull Results in more objective decisions thanpurely qualitative analysis

bull Incorporates advances in computational

technologies to managerial problem-solving

Why Quantitative Approach



bull A Model

ndash An abstraction of reality It is a simplified and

often idealized representation of realitybull Examples an equation an outline a diagram

and a map

ndash

Models



bull A Model



and a map

ndash

Models



bull A Model



and a map

ndash

Models

+



bull A Model



and a map

ndash By its very nature a model is incomplete

ndash Provides an alternative to working with reality

bull Symbolic models

ndash Use numbers and algebraic symbols

bull Mathematical models

ndash Decision variables

ndash Uncontrollable variables

Models



How to Solve

Problem

Definition

MODEL

Analysis

Implementation

Evaluation

Assumptions

Finding Solution

Testing SolutionAnalysing soln

P bl l i P



Problem-solving Process

bull Pre-modeling function

Recognition of a need

Criteria or objectives

Surrogates

Problem Formulation

Define objective function variables parameters and constraints

bull The Modeling function

Model Construction Role of Criteria Level of Aggregation

Data collection MIS Scale and measurement Estimation amp Forecasting

Model solution LPP Queuing Models Dynamic Programming etc

Model validation and sensitivity analysis

Verify whether the solution is better than other alternatives

Degree of stability in the results




bull The post-modeling function

Interpretation of results and Implications

Decision making Implementation and Control



bull Deterministic models

ndash Used for problems in which information is knownwith a high degree of certainty

ndash Used to determine an optimal solution to theproblem

bull Probabilistic models

ndash Used when it cannot be determined preciselywhat values (requiring probabilities) will occur(usually in the future)

Type of Models

S



ORMS Models

Dynamic

Non LinearLinear

Multi modal

UnimodalUnconstrainedDM Models

Multiobjective

ILPBLPTransportaion Assignment

Network

Appl Heuris

tics

SoftOR

TIME

Unconstrained

COST

LPP

Solution Approaches

UNCERTAINTYUNCERTAINTY

MarkovSimul

C i i f OR



Composition of OR

bull Tools

bull Techniques

bull Methodology

Choice depends on the complex nature

of the problem

K D i f I l ti OR M d l



Key Drivers for Implementing OR Models

bull Selection of an Appropriate Methodology in

Modeling a Situation

bull An optimal mix of contextual relevance user

sophistication and professional satisfaction

of OR Practitioners would maximize the

chances of model implementation

bull Top management involvement is critical to

implementation





bull The implementation pace and its impact is

strongly influenced by the training andorientation of the mid-level executives in the

organization

bull The intensity of competition accelerates theadoption of effective management models

bull The managementrsquos effective handling of the

perceived fear and anticipated accountability bythe middle management in the context of the

proposed new solution is a facilitator for

implementation



bullStarthellip AnyQuestions



Introduction

bull What is Operations Research

(Management Science)

A Scientific Approach of applying

advanced analytical methods to help

make better decisions

It is concerned with the development

and application of quantitative analyses

to the solution of problems faced by the

managers








architecture










resources etchellip

Alternatives


CONSTRAINTS






Location Decisions

Routing Decisions






bull


Routing Decisions

Location Decisions








Routing Decisions

Location Decisions








Routing Decisions

Location Decisions







bull HR Decisions

bull etc Etc


Routing Decisions

Location Decisions




Decision Problems

bull Objective(s)

bull Decision(s)

bull Constraint(s)

Example

Maximise Utility



How to DECIDE






1The problem is


familiar








Problem Solving





problems







bull A Model



and a map

ndash

Models



bull A Model



and a map

ndash

Models



bull A Model



and a map

ndash

Models

+



bull A Model



and a map








Models



How to Solve

Problem

Definition

MODEL

Analysis

Implementation

Evaluation

Assumptions

Finding Solution


P bl l i P







Surrogates

Problem Formulation






















Type of Models

S



ORMS Models

Dynamic

Non LinearLinear

Multi modal


Multiobjective


Network

Appl Heuris

tics

SoftOR

TIME

Unconstrained

COST

LPP

Solution Approaches


MarkovSimul

C i i f OR



Composition of OR

bull Tools

bull Techniques

bull Methodology


of the problem












implementation







organization





implementation











architecture










resources etchellip

Alternatives


CONSTRAINTS






Location Decisions

Routing Decisions






bull


Routing Decisions

Location Decisions








Routing Decisions

Location Decisions








Routing Decisions

Location Decisions







bull HR Decisions

bull etc Etc


Routing Decisions

Location Decisions




Decision Problems

bull Objective(s)

bull Decision(s)

bull Constraint(s)

Example

Maximise Utility



How to DECIDE






1The problem is


familiar








Problem Solving





problems







bull A Model



and a map

ndash

Models



bull A Model



and a map

ndash

Models



bull A Model



and a map

ndash

Models

+



bull A Model



and a map








Models



How to Solve

Problem

Definition

MODEL

Analysis

Implementation

Evaluation

Assumptions

Finding Solution


P bl l i P







Surrogates

Problem Formulation






















Type of Models

S



ORMS Models

Dynamic

Non LinearLinear

Multi modal


Multiobjective


Network

Appl Heuris

tics

SoftOR

TIME

Unconstrained

COST

LPP

Solution Approaches


MarkovSimul

C i i f OR



Composition of OR

bull Tools

bull Techniques

bull Methodology


of the problem












implementation







organization





implementation









resources etchellip

Alternatives


CONSTRAINTS






Location Decisions

Routing Decisions






bull


Routing Decisions

Location Decisions








Routing Decisions

Location Decisions








Routing Decisions

Location Decisions







bull HR Decisions

bull etc Etc


Routing Decisions

Location Decisions




Decision Problems

bull Objective(s)

bull Decision(s)

bull Constraint(s)

Example

Maximise Utility



How to DECIDE






1The problem is


familiar








Problem Solving





problems







bull A Model



and a map

ndash

Models



bull A Model



and a map

ndash

Models



bull A Model



and a map

ndash

Models

+



bull A Model



and a map








Models



How to Solve

Problem

Definition

MODEL

Analysis

Implementation

Evaluation

Assumptions

Finding Solution


P bl l i P







Surrogates

Problem Formulation






















Type of Models

S



ORMS Models

Dynamic

Non LinearLinear

Multi modal


Multiobjective


Network

Appl Heuris

tics

SoftOR

TIME

Unconstrained

COST

LPP

Solution Approaches


MarkovSimul

C i i f OR



Composition of OR

bull Tools

bull Techniques

bull Methodology


of the problem












implementation







organization





implementation









Location Decisions

Routing Decisions






bull


Routing Decisions

Location Decisions








Routing Decisions

Location Decisions








Routing Decisions

Location Decisions







bull HR Decisions

bull etc Etc


Routing Decisions

Location Decisions




Decision Problems

bull Objective(s)

bull Decision(s)

bull Constraint(s)

Example

Maximise Utility



How to DECIDE






1The problem is


familiar








Problem Solving





problems







bull A Model



and a map

ndash

Models



bull A Model



and a map

ndash

Models



bull A Model



and a map

ndash

Models

+



bull A Model



and a map








Models



How to Solve

Problem

Definition

MODEL

Analysis

Implementation

Evaluation

Assumptions

Finding Solution


P bl l i P







Surrogates

Problem Formulation






















Type of Models

S



ORMS Models

Dynamic

Non LinearLinear

Multi modal


Multiobjective


Network

Appl Heuris

tics

SoftOR

TIME

Unconstrained

COST

LPP

Solution Approaches


MarkovSimul

C i i f OR



Composition of OR

bull Tools

bull Techniques

bull Methodology


of the problem












implementation







organization





implementation









bull


Routing Decisions

Location Decisions








Routing Decisions

Location Decisions








Routing Decisions

Location Decisions







bull HR Decisions

bull etc Etc


Routing Decisions

Location Decisions




Decision Problems

bull Objective(s)

bull Decision(s)

bull Constraint(s)

Example

Maximise Utility



How to DECIDE






1The problem is


familiar








Problem Solving





problems







bull A Model



and a map

ndash

Models



bull A Model



and a map

ndash

Models



bull A Model



and a map

ndash

Models

+



bull A Model



and a map








Models



How to Solve

Problem

Definition

MODEL

Analysis

Implementation

Evaluation

Assumptions

Finding Solution


P bl l i P







Surrogates

Problem Formulation






















Type of Models

S



ORMS Models

Dynamic

Non LinearLinear

Multi modal


Multiobjective


Network

Appl Heuris

tics

SoftOR

TIME

Unconstrained

COST

LPP

Solution Approaches


MarkovSimul

C i i f OR



Composition of OR

bull Tools

bull Techniques

bull Methodology


of the problem












implementation







organization





implementation











Routing Decisions

Location Decisions








Routing Decisions

Location Decisions







bull HR Decisions

bull etc Etc


Routing Decisions

Location Decisions




Decision Problems

bull Objective(s)

bull Decision(s)

bull Constraint(s)

Example

Maximise Utility



How to DECIDE






1The problem is


familiar








Problem Solving





problems







bull A Model



and a map

ndash

Models



bull A Model



and a map

ndash

Models



bull A Model



and a map

ndash

Models

+



bull A Model



and a map








Models



How to Solve

Problem

Definition

MODEL

Analysis

Implementation

Evaluation

Assumptions

Finding Solution


P bl l i P







Surrogates

Problem Formulation






















Type of Models

S



ORMS Models

Dynamic

Non LinearLinear

Multi modal


Multiobjective


Network

Appl Heuris

tics

SoftOR

TIME

Unconstrained

COST

LPP

Solution Approaches


MarkovSimul

C i i f OR



Composition of OR

bull Tools

bull Techniques

bull Methodology


of the problem












implementation







organization





implementation











Routing Decisions

Location Decisions







bull HR Decisions

bull etc Etc


Routing Decisions

Location Decisions




Decision Problems

bull Objective(s)

bull Decision(s)

bull Constraint(s)

Example

Maximise Utility



How to DECIDE






1The problem is


familiar








Problem Solving





problems







bull A Model



and a map

ndash

Models



bull A Model



and a map

ndash

Models



bull A Model



and a map

ndash

Models

+



bull A Model



and a map








Models



How to Solve

Problem

Definition

MODEL

Analysis

Implementation

Evaluation

Assumptions

Finding Solution


P bl l i P







Surrogates

Problem Formulation






















Type of Models

S



ORMS Models

Dynamic

Non LinearLinear

Multi modal


Multiobjective


Network

Appl Heuris

tics

SoftOR

TIME

Unconstrained

COST

LPP

Solution Approaches


MarkovSimul

C i i f OR



Composition of OR

bull Tools

bull Techniques

bull Methodology


of the problem












implementation







organization





implementation










bull HR Decisions

bull etc Etc


Routing Decisions

Location Decisions




Decision Problems

bull Objective(s)

bull Decision(s)

bull Constraint(s)

Example

Maximise Utility



How to DECIDE






1The problem is


familiar








Problem Solving





problems







bull A Model



and a map

ndash

Models



bull A Model



and a map

ndash

Models



bull A Model



and a map

ndash

Models

+



bull A Model



and a map








Models



How to Solve

Problem

Definition

MODEL

Analysis

Implementation

Evaluation

Assumptions

Finding Solution


P bl l i P







Surrogates

Problem Formulation






















Type of Models

S



ORMS Models

Dynamic

Non LinearLinear

Multi modal


Multiobjective


Network

Appl Heuris

tics

SoftOR

TIME

Unconstrained

COST

LPP

Solution Approaches


MarkovSimul

C i i f OR



Composition of OR

bull Tools

bull Techniques

bull Methodology


of the problem












implementation







organization





implementation






Decision Problems

bull Objective(s)

bull Decision(s)

bull Constraint(s)

Example

Maximise Utility



How to DECIDE






1The problem is


familiar








Problem Solving





problems







bull A Model



and a map

ndash

Models



bull A Model



and a map

ndash

Models



bull A Model



and a map

ndash

Models

+



bull A Model



and a map








Models



How to Solve

Problem

Definition

MODEL

Analysis

Implementation

Evaluation

Assumptions

Finding Solution


P bl l i P







Surrogates

Problem Formulation






















Type of Models

S



ORMS Models

Dynamic

Non LinearLinear

Multi modal


Multiobjective


Network

Appl Heuris

tics

SoftOR

TIME

Unconstrained

COST

LPP

Solution Approaches


MarkovSimul

C i i f OR



Composition of OR

bull Tools

bull Techniques

bull Methodology


of the problem












implementation







organization





implementation







1The problem is


familiar








Problem Solving





problems







bull A Model



and a map

ndash

Models



bull A Model



and a map

ndash

Models



bull A Model



and a map

ndash

Models

+



bull A Model



and a map








Models



How to Solve

Problem

Definition

MODEL

Analysis

Implementation

Evaluation

Assumptions

Finding Solution


P bl l i P







Surrogates

Problem Formulation






















Type of Models

S



ORMS Models

Dynamic

Non LinearLinear

Multi modal


Multiobjective


Network

Appl Heuris

tics

SoftOR

TIME

Unconstrained

COST

LPP

Solution Approaches


MarkovSimul

C i i f OR



Composition of OR

bull Tools

bull Techniques

bull Methodology


of the problem












implementation







organization





implementation








problems







bull A Model



and a map

ndash

Models



bull A Model



and a map

ndash

Models



bull A Model



and a map

ndash

Models

+



bull A Model



and a map








Models



How to Solve

Problem

Definition

MODEL

Analysis

Implementation

Evaluation

Assumptions

Finding Solution


P bl l i P







Surrogates

Problem Formulation






















Type of Models

S



ORMS Models

Dynamic

Non LinearLinear

Multi modal


Multiobjective


Network

Appl Heuris

tics

SoftOR

TIME

Unconstrained

COST

LPP

Solution Approaches


MarkovSimul

C i i f OR



Composition of OR

bull Tools

bull Techniques

bull Methodology


of the problem












implementation







organization





implementation






bull A Model



and a map

ndash

Models



bull A Model



and a map

ndash

Models



bull A Model



and a map

ndash

Models

+



bull A Model



and a map








Models



How to Solve

Problem

Definition

MODEL

Analysis

Implementation

Evaluation

Assumptions

Finding Solution


P bl l i P







Surrogates

Problem Formulation






















Type of Models

S



ORMS Models

Dynamic

Non LinearLinear

Multi modal


Multiobjective


Network

Appl Heuris

tics

SoftOR

TIME

Unconstrained

COST

LPP

Solution Approaches


MarkovSimul

C i i f OR



Composition of OR

bull Tools

bull Techniques

bull Methodology


of the problem












implementation







organization





implementation






bull A Model



and a map

ndash

Models



bull A Model



and a map

ndash

Models

+



bull A Model



and a map








Models



How to Solve

Problem

Definition

MODEL

Analysis

Implementation

Evaluation

Assumptions

Finding Solution


P bl l i P







Surrogates

Problem Formulation






















Type of Models

S



ORMS Models

Dynamic

Non LinearLinear

Multi modal


Multiobjective


Network

Appl Heuris

tics

SoftOR

TIME

Unconstrained

COST

LPP

Solution Approaches


MarkovSimul

C i i f OR



Composition of OR

bull Tools

bull Techniques

bull Methodology


of the problem












implementation







organization





implementation






bull A Model



and a map

ndash

Models

+



bull A Model



and a map








Models



How to Solve

Problem

Definition

MODEL

Analysis

Implementation

Evaluation

Assumptions

Finding Solution


P bl l i P







Surrogates

Problem Formulation






















Type of Models

S



ORMS Models

Dynamic

Non LinearLinear

Multi modal


Multiobjective


Network

Appl Heuris

tics

SoftOR

TIME

Unconstrained

COST

LPP

Solution Approaches


MarkovSimul

C i i f OR



Composition of OR

bull Tools

bull Techniques

bull Methodology


of the problem












implementation







organization





implementation






bull A Model



and a map








Models



How to Solve

Problem

Definition

MODEL

Analysis

Implementation

Evaluation

Assumptions

Finding Solution


P bl l i P







Surrogates

Problem Formulation






















Type of Models

S



ORMS Models

Dynamic

Non LinearLinear

Multi modal


Multiobjective


Network

Appl Heuris

tics

SoftOR

TIME

Unconstrained

COST

LPP

Solution Approaches


MarkovSimul

C i i f OR



Composition of OR

bull Tools

bull Techniques

bull Methodology


of the problem












implementation







organization





implementation






How to Solve

Problem

Definition

MODEL

Analysis

Implementation

Evaluation

Assumptions

Finding Solution


P bl l i P







Surrogates

Problem Formulation






















Type of Models

S



ORMS Models

Dynamic

Non LinearLinear

Multi modal


Multiobjective


Network

Appl Heuris

tics

SoftOR

TIME

Unconstrained

COST

LPP

Solution Approaches


MarkovSimul

C i i f OR



Composition of OR

bull Tools

bull Techniques

bull Methodology


of the problem












implementation







organization





implementation










Surrogates

Problem Formulation






















Type of Models

S



ORMS Models

Dynamic

Non LinearLinear

Multi modal


Multiobjective


Network

Appl Heuris

tics

SoftOR

TIME

Unconstrained

COST

LPP

Solution Approaches


MarkovSimul

C i i f OR



Composition of OR

bull Tools

bull Techniques

bull Methodology


of the problem












implementation







organization





implementation

















Type of Models

S



ORMS Models

Dynamic

Non LinearLinear

Multi modal


Multiobjective


Network

Appl Heuris

tics

SoftOR

TIME

Unconstrained

COST

LPP

Solution Approaches


MarkovSimul

C i i f OR



Composition of OR

bull Tools

bull Techniques

bull Methodology


of the problem












implementation







organization





implementation











Type of Models

S



ORMS Models

Dynamic

Non LinearLinear

Multi modal


Multiobjective


Network

Appl Heuris

tics

SoftOR

TIME

Unconstrained

COST

LPP

Solution Approaches


MarkovSimul

C i i f OR



Composition of OR

bull Tools

bull Techniques

bull Methodology


of the problem












implementation







organization





implementation






ORMS Models

Dynamic

Non LinearLinear

Multi modal


Multiobjective


Network

Appl Heuris

tics

SoftOR

TIME

Unconstrained

COST

LPP

Solution Approaches


MarkovSimul

C i i f OR



Composition of OR

bull Tools

bull Techniques

bull Methodology


of the problem












implementation







organization





implementation






Composition of OR

bull Tools

bull Techniques

bull Methodology


of the problem












implementation







organization





implementation














implementation







organization





implementation









organization





implementation







Documents

1 Introduction to Or