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Operations ResearchOperations Research

The OR Process

2005.9.13

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Topics

What is OR?

Modeling and the problem solving process

Deterministic vs. stochastic models

OR techniques

Using the Excel add-ins to find solutions

Solving real problems

Lecture 1 – Operations ResearchLecture 1 – Operations Research

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Systems ApproachInclude broad implications of decisions for the organization at each stage in analysis. Both quantitative and qualitative factors are considered.

Optimal SolutionA solution to the model that optimizes (maximizes or minimizes) some measure of merit over all feasible solutions. TeamA group of individuals bringing various skills and viewpoints to a problem.  Operations Research TechniquesA collection of general mathematical models, analytical procedures, and algorithms.

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It is a Process

It assists Decision Makers

It has a set of Tools

It is applicable in many Situations

What is OR?What is OR?

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1. OR professionals aim to provide rational bases for decision making by seeking to understand and structure complex situations and to use this understanding to predict system behavior and improve system performance.

2. Much of this work is done using analytical and numerical techniques to develop and manipulate mathematical and computer models of organizational systems composed of people, machines, and procedures.

Definition of OR?Definition of OR?

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Data

ManufacturingPlanning

Design

Scheduling

Dealing with Defects

Dealing with Variability

Dealing with Inventory

…

Situation

The Process: Recognize the ProblemThe Process: Recognize the Problem

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Service Industries

Logistics

Transportation

Environment

Health Care

Situations with complexity

Situations with uncertaintyData

Situation

Other applicationsOther applications

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Data

Solution

Find a Solution

Tools

Situation

Formulate the Problem

Problem Statement

Test the Model and the Solution

Solution

Establish a Procedure

Implement the Solution

Construct a Model

Model

Implement a Solution

Goal: solve a problemModel must be validModel must be tractableSolution must be useful

Problem Solving ProcessProblem Solving Process

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Define the problem

Delimit the system

Select measures

Formulate the Problem

Problem Statement

Data

Situation

Determine variables

Identify constraints

Formulate the ProblemFormulate the Problem

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• May involve current operations or proposed expansions due to expected market shifts

• May become apparent through consumer complaints or through employee suggestions

• May be a conscious effort to improve efficiency or response to an unexpected crisis.

Example: Internal nursing staff not happy with their schedules; hospital using too many external nurses.

Data

Situation

The SituationThe Situation

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Define variables

Define constraints

Data requirements

Example: Maximize individual nurse preferences subject to demand requirements.

Formulate the Problem

Problem Statement

Data

Situation

• Describe system• Define boundaries • State assumptions• Select performance measures

Problem FormulationProblem Formulation

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Long-term planning

– FTRs, PTRs, PTFs

– Shifts

– Days off

Weekly scheduling

– Vacations, leave

– Overtime

– PTFs, casuals

– Task assignments

Real-time control

– Emergencies

– Daily adjustments

– Sick leave

– Overtime

Personnel Planning and Scheduling: Personnel Planning and Scheduling: Example of Bounding a ProblemExample of Bounding a Problem

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Construct a ModelConstruct a Model

Math. Programming Model

Stochastic Model

Statistical Model

Simulation Model

Construct a Model

Model

Formulate the Problem

Problem Statement

Data

Situation

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Problem must be translated from verbal, qualitative terms to logical, quantitative terms

A logical model is a series of rules, usually embodied in a computer program

Example: Define relationships between individual nurse assignments and preference violations; define tradeoffs between the use of internal and external nursing resources.

Constructa Model

Model

Formulate the Problem

Problemstatement

Data

Situation

• A mathematical model is a collection of functional relationships by which allowable actions are delimited and evaluated.

Constructing a ModelConstructing a Model

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Many tools are available as discussed in this course

Some lead to “optimal” solutionsOthers only evaluate candidates trial and

error to find “best” course of action

Example: Read nurse profiles and demand requirements, apply algorithm, post-processes results to get monthly schedules.

Model

Solution

Find asolution

Tools

Solving the Mathematical ModelSolving the Mathematical Model

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Linear Programming

Nonlinear Programming

Regression

Direct Search

Stochastic Optimization

Trial and Error

Construct a Model

Model

Formulate the Problem

Problem Statement

Data

Situation

Solution

Find a Solution

Tools

Find a SolutionFind a Solution

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Production software

Easy to use

Easy to maintain

Acceptable to the user

Solution

Establish a Procedure

Solution

Find a Solution

Tools

Construct a Model

Model

Formulate the Problem

Problem Statement

Data

Situation

Establish a ProcedureEstablish a Procedure

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The model must be valid

The model must be tractable

The solution must be useful

Data

Solution

Find a Solution

Tools

Situation

Formulate the Problem

Problem Statement

Test the Model and the Solution

Solution

Establish a Procedure

Implement the Solution

Construct a Model

Model

Implement a Solution

The Goal is to Solve the ProblemThe Goal is to Solve the Problem

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Change for the organization

Change is difficult

Establish controls to recognize change in the situation

Solution

Establish a Procedure

Solution

Find a Solution

Tools

Construct a Model

Model

Formulate the Problem

Problem Statement

Data

Situation

Implement the Solution

Implement the SolutionImplement the Solution

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A solution to a problem usually implies changes for some individuals in the organization

Often there is resistance to change, making the implementation difficult

User-friendly system neededThose affected should go through training

Situation

Procedure

Implement the Procedure

Example: Implement nurse scheduling system in one unit at a time. Integrate with existing HR and T&A systems. Provide training sessions during the workday.

ImplementationImplementation

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Data base (nurse profiles, external resources, rules)

Graphical User Interface (GUI); web enabled using java or VBA

Algorithms, pre- and post- processor

What-if analysis

Report generators

Components of Components of OR-Based Decision Support SystemOR-Based Decision Support System

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Real World Situation

Problems

Models

Methods

TP

LP NFP

simplexinterior

LP

TP

DS

Real WorldSituation

Problems

Models

Methods

Problems, Models and MethodsProblems, Models and Methods

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Operations Research Models

Deterministic Models Stochastic Models

• Linear Programming • Discrete-Time Markov Chains

• Network Optimization • Continuous-Time Markov Chains

• Integer Programming • Queueing

• Nonlinear Programming • Decision Analysis

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Deterministic models – 60% of course

Stochastic (or probabilistic) models – 40% of course

Deterministic models assume all data are known with certainty

Stochastic models explicitly represent uncertain data via random variables or stochastic processes.

Deterministic models involve optimization

Stochastic models characterize / estimate system performance.

Deterministic vs. Stochastic ModelsDeterministic vs. Stochastic Models

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Rescheduling aircraft in response to groundings and delaysPlanning production for printed circuit board assemblyScheduling equipment operators in mail processing & distribution centersDeveloping routes for propane deliveryAdjusting nurse schedules in light of daily fluctuations in demand

Examples of OR ApplicationsExamples of OR Applications

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Problem formulation

Model building

Data collection

Data analysis

Coding

Experimental design

Analysis of results

Fine-tune model

Model verification and

validation

No

Yes

2

4

6

8

1

3

5

7

Steps in OR StudySteps in OR Study

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How decision-making problems are characterized

OR terminology

What a model is and how to assess its value

How to go from a conceptual problem to a quantitative solution

How to find solutions with the Excel add-ins

What you Should Know about What you Should Know about Operations ResearchOperations Research

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Operations Research/Management ScienceOperations Research/Management Science

Institute for Operations Research and the Management Sciences

OR/MS Professionals aim to provide rational bases for decision making by seeking to understand and structure complex situations and to use this understanding to predict system behavior and improve system performance. Much of this work is done using analytical and numerical techniques to develop and manipulate mathematical and computer models of organizational systems composed of people, machines, and procedures.

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OperationsThe activities carried out in an organization. ResearchThe process of observation and testing characterized by the scientific method. Situation, problem statement, model construction, validation, experimentation, candidate solutions. ModelAn abstract representation of reality. Mathematical, physical, narrative, set of rules in computer program.

What is Operations Research?What is Operations Research?

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Philosophy Why are we here?

Theology What is going to become of us?

Science What is it, how and why does it work?

Mathematic How do we prove it?

Engineering How do we make it?

OR/MS How do we get it to work efficiently (optimally)?

Psychology How do we feel about it?

Sociology How does it affect us and how do we affect it?

Politics How can we agree on getting it to work?

Business How do we convert it to an opportunity and make money out of it?

Law How do we create doubt about why it happened so we can win and make big money?

Psychiatry What is the bright side of looking at it?

Medicine How do we get it going again?