1. operations research - an introduction

Introduction toOperations Research

A B Raju

What is Operations Research?OR is a discipline that applies advanced mathematical

techniques to help institutions (private, public, non-profit) and individuals make better decisions. OR has recently been called “the science of better”.

http://www.scienceofbetter.org

OR focuses on finding ways to allocate scarce resources to activities often in an uncertain environment in order to “optimize one or more objectives”. Institute for Operations Research and the Management Sciences

(INFORMS) - http://www.informs.org

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Introduction to Operations ResearchOperations research/management science

Winston: “a scientific approach to decision making, which seeks to determine how best to design and operate a system, usually under conditions requiring the allocation of scarce resources.”

Kimball & Morse: “a scientific method of providing executive departments with a quantitative basis for decisions regarding the operations under their control.”

Partial list of OR topicsLinear ProgrammingNon-linear ProgrammingInteger ProgrammingDynamic ProgrammingDecision AnalysisMarkov chains , Markov Decision ProblemsQueueing TheoryGame TheorySimulationNetwork OptimizationStochastic Programming

Basic CharacteristicsApplies scientific methodsAdopts a systems approachUtilises a team conceptRelies on computer technologies

Some Examples of Typical Decision ProblemsHow many cars of various models to produce? What intensity of radiation to use in cancer treatment? How many outpatients to schedule every day? Whether to undertake a new project? Whether to invest in a particular stock? Which retirement

plan to choose? How many medical service centers to open in a county? How many warehouses to open? What and how much to stock in these warehouses? How many nurses to employ? Which doctors to have on call? How to schedule flights? How to route road traffic / air traffic? Whether to use two-finger screening or ten-finger

screening? How to schedule multiple projects? When to replenish inventory?

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Introduction to Operations Research

Provides rational basis for decision makingSolves the type of complex problems that

turn up in the modern business environmentBuilds mathematical and computer models

of organizational systems composed of people, machines, and procedures

Uses analytical and numerical techniques to make predictions and decisions based on these models

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Introduction to Operations Research Draws upon

engineering, management, mathematics

Closely related to the "decision sciences" applied mathematics, computer science,

economics, industrial engineering and systems engineering

Origins and Applications of OR Initial research in OR is typically attributed to World War

II.

The first formal activities of Operations Research (OR) were initiated in England during World War II, when a team of British scientists set out to make scientifically based decisions regarding the best utilization of war materiel.

After the war, the ideas advanced in military operations were adapted to improve efficiency and productivity in the civilian sector.

Eg.: What would be the width and the height of the maximum-area rectangle formed out of a piece of wire of length L inches?

ApplicationsSince the early 1940, OR has grown to be a vast field of study

with applications to Healthcare emergency/disaster management Telecommunications Finance business modeling Medicine logistics/transportation inventory management Manufacturing Sports engineering design Economics natural sciences e-commerce forest management supply chain management, …….

Applications Finance & Accounts

Dividend policy, portfolio mgmt, capital budgeting etc.,

Marketing Product mix, Ad & media planning, sales effort allocation etc.,

Materials Management Optimal buying, vendor analysis, transportation analsis etc.,

Production Facilities planning, manufacturing, maintenance etc.,

Personnel Manpower planning, training scheduling, skills & wages

balancing

General Management DSS, MIS, forecasting, project mgmt, strategic planning etc.,

Models & Modelling in OR

Models & Modelling in ORPhysical modelsSymbolic models

Verbal models : booksMathematical models

Descriptive models : organisation chartPredictive models : what if?Normative (or optimisation) modelsStatic models : EOQ modelDynamic modelsDeterministic modelsProbabilistic (stochastic) modelsAnalytical modelsSimulation models

The OR Problem Solving methodology

Solution

Formulation

Realization

Modelling

Analysis

Implementation

Monitoring

In Practice

Solution

Formulation

Realization

Modelling

Analysis

Implementation

Monitoring

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Methodology of Operations Research*The Seven Steps to a Good OR Analysis

Feedback loopsat all levels!

*Adapted from Winston, Wayne L., Operations Research: Applications and Algorithms, 3rd Edition, Duxbury Press, 1994, p. 2.

Identify the Problemor Opportunity

Understand the System

Formulate a Mathematical Model

Verify the Model

Select the Best Alternative

Implement and Evaluate

Present the Results ofthe Analysis

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Verify the Model




• What are the objectives?

• Is the proposed problem too narrow?

• Is it too broad?

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Verify the Model




• What data should be collected?

• How will data be collected?

• How do different components of the system interact with each other?

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Verify the Model




• What kind of model should be used?

• Is the model accurate?

• Is the model too complex?

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Verify the Model




• Do outputs match current observations for current inputs?

• Are outputs reasonable?

• Could the model be erroneous?

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Verify the Model




• What if there are conflicting objectives?

• Inherently the most difficult step.

• This is where software tools will help us!

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Verify the Model




• Must communicate results in layman’s terms.

• System must be user friendly!

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Verify the Model




• Users must be trained on the new system.

• System must be observed over time to ensure it works properly.

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Successful OR Applications

Patel Products - Break-Even Analysis The Patel Products Company produces expensive and unusual gifts. The latest new-product proposal is a limited edition grandfather

clock. Data:

If they go ahead with this product, a fixed cost of $50,000 is incurred.

The variable cost is $400 per clock produced.Each clock sold would generate $900 in

revenue.A sales forecast will be obtained.

Question: Should they produce the clocks, and if so, how many?

Expressing the Problem Mathematically Decision variable:

Q = Number of grandfather clocks to produce Costs:

Fixed Cost = $50,000 (if Q > 0)Variable Cost = $400 QTotal Cost =

0, if Q = 0 $50,000 + $400 Q, if Q > 0

Profit:

Profit = Total revenue – Total cost Profit = 0, if Q = 0 Profit = $900Q – ($50,000 + $400Q) = –$50,000 +

$500Q, if Q > 0

Patel Products Co. Spreadsheet

34567

E FResults

Total Revenue =UnitRevenue*MIN(SalesForecast,ProductionQuantity)Total Fixed Cost =IF(ProductionQuantity>0,FixedCost,0)

Total Variable Cost =MarginalCost*ProductionQuantityProfit (Loss) =TotalRevenue-(TotalFixedCost+TotalVariableCost)

Range Name CellFixedCost C5MarginalCost C6ProductionQuantity C9Profit F7SalesForecast C7TotalFixedCost F5TotalRevenue F4TotalVariableCost F6UnitRevenue C4

3456789

B C D E FData Results

Unit Revenue $900 Total Revenue $180,000Fixed Cost $50,000 Total Fixed Cost $50,000

Marginal Cost $400 Total Variable Cost $80,000Sales Forecast 300 Profit (Loss) $50,000

Production Quantity 200

Analysis of the Problem

$

$40,000

$80,000

$120,000

$160,000

$200,000

0 40 80 120 160 200

Revenue = $900 x

Fixed cost

Loss

Profit

Cost = $50,000 + $400 x

x

Breakeven point = 100 units

Management Science Interactive Modules

Sensitivity analysis can be performed using the Break-Even module in the Interactive Management Science Modules (available on your MS Courseware CD packaged with the text).

Here we see the impact of changing the fixed cost to $75,000.

Special Products Co. Spreadsheet

Range Name CellFixedCost C5MarginalCost C6ProductionQuantity C9Profit F7SalesForecast C7TotalFixedCost F5TotalRevenue F4TotalVariableCost F6UnitRevenue C4

3456789

B C D E FData Results

Unit Revenue $900 Total Revenue $270,000Fixed Cost $50,000 Total Fixed Cost $50,000

Marginal Cost $400 Total Variable Cost $120,000Sales Forecast 300 Profit (Loss) $100,000

Production Quantity 300 Break-Even Point 100

3456789

E FResults

Total Revenue =UnitRevenue*MIN(SalesForecast,ProductionQuantity)Total Fixed Cost =IF(ProductionQuantity>0,FixedCost,0)

Total Variable Cost =MarginalCost*ProductionQuantityProfit (Loss) =TotalRevenue-(TotalFixedCost+TotalVariableCost)

Break-Even Point =FixedCost/(UnitRevenue-MarginalCost)

1. operations research - an introduction

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