quantitative methods intro 2nd term.pptx

7/23/2019 quantitative methods intro 2nd term.pptx

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Introduction to Operations

Research

1



Introduction

Operations Research is an Art and Science

It had its early roots in World War II and isfourishing in business and industry with the aid

o computerPrimary applications areas o Operations

Research include orecasting, productionscheduling, inventory control, capital

budgeting, and transportation

2



What is Operations Research?

3

Operations

The activities carried out in an organization. Research

The process of observation and testing

characterized by the scientific method.Situation, problem statement, modelconstruction, validation, experimentation,candidate solutions.

Operations Research is a quantitative approach todecision making based on the scientific method of problemsolving.



What is Operations Research! Operations Research is the scienti"c

approach to e#ecute decision ma$ing, whichconsists o%

&he art o mathematical modeling o comple# situations

&he science o the development osolution techniques used to solve

these models &he ability to e'ectively

communicate the results to the

decision ma$er 4



What (o We do

5

1.OR professionals aim to provide rational bases fordecision making by seeking tounderstand andstructure complex situations and to use this

understanding topredict system behavior andimprove system performance.

2.Much of this work is done usinganalytical andnumericaltechniques to develop and manipulate

mathematical and computer models oforganizational systems composed of people,machines, and procedures.



&erminology &he )ritish*+uropeans reer to OperationalResearch-, the Americans to OperationsResearch- . but both are oten shortened to /ust-OR-

Another term used or this "eld is ManagementScience- 0-1S-2 In 3S OR and 1S are combinedtogether to orm -OR*1S- or -OR1S-

4et other terms sometimes used are IndustrialEngineering- 0-I+-2 and Decision Science- 0-(S-2

6



Operations Research Models

Deterministic Models Stochastic Models

• Linear Programming• Discrete-Time Markov Chains

• Network Optimization• Continuous-Time Markov Chains• Integer Programming• Queuing Theory (waiting lines)

• Nonlinear Programming• Decision Analysis

• Inventory Models Game Theory

Inventory models

Simulation



eterministic vs. !tochastic "odels

Deterministic models assume all data are known withcertainty

Stochastic models

explicitly represent uncertain data viarandom variables or stochastic processes.

Deterministic models involveoptimization

Stochastic models characterize/estimate system performance.



5istory o OROR is a relatively new discipline

67 years ago it would have been

possible to study mathematics,physics or engineering atuniversity it would not have been

possible to study ORIt was really only in the late89:7;s that operationas research

began in a systematic way #


http://slidepdf.com/reader/full/quantitative-methods-intro-2nd-termpptx 10/901$

1890

Frederick TaylorScientificManagement[Industrial

Engineering]

1900

• Henry Gannt[Project Scheduling]• Andrey A. Markov[Markov Processes]

• Assignment[Networks]

1910• F. W. Harris[Inventory Theory]• E. K. Erlang[Queuing Theory]

1920

• William Shewart[Control Charts]• H.Dodge –H.Roming

[Quality Theory]

1930

Jon Von Neuman –Oscar Morgenstern[Game Theory]

1940

• World War 2• George Dantzig[Linear

Programming]• First Computer

1950

• H.Kuhn - A.Tucker[Non-Linear Prog.]• Ralph Gomory[Integer Prog.]• PERT/CPM• Richard Bellman[Dynamic Prog.]ORSA and TIMS

1960

• John D.C. Litle[Queuing Theory]• Simscript - GPSS

[Simulation]

1970

• Microcomputer1980

• H. Karmarkar[Linear Prog.]• Personalcomputer

• OR/MS Softwares

1990

• SpreadsheetPackages

• INFORMS

2006

• You are here



(ecision 1a$ing

6 Steps o Problem Solving0<irst = steps are the process o decision ma$ing2

Identiy and de"ne the problem

(etermine the set o alternative solutions

(etermine the criteria or evaluating thealternatives

+valuate the alternatives

>hoose an alternative

...............................................................Implement the chosen alternative

+valuate the results

11



?uantitative Analysis and(ecision 1a$ing

Potential Reasons or a ?uantitative AnalysisApproach to (ecision 1a$ing &he problem is comple#

&he problem is very important

&he problem is new

&he problem is repetitive

12



Problem Solving Process

13

Data

Solution

Finda Solution

Tools

Situation

Formulate the

Problem Problem

Statement

Test the Modeland the Solution

Solution

Establisha Procedure

Implementthe Solution

Constructa Model

Model

Implement a Solution

Goal: solve a problem

• Model must be valid

• Model must be

tractable• Solution must beuseful



&he Situation

14

• "a% involve current operationsor proposed e&pansions due to

e&pected market shifts

• "a% become apparent through

consumer complaints or throughemplo%ee suggestions

• "a% be a conscious effort to

improve efficienc% or response to

an une&pected crisis.

Example' (nternal nursing staff not happ% )ith their schedules*

hospital using too man% e&ternal nurses.

Data

Situation



Problem <ormulation

(e"ne variables

(e"ne

constraints(ata

re@uirements

15

Example' "a&imi+e individual nurse preferences

sub,ect to demand requirements.

Formulate the

ProblemProblem

Statement

Data

Situation

• escribe s%stem

• efine boundaries

• !tate assumptions• !elect performance measures



(ata Preparation(ata preparation is not a trivial step, due to

the time re@uired and the possibility o datacollection errors

A model with =7 decision variables and =

constraints could have over 8:77 dataelementsB

Oten, a airly large data base is needed

Inormation systems specialists might be

needed

16



>onstructing a 1odel

Problem must be translatedfrom verbal, qualitative terms tological, quantitative terms

A logical model is a series of

rules, usually embodied in acomputer program

17

Example' efine relationships bet)een individual nurse assignments

and preference violations* define tradeoffs bet)een the use

of internal and e&ternal nursing resources.

Construct

a Model

Model

Formulate the

Problem

Problem

statement

Data

Situation

• A mathematical model is a collection of

functional relationships by which allowable

actions are delimited and evaluated.



1odel (evelopment1odels are representations o real ob/ects or

situations &hree orms o models are iconic, analog, and

mathematicalIconic models are physical replicas 0scalar

representations2 o real ob/ectsAnalog models are physical in orm, but do not

physically resemble the ob/ect being modeled

1athematical models represent real world

problems through a system o mathematicalormulas and e#pressions based on $eyassumptions, estimates, or statistical analyses

18



Advantages o 1odelsCenerally, e#perimenting with models

0compared to e#perimenting with the realsituation2%re@uires less time

is less e#pensive

involves less ris$

1#



1athematical 1odels

>ost*bene"t considerations must be made inselecting an appropriate mathematicalmodel

<re@uently a less complicated 0and perhaps

less precise2 model is more appropriate thana more comple# and accurate one due tocost and ease o solution considerations

2$



1athematical 1odelsRelate decision variables 0controllable inputs2

with "#ed or variable parameters 0uncontrollable inputs2

<re@uently see$ to ma#imiDe or minimiDesome ob/ective unction sub/ect to

constraintsAre said to be stochastic i any o the

uncontrollable inputs 0parameters2 is sub/ect

to variation 0random2, otherwise are said tobe deterministic

Cenerally, stochastic models are morediEcult to analyDe

&he values o the decision variables that 21



&ransorming 1odel

Inputs into Output

22

3ncontrollable Inputs0+nvironmental <actors2

3ncontrollable Inputs0+nvironmental <actors2

>ontrollableInputs

0(ecision Fariables2

>ontrollableInputs

0(ecision Fariables2

Output0Pro/ected Results2

Output0Pro/ected Results2

1athematical1odel

1athematical1odel



Scheduling

>onsider a construction company buildinga =7.unit apartment comple# &he pro/ectconsists o hundreds o activities involvinge#cavating, raming, wiring, plastering,painting, landscaping, and more Some o theactivities must be done se@uentially andothers can be done simultaneously Also,

some o the activities can be completedaster than normal by purchasing additionalresources 0wor$ers, e@uipment, etc2

What is the best schedule or the activities

and or which activities should additional 23

#amp e ro ec



#amp e% ro ecScheduling

?uestion%Suggest assumptions that could be made to

simpliy the model

Answer%

1a$e the model deterministic by assumingnormal and e#pedited activity times are $nownwith certainty and are constant &he sameassumption might be made about the otherstochastic, uncontrollable inputs

24



Scheduling?uestion%

5ow could management science be usedto solve this problem!

Answer%

1anagement science can provide astructured, @uantitative approach ordetermining the minimum pro/ectcompletion time based on the activities;

normal times and then based on theactivities; e#pedited 0reduced2 times

25



Scheduling

?uestion%What would be the uncontrollable

inputs!

Answer%

Gormal and e#pedited activity completiontimes

Activity e#pediting costs

<unds available or e#pediting

Precedence relationships o the activities

26

#amp e% ro ec



#amp e% ro ecScheduling

?uestion%

What would be the decision variables o themathematical model! &he ob/ective unction!

&he constraints!

Answer%(ecision variables% which activities to e#pedite

and by how much, and when to start each activity

Ob/ective unction% minimiDe pro/ect completion

time>onstraints% do not violate any activity

precedence relationships and do not e#pedite ine#cess o the unds available

27



Scheduling

?uestion%Is the model deterministic or stochastic!

Answer%

Stochastic Activity completion times, both

normal and e#pedited, are uncertain andsub/ect to variation Activity e#pediting costsare uncertain &he number o activities andtheir precedence relationships might change

beore the pro/ect is completed due to a pro/ectdesign change

28



1athematical 1odel

1any tools areavailable as discussedbeore

Some lead to

optimalH solutions0deterministic 1odels2Others only evaluate

candidates trial anderror to "nd bestHcourse o action

2#

Example' -ead nurse profiles and demand requirements appl%

algorithm post/processes results to get monthl%

schedules.

Model

Solution

0ind a

solution

Tools



1odel SolutionInvolves identiying the values o the

decision variables that provide the bestHoutput or the model

One approach is trial.and.error

might not provide the best solutionineEcient 0numerous calculations re@uired2

Special solution procedures have beendeveloped or speci"c mathematical

modelssome small models*problems can be solved by

hand calculations

most practical applications re@uire using a

computer 3$



>omputer SotwareA variety o sotware pac$ages are

available or solving mathematical models,some are%Spreadsheet pac$ages such as Microsoft

Excel

The Management Scientist (MS)

Quantitative system for business (QSB)

LIN!" LIN#!

Quantitative mo$els (QM)

(ecision Science 0(S2

31

o e es ng an



o e es ng anFalidation

Oten, the goodness*accuracy o a modelcannot be assessed until solutions aregenerated

Small test problems having $nown, or atleast e#pected, solutions can be used ormodel testing and validation

I the model generates e#pected solutions%

use the model on the ull.scale problemI inaccuracies or potential shortcomings

inherent in the model are identi"ed, ta$ecorrective action such as%collection o more.accurate input data 32



Implementation

A solution to a problemusually implies changesor some individuals inthe organiDation

Oten there is resistanceto change, ma$ing theimplementation diEcult

3ser.riendly system

needed &hose a'ected should go

through training

33

Situation

Procedure

Implementthe Procedure

Example' (mplement nurse scheduling s%stem in one unit at a

time. (ntegrate )ith e&isting - and s%stems.

rovide training sessions during the )orkda%.



<ollow.3p

Successul implementation o model results iso critical importance

Secure as much user involvement as possiblethroughout the modeling process

>ontinue to monitor the contribution o themodel

It might be necessary to re"ne or e#pand themodel

34



Report CenerationA managerial report, based on the results o

the model, should be prepared &he report should be easily understood by the

decision ma$er

&he report should include%the recommended decision

other pertinent inormation about the results 0ore#ample, how sensitive the model solution is tothe assumptions and data used in the model2

35



)ased (ecision Support

System(ata base 0nurse

pro"les, e#ternal

resources, rules2Craphical 3ser Interace

0C3I2 web enabled using /ava or F)A

Algorithms, pre. andpost. processor

What.i analysis

Report generators 36



Applications

Rescheduling aircrat in response togroundings and delays

Planning production or printed circuit boardassembly

Scheduling e@uipment operators in mailprocessing J distribution centers

(eveloping routes or propane deliveryAd/usting nurse schedules in light o daily

fuctuations in demand

37



Auction

An auctioneer has developed a simplemathematical model or deciding thestarting bid he will re@uire when auctioninga used automobile +ssentially, he sets

the starting bid at seventy percent o whathe predicts the "nal winning bid will 0orshould2 be 5e predicts the winning bid bystarting with the car;s original selling price

and ma$ing two deductions, one based onthe car;s age and the other based on thecar;s mileage

&he age deduction is KL77 per year andthe mileage deduction is K7= per mile 38

#amp e% us n u o



#amp e% us n u oAuction

?uestion%(evelop the mathematical model that will

give the starting bid 0B2 or a car in terms othe car;s original price 0%2, current age 0 &2

and mileage 0M2Answer%

&he e#pected winning bid can be

e#pressed as%% . L770 &2 . 7=0M2

&he entire model is%

B M 60e#pected winning bid2 or

B M 6 % . L77 & . 7= M or 3#

#amp e% us n u o



#amp e% us n u oAuction

?uestion%Suppose a our.year old car with N7,777

miles on the odometer is up or auction I itsoriginal price was K8,=77, what starting bid

should the auctioneer re@uire!Answer%

B M 608,=772 . =N702 . 786=0N7,7772 MK=N7

4$



Auction?uestion%

&he model is based on what assumptions!

Answer%

&he model assumes that the only actors

infuencing the value o a used car are theoriginal price, age, and mileage 0notcondition, rarity, or other actors2

Also, it is assumed that age and mileagedevalue a car in a linear manner and withoutlimit 0Gote, the starting bid or a very oldcar might be negativeB2

41

+ l I W $ I



+#ample% Iron Wor$s, Inc

Iron Wor$s, Inc 0IWI2 manuactures two

products made rom steel and /ust received thismonth;s allocation o b pounds o steel It ta$esa8 pounds o steel to ma$e a unit o product 8

and it ta$es a pounds o steel to ma$e a unit o

product et x 8 and x denote this month;s production

level o product 8 and product , respectively(enote by '8 and ' the unit pro"ts or products

8 and , respectively

&he manuacturer has a contract calling orat least m units o product 8 this month &he

"rm;s acilities are such that at most u units oroduct ma be roduced monthl 42

#amp e% ron or s



#amp e% ron or s,Inc

1athematical 1odel &he total monthly pro"t M

0pro"t per unit o product 82

# 0monthly production o product 82

Q 0pro"t per unit o product 2


M '8 x 8 Q ' x

We want to ma#imiDe total monthly pro"t%

1a# '8 x 8 Q ' x

43

#amp e% ron or s



#amp e% ron or s,Inc1athematical 1odel 0continued2

&he total amount o steel used duringmonthly production M

0steel re@uired per unit o product 82


Q 0steel re@uired per unit o product 2


M a8 x 8 Q a x

&his @uantity must be less than ore@ual to the allocated b pounds osteel%

a8 x 8 Q a x b44



,Inc1athematical 1odel 0continued2

&he monthly production level o product 8must be greater than or e@ual to m%

x 8 m

&he monthly production level o product must be less than or e@ual to u%

x u

5owever, the production level or product

cannot be negative% x 7

45

+ l I W $



+#ample% Iron Wor$s,

Inc1athematical 1odel Summary

1a# '8 x 8 Q ' x

st a8#8 Q a x b

x 8 m

x u

x 7

46

#amp e% ron or s




?uestion%Suppose b M 777, a8 M , a M :, m M N7, u M

67, '8 M 877, ' M 77 Rewrite the model with

these speci"c values or the uncontrollable inputs

Answer%Substituting, the model is%

1a# 877 x 8 Q 77 x

st x 8 Q : x 777

x 8 N7

x 67

x 7

47

#amp e% ron or s




?uestion%

&he optimal solution to the current modelis x 8 M N7 and x M NN *: I the product

were engines, e#plain why this is not a true

optimal solution or the -real.lie- problemAnswer%

One cannot produce and sell *: o an

engine &hus the problem is urtherrestricted by the act that both x 8 and x must

be integers &hey could remain ractions i itis assumed these ractions are wor$ in

progress to be completed the ne#t month 48

+ l I W $ I



+#ample% Iron Wor$s, Inc

4#

3ncontrollable Inputs3ncontrollable Inputs

K877 pro"t per unit Prod 8K77 pro"t per unit Prod lbs steel per unit Prod 8: lbs Steel per unit Prod

777 lbs steel allocated

N7 units minimum Prod 867 units ma#imum Prod

7 units minimum Prod

K877 pro"t per unit Prod 8K77 pro"t per unit Prod lbs steel per unit Prod 8: lbs Steel per unit Prod

777 lbs steel allocated

N7 units minimum Prod 867 units ma#imum Prod

7 units minimum Prod

N7 units Prod 8

NNN6 units Prod

N7 units Prod 8

NNN6 units Prod

>ontrollable Inputs>ontrollable Inputs

Pro"t M K8:8,:::::

Steel 3sed M 777

Pro"t M K8:8,:::::

Steel 3sed M 777

OutputOutput

1athematical 1odel1athematical 1odel

1a# 8770N72 Q 770NNN62

st 0N72 Q :0NNN62 777 N7 N7 NNN6 67 NNN6 7

1a# 8770N72 Q 770NNN62

st 0N72 Q :0NNN62 777 N7 N7 NNN6 67 NNN6 7



(evelopment >orp

Ponderosa (evelopment >orporation 0P(>2 is asmall real estate developer operating in theRivertree Falley It has seven permanent employeeswhose monthly salaries are given in the table on thene#t slide

P(> leases a building or K,777 per month &hecost o supplies, utilities, and leased e@uipment runsanother K:,777 per month

P(> builds only one style house in the valley

and or each house costs K==,777 and lumber,supplies, etc run another KL,777 per house &otallabor costs are "gured at K7,777 per house &heone sales representative o P(> is paid a

commission o K,777 on the sale o each house 5$

#amp e% on erosa



#amp e% on erosa(evelopment >orp

Employee Monthly Salary

President K87,777

FP, (evelopment N,777

FP, 1ar$eting ,=77Pro/ect 1anager =,=77

>ontroller ,777

OEce 1anager :,777

Receptionist ,777

51

#amp e% on erosa



#amp e% on erosa(evelopment >orp?uestion%

Identiy all costs and denote the marginal costand marginal revenue or each house

Answer%

&he monthly salaries total K:=,777 and monthlyoEce lease and supply costs total another K=,777

&his K7,777 is a monthly "#ed cost

&he total cost o land, material, labor, and sales

commission per house, K87=,777, is the marginalcost or a house

&he selling price o K88=,777 is the marginalrevenue per house

52

#amp e% on erosa



#amp e% on erosa(evelopment >orp?uestion%

Write the monthly cost unction c0 x 2,revenue unction r 0 x 2, and pro"t unction

'0 x 2

Answer%

c0 x 2 M variable cost Q "#ed cost M87=,777 x Q 7,777

r 0 x 2 M 88=,777 x '0 x 2 M r 0 x 2 . c0 x 2 M 87,777 x . 7,777

53

+#ample% Ponderosa



+#ample% Ponderosa(evelopment >orp?uestion%

What is the brea$even point or monthly sales othe houses!

Answer%

r 0 x 2 M c0 x 2 or 88=,777 x M 87=,777 x Q 7,777

Solving, x M

?uestion%

What is the monthly pro"t i 8 houses per monthare built and sold!

Answer%

'082 M 87,777082 . 7,777 M KL7,777 monthly

pro"t 54

>



>orp

Craph o )rea$.+ven Analysis

55

0

200

400

600

800

1000

1200

0 1 2 4 ! 6 " 8 # 10

$um%er o& 'ouses Sold ()*

+ h o

u s a n d s o

& D o l l a r s

Break-Even Point = 4 Houses

Total Cost =

40,000 + 105,000x

Total Revenue = 115,000x

Problem formulation1



Steps in OR Study

56

Problem formulation

Model building

Data collection

Data analysis

Coding

Experimental design

Analysis of results

Fine-tunemodel

Modelverification and

validation

No

Yes

2

4

6

8

3

5

7



Success Stories o&

OR

57



Application AreasStrategic planning

Supply chain management

Pricing and revenue management

ogistics and site location

OptimiDation

1ar$eting research

58



Applications Areas 0cont2Scheduling

Portolio management

Inventory analysis

<orecasting

Sales analysis

Auctioning

Ris$ analysis

5#

+#amples



+#amples)ritish &elecom used OR to schedule wor$orce or

more than 7,777"led engineers &he system was

saving K8=7 million a year rom 8996T 777 &hewor$orce is pro/ected to save K=7 million

Sears 3ses OR to create a Fehicle Routing andScheduling System which to run its delivery andhome service feet more eEciently .. K million inannual savings

3PS use OR to redesign its overnight delivery

networ$, KL6 million in savings obtained rom 777T 77 Another K8L9 million anticipated over theollowing decade

3SPS uses OR to schedule the e@uipment andwor$orce in its mail processing and distribution 6$

A Short ist o Successul Stories



S o s o Success u S o es082Air Gew Uealand

Air Gew Uealand 1asters the Art o >rew SchedulingA&J& Getwor$

(elivering Rapid Restoration >apacity or the A&J& Getwor$)an$ 5apoalim

)an$ 5apoalim O'ers Investment (ecision Support or Individual >ustomers

)ritish &elecommunications(ynamic Wor$orce Scheduling or )ritish &elecommunications

>anadian Paci"c Railway Perecting the Scheduled Railroad at >anadian Paci"c Railway

>ontinental Airlines <aster >rew Recovery at >ontinental Airlines

<AA >ollaborative (ecision 1a$ing Improves the <AA Cround.(elay Program

61


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02<ord 1otor >ompany

OptimiDing Prototype Fehicle &esting at <ord 1otor >ompanyCeneral 1otors

>reating a Gew )usiness 1odel or OnStar at Ceneral 1otors I)1 1icroelectronics

1atching Assets to Supply >hain (emand at I)1 1icroelectronics

I)1 Personal Systems Croup +#tending +nterprise Supply >hain 1anagement at I)1 Persona

l Systems Croup Van de Wit >ompany

OptimiDing Production Planning and &rade at Van de Wit >ompany

Veppesen Sanderson Improving Perormance and <le#ibility at Veppesen Sanderson

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0:21ars

Online Procurement Auctions )ene"t 1ars and Its Suppliers

1enlo Worldwide <orwarding &urning Getwor$ Routing into Advantage or 1enlo <orwarding

1errill ynch SeiDing 1ar$etplace Initiative with 1errill ynch Integrated >hoi

ceG)>

Increasing Advertising Revenues and Productivity at G)>PSA Peugeot >itroen

Speeding >ar )ody Production at PSA Peugeot >itroenRhenania

Rhenania OptimiDes Its 1ail.Order )usiness with (ynamic 1ultilevel 1odeling

Samsung Samsung >uts 1anuacturing >ycle &ime and Inventory to >omp

ete

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02Spicer

Spicer Improves Its ead.&ime and Scheduling PerormanceSyngenta1anaging the Seed.>orn Supply >hain at Syngenta

&owers Perrin &owers Perrin Improves Investment (ecision 1a$ing

3S Army

Reinventing 3S Army Recruiting3S (epartment o +nergy

5andling Guclear Weapons or the 3S (epartment o +nergy3PS

1ore +Ecient Planning and (elivery at 3PSFisteon

(ecision Support Wins Fisteon 1ore Production or ess

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http://www.scienceofbetter.org/can_do/success_stories/mscscs.htm

http://www.scienceofbetter.org/can_do/success_stories/tpiidm.htm

http://www.scienceofbetter.org/can_do/success_stories/rusar.htm

http://www.scienceofbetter.org/can_do/success_stories/hnwusde.htm

http://www.scienceofbetter.org/can_do/success_stories/mepdu.htm

http://www.scienceofbetter.org/can_do/success_stories/dswvmpl.htm

http://www.scienceofbetter.org/can_do/success_stories/dswvmpl.htm

http://www.scienceofbetter.org/can_do/success_stories/mepdu.htm

http://www.scienceofbetter.org/can_do/success_stories/hnwusde.htm

http://www.scienceofbetter.org/can_do/success_stories/rusar.htm

http://www.scienceofbetter.org/can_do/success_stories/tpiidm.htm

http://www.scienceofbetter.org/can_do/success_stories/mscscs.htm

http://www.scienceofbetter.org/can_do/success_stories/siiltsp.htm



<inale

65

Please Go to www.scienceofbetter.org

For details on these successful stories

> 8 > ti t l



>ase 8% >ontinental

Airlines Survives 9*88Problem% ong beore September 88, 778,

>ontinental as$ed what crises plan it coulduse to plan recovery rom potentialdisasters such as limited and massiveweather delays

66



>ontinental Airlines 0cont2Strategic Ob/ectives and Re@uirements are to

accommodate%8,77 daily fights

=,777 pilots

9,777 fight attendants

<AA regulations

3nion contracts

67



>ontinental Airlines 0cont2

1odel Structure% Wor$ing with >A+) &echnologies, >ontinental used anoptimiDation model to generate optimalassignments o pilots J crews &he solutiono'ers a system.wide view o the disruptedfight schedule and all available crewinormation

68



>ontinental Airlines 0cont2

Pro/ect Falue% 1illions o dollars andthousands o hours saved or the airline

and its passengers Ater 9*88, >ontinentalwas the "rst airline to resume normaloperations

6#

> 1 ill h



>ase % 1errill ynch

Integrated >hoiceProblem% 5ow should 1errill ynch deal

with online investment "rms withoutalienating "nancial advisors, undervaluingits services, or incurring substantialrevenue ris$!

7$



1errill ynch 0cont2

Ob/ectives and Re@uirements% +valuatenew products and pricing options, andoptions o online vs traditional advisor.based services

71



1errill ynch 0cont2

1odel Structure% 1errill ynchs1anagement Science Croup simulatedclient.choice behavior, allowing it to%+valuate the total revenue at ris$

Assess the impact o various pricingschedules

AnalyDe the bottom.line impact ointroducing di'erent online and oXineinvestment choices

72



1errill ynch 0cont2

Pro/ect Falue%Introduced two new products which garnered

KL: billion 0K billion in new assets2 andproduced KL7 million in incremental revenue

5elped management identiy and mitigaterevenue ris$ o as much as K8 billion

Reassured "nancial advisors

73

>ase : G)>s



>ase :% G)>s

OptimiDation o Ad SalesProblem% G)> sales sta' had to manually

develop sales plans or advertisers, a long

and laborious process to balance the needso G)> and its clients &he company alsosought to improve the pricing o its ad slotsas a way o boosting revenue

74



G)> Ad Sales 0cont2

Strategic Ob/ectives and Re@uirements%>omplete intricate sales plans while

reducing labor cost and ma#imiDingincome

75



G)> Ad Sales 0cont21odel Structure% G)> used optimiDation

models to reduce labor time and revenue

management to improve pricing o its adspots, which were viewed as a perishablecommodity

76



G)> Ad Sales 0cont2

Pro/ect Falue% In its "rst our years, thesystems increased revenues by over K77

million, improved sales.orce productivity,and improved customer satisaction

77



>ase % <ord 1otor Prototype

Fehicle &esting

Problem% (eveloping prototypes or newcars and modi"ed products is enormouslye#pensive <ord sought to reduce costs onthese uni@ue, "rst.o.a.$ind creations

78



<ord 1otor 0cont2

Strategic Ob/ectives and Re@uirements%<ord needs to veriy the designs o its

vehicles and perorm all necessary tests5istorically, prototypes sit idle much o thetime waiting or various tests, so increasingtheir usage would have a clear bene"t

7#



<ord 1otor 0cont2

1odel Structure% <ord and a team romWayne State 3niversity developed a

Prototype OptimiDation 1odel 0PO12 toreduce the number o prototype vehicles &he model determines an optimal set ovehicles that can be shared and used to

satisy all testing needs

8$



<ord 1otor 0cont2

Pro/ect Falue% <ord reduced annual

prototype costs by K=7 million

81

>ase =% Procter J Camble



>ase =% Procter J Camble

Supply >hainProblem% &o ensure smart growth, PJC

needed to improve its supply chain,streamline wor$ processes, drive out non.value.added costs, and eliminateduplication

82



PJC Supply >hain 0cont2

Strategic Ob/ectives and Re@uirements%PJC recogniDed that there were potentiallymillions o easible options or its :7product.strategy teams to consider+#ecutives needed sound analyticalsupport to realiDe PJCs goal within thetight, one.year ob/ective

83



PJC Supply >hain 0cont21odel Structure% &he PJC operations research

department and the 3niversity o >incinnaticreated decision.ma$ing models and sotware

&hey ollowed a modeling strategy o solvingtwo easier.to.handle subproblems%(istribution*location

Product sourcing

84



PJC Supply >hain 0cont2

Pro/ect Falue% &he overall StrengtheningClobal +'ectiveness 0SC+2 e'ort savedK77 million a year beore ta# and allowedPJC to write o' K8 billion o assets andtransition costs

85

>ase N% American Airlines



>ase N% American Airlines

RevolutioniDes Pricing)usiness Problem% &o compete e'ectively

in a "erce mar$et, the company needed tosell the right seats to the right customersat the right pricesH

86



American Airlines 0cont2Strategic Ob/ectives and Re@uirements%Airline seats are a perishable commodity

&heir value varies Y at times o scarcity

theyre worth a premium, ater the fightdeparts, theyre worthless &he new systemhad to develop an approach to pricing whilecreating sotware that could accommodatemillions o boo$ings, cancellations, and

corrections

87



American Airlines 0cont21odel Structure% &he team developed yield

management, also $nown as revenuemanagement and dynamic pricing &he

model bro$e down the problem into threesubproblems%Overboo$ing

(iscount allocation

&raEc management

&he model was adapted to AmericanAirlines computers

88



American Airlines 0cont2

Pro/ect Falue% In 8998, American Airlinesestimated a bene"t o K8 billion over the

previous three years Since then, yieldmanagement was adopted by otherairlines, and spread to hotels, car rentals,and cruises, resulting in added pro"ts goinginto billions o dollars

8#

about Operations



about OperationsResearch

5ow decision.ma$ing problems arecharacteriDed

OR terminology

What a model is and how to assess its value

5ow to go rom a conceptual problem to a@uantitative solution

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