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Introduction to Operations
Research
1
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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
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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.
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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
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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.
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&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
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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• Queuing Theory (waiting lines)
• Nonlinear Programming• Decision Analysis
• Inventory Models Game Theory
Inventory models
Simulation
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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.
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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 #
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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
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(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
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?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
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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
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&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
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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
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(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
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>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.
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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 $eyassumptions, estimates, or statistical analyses
18
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Advantages o 1odelsCenerally, e#perimenting with models
0compared to e#perimenting with the realsituation2%re@uires less time
is less e#pensive
involves less ris$
1#
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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$
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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
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&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
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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$ers, e@uipment, etc2
What is the best schedule or the activities
and or which activities should additional 23
#amp e ro ec
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#amp e% ro ecScheduling
?uestion%Suggest assumptions that could be made to
simpliy the model
Answer%
1a$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
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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
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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
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#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
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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
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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
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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$
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>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
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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
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Implementation
A solution to a problemusually implies changesor some individuals inthe organiDation
Oten there is resistanceto change, ma$ing theimplementation diEcult
3ser.riendly system
needed &hose a'ected should go
through training
33
Situation
Procedure
Implementthe Procedure
Example' (mplement nurse scheduling s%stem in one unit at a
time. (ntegrate )ith e&isting - and s%stems.
rovide training sessions during the )orkda%.
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<ollow.3p
Successul implementation o model results iso critical importance
Secure as much user involvement as possiblethroughout the modeling process
>ontinue to monitor the contribution o themodel
It might be necessary to re"ne or e#pand themodel
34
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Report CenerationA managerial report, based on the results o
the model, should be prepared &he report should be easily understood by the
decision ma$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
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)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
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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
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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$ing two deductions, one based onthe car;s age and the other based on thecar;s mileage
&he age deduction is KL77 per year andthe mileage deduction is K7= per mile 38
#amp e% us n u o
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#amp e% us n u oAuction
?uestion%(evelop the mathematical model that will
give the starting bid 0B2 or a car in terms othe car;s original price 0%2, current age 0 &2
and mileage 0M2Answer%
&he e#pected winning bid can be
e#pressed as%% . L770 &2 . 7=0M2
&he entire model is%
B M 60e#pected winning bid2 or
B M 6 % . L77 & . 7= M or 3#
#amp e% us n u o
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#amp e% us n u oAuction
?uestion%Suppose a our.year old car with N7,777
miles on the odometer is up or auction I itsoriginal price was K8,=77, what starting bid
should the auctioneer re@uire!Answer%
B M 608,=772 . =N702 . 786=0N7,7772 MK=N7
4$
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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
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+#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
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#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
# 0monthly production 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
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#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
# 0monthly production o product 82
Q 0steel re@uired per unit o product 2
# 0monthly production 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
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,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 $
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+#ample% Iron Wor$s,
Inc1athematical 1odel Summary
1a# '8 x 8 Q ' x
st a8#8 Q a x b
x 8 m
x u
x 7
46
#amp e% ron or s
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#amp e% ron or s,Inc
?uestion%Suppose b M 777, a8 M , a M :, m M N7, u M
67, '8 M 877, ' M 77 Rewrite the model with
these speci"c values or the uncontrollable inputs
Answer%Substituting, the model is%
1a# 877 x 8 Q 77 x
st x 8 Q : x 777
x 8 N7
x 67
x 7
47
#amp e% ron or s
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#amp e% ron or s,Inc
?uestion%
&he optimal solution to the current modelis x 8 M N7 and x M NN *: I the product
were engines, e#plain why this is not a true
optimal solution or the -real.lie- problemAnswer%
One cannot produce and sell *: o an
engine &hus the problem is urtherrestricted by the act that both x 8 and x must
be integers &hey could remain ractions i itis assumed these ractions are wor$ in
progress to be completed the ne#t month 48
+ l I W $ I
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+#ample% Iron Wor$s, Inc
4#
3ncontrollable Inputs3ncontrollable Inputs
K877 pro"t per unit Prod 8K77 pro"t per unit Prod lbs steel per unit Prod 8: lbs Steel per unit Prod
777 lbs steel allocated
N7 units minimum Prod 867 units ma#imum Prod
7 units minimum Prod
K877 pro"t per unit Prod 8K77 pro"t per unit Prod lbs steel per unit Prod 8: lbs Steel per unit Prod
777 lbs steel allocated
N7 units minimum Prod 867 units ma#imum Prod
7 units minimum Prod
N7 units Prod 8
NNN6 units Prod
N7 units Prod 8
NNN6 units Prod
>ontrollable Inputs>ontrollable Inputs
Pro"t M K8:8,:::::
Steel 3sed M 777
Pro"t M K8:8,:::::
Steel 3sed M 777
OutputOutput
1athematical 1odel1athematical 1odel
1a# 8770N72 Q 770NNN62
st 0N72 Q :0NNN62 777 N7 N7 NNN6 67 NNN6 7
1a# 8770N72 Q 770NNN62
st 0N72 Q :0NNN62 777 N7 N7 NNN6 67 NNN6 7
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(evelopment >orp
Ponderosa (evelopment >orporation 0P(>2 is asmall real estate developer operating in theRivertree Falley It has seven permanent employeeswhose monthly salaries are given in the table on thene#t slide
P(> leases a building or K,777 per month &hecost o supplies, utilities, and leased e@uipment runsanother K:,777 per month
P(> builds only one style house in the valley
and or each house costs K==,777 and lumber,supplies, etc run another KL,777 per house &otallabor costs are "gured at K7,777 per house &heone sales representative o P(> is paid a
commission o K,777 on the sale o each house 5$
#amp e% on erosa
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#amp e% on erosa(evelopment >orp
Employee Monthly Salary
President K87,777
FP, (evelopment N,777
FP, 1ar$eting ,=77Pro/ect 1anager =,=77
>ontroller ,777
OEce 1anager :,777
Receptionist ,777
51
#amp e% on erosa
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#amp e% on erosa(evelopment >orp?uestion%
Identiy all costs and denote the marginal costand marginal revenue or each house
Answer%
&he monthly salaries total K:=,777 and monthlyoEce lease and supply costs total another K=,777
&his K7,777 is a monthly "#ed cost
&he total cost o land, material, labor, and sales
commission per house, K87=,777, is the marginalcost or a house
&he selling price o K88=,777 is the marginalrevenue per house
52
#amp e% on erosa
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#amp e% on erosa(evelopment >orp?uestion%
Write the monthly cost unction c0 x 2,revenue unction r 0 x 2, and pro"t unction
'0 x 2
Answer%
c0 x 2 M variable cost Q "#ed cost M87=,777 x Q 7,777
r 0 x 2 M 88=,777 x '0 x 2 M r 0 x 2 . c0 x 2 M 87,777 x . 7,777
53
+#ample% Ponderosa
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+#ample% Ponderosa(evelopment >orp?uestion%
What is the brea$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
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>orp
Craph o )rea$.+ven Analysis
55
0
200
400
600
800
1000
1200
0 1 2 4 ! 6 " 8 # 10
$um%er o& 'ouses Sold ()*
+ h o
u s a n d s o
& D o l l a r s
Break-Even Point = 4 Houses
Total Cost =
40,000 + 105,000x
Total Revenue = 115,000x
Problem formulation1
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Steps in OR Study
56
Problem formulation
Model building
Data collection
Data analysis
Coding
Experimental design
Analysis of results
Fine-tunemodel
Modelverification and
validation
No
Yes
2
4
6
8
3
5
7
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Success Stories o&
OR
57
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Application AreasStrategic planning
Supply chain management
Pricing and revenue management
ogistics and site location
OptimiDation
1ar$eting research
58
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Applications Areas 0cont2Scheduling
Portolio management
Inventory analysis
<orecasting
Sales analysis
Auctioning
Ris$ analysis
5#
+#amples
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+#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
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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
A Short ist o Successul Stories
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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
62
A Short ist o Successul Stories
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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$etplace Initiative with 1errill ynch Integrated >hoi
ceG)>
Increasing Advertising Revenues and Productivity at G)>PSA Peugeot >itroen
Speeding >ar )ody Production at PSA Peugeot >itroenRhenania
Rhenania OptimiDes Its 1ail.Order )usiness with (ynamic 1ultilevel 1odeling
Samsung Samsung >uts 1anuacturing >ycle &ime and Inventory to >omp
ete
63
A Short ist o Successul Stories
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02Spicer
Spicer Improves Its ead.&ime and Scheduling PerormanceSyngenta1anaging the Seed.>orn Supply >hain at Syngenta
&owers Perrin &owers Perrin Improves Investment (ecision 1a$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
64
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<inale
65
Please Go to www.scienceofbetter.org
For details on these successful stories
> 8 > ti t l
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>ase 8% >ontinental
Airlines Survives 9*88Problem% ong beore September 88, 778,
>ontinental as$ed what crises plan it coulduse to plan recovery rom potentialdisasters such as limited and massiveweather delays
66
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>ontinental Airlines 0cont2Strategic Ob/ectives and Re@uirements are to
accommodate%8,77 daily fights
=,777 pilots
9,777 fight attendants
<AA regulations
3nion contracts
67
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>ontinental Airlines 0cont2
1odel Structure% Wor$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
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>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
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>ase % 1errill ynch
Integrated >hoiceProblem% 5ow should 1errill ynch deal
with online investment "rms withoutalienating "nancial advisors, undervaluingits services, or incurring substantialrevenue ris$!
7$
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1errill ynch 0cont2
Ob/ectives and Re@uirements% +valuatenew products and pricing options, andoptions o online vs traditional advisor.based services
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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
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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
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>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
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G)> Ad Sales 0cont2
Strategic Ob/ectives and Re@uirements%>omplete intricate sales plans while
reducing labor cost and ma#imiDingincome
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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
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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
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>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.$ind creations
78
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<ord 1otor 0cont2
Strategic Ob/ectives and Re@uirements%<ord needs to veriy the designs o its
vehicles and perorm all necessary tests5istorically, prototypes sit idle much o thetime waiting or various tests, so increasingtheir usage would have a clear bene"t
7#
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<ord 1otor 0cont2
1odel Structure% <ord and a team romWayne State 3niversity developed a
Prototype OptimiDation 1odel 0PO12 toreduce the number o prototype vehicles &he model determines an optimal set ovehicles that can be shared and used to
satisy all testing needs
8$
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<ord 1otor 0cont2
Pro/ect Falue% <ord reduced annual
prototype costs by K=7 million
81
>ase =% Procter J Camble
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>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
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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
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PJC Supply >hain 0cont21odel Structure% &he PJC operations research
department and the 3niversity o >incinnaticreated decision.ma$ing models and sotware
&hey ollowed a modeling strategy o solvingtwo easier.to.handle subproblems%(istribution*location
Product sourcing
84
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PJC Supply >hain 0cont2
Pro/ect Falue% &he overall StrengtheningClobal +'ectiveness 0SC+2 e'ort savedK77 million a year beore ta# and allowedPJC to write o' K8 billion o assets andtransition costs
85
>ase N% American Airlines
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>ase N% American Airlines
RevolutioniDes Pricing)usiness Problem% &o compete e'ectively
in a "erce mar$et, the company needed tosell the right seats to the right customersat the right pricesH
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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
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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$ing
(iscount allocation
&raEc management
&he model was adapted to AmericanAirlines computers
88
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American Airlines 0cont2
Pro/ect Falue% In 8998, American Airlinesestimated a bene"t o K8 billion over the
previous three years Since then, yieldmanagement was adopted by otherairlines, and spread to hotels, car rentals,and cruises, resulting in added pro"ts goinginto billions o dollars
8#
about Operations
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about OperationsResearch
5ow decision.ma$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