Operations Research
Operations Research (OR) is the field
of how to form mathematical models
of complex management decision
problems and how to analyze the
models to gain insight about possible
solutions.
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History of OR
Although scientists had (plainly) been involved in the
hardware side of warfare (designing better planes,
bombs, tanks, etc) scientific analysis of the operational
use of military resources had never taken place in a
systematic fashion before the Second World War.
Military personnel, often by no means stupid, were
simply not trained to undertake such analysis.
J E Beasley, Imperial College, London
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History of OR
These early OR workers came from many different
disciplines, one group consisted of a physicist, two
physiologists, two mathematical physicists and a
surveyor. What such people brought to their work were
"scientifically trained" minds, used to querying
assumptions, logic, exploring hypotheses, devising
experiments, collecting data, analysing numbers, etc.
Many too were of high intellectual calibre (at least four
wartime OR personnel were later to win Nobel prizes
when they returned to their peacetime disciplines).
J E Beasley, Imperial College, London
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History of OR
Following the end of the war OR took a different course
in the UK as opposed to in the USA. In the UK (as
mentioned above) many of the distinguished OR workers
returned to their original peacetime disciplines. As such
OR did not spread particularly well, except for a few
isolated industries (iron/steel and coal). In the USA OR
spread to the universities so that systematic training
in OR began.
J E Beasley, Imperial College, London
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History of OR
OR started just before World War II in Britain with the
establishment of teams of scientists to study the strategic
and tactical problems involved in military operations.
The objective was to find the most effective utilisation
of limited military resources by the use of quantitative
techniques.
J E Beasley, Imperial College, London
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History of OR
You should be clear that the growth of OR since it began
(and especially in the last 30 years) is, to a large extent,
the result of the increasing power and widespread
availability of computers. Most (though not all) OR
involves carrying out a large number of numeric
calculations. Without computers this would simply not be
possible.
J E Beasley, Imperial College, London
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History of OR
Manufacturers used operations research to make
products more efficiently, schedule equipment
maintenance, and control inventory and distribution. And
success in these areas led to expansion into strategic
and financial planning … and into such diverse areas as
criminal
justice,
education,
meteorology,
and
communications.
J E Beasley, Imperial College, London
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Future of OR
A number of major social and economic trends are
increasing the need for operations researchers. In
today’s global marketplace, enterprizes must compete
more effectively for their share of profits than ever
before. And public and non-profit agencies must compete
for ever-scarcer funding dollars.
J E Beasley, Imperial College, London
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Future of OR
This means that all of us must become more productive.
Volume must be increased. Consumers’ demands for
better products and services must be met. Manufacturing
and distribution must be faster. Products and people
must be available just in time.
J E Beasley, Imperial College, London
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Terminology
• OR
• MS
• OM
• DS
Operations Research
Operational Research
Management Science
Operations Management
Decision Science
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Applications
grouped by function
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Planning, Strategic Decision-Making
Production
Distribution, Logistics, Transportation
Supply Chain Management
Marketing Engineering
• Financial Engineering
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Build Your Knowledge
to increase your success in practice
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Linear Programming
Non-linear Programming
Dynamic Programming
Markov Decision Processes
Multiple Criteria Decision Making
Queuing Models
General Simulation
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OR Journals
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Operations Research
Management Science
MS/OR Today (Management Science/Operations Res.)
European Journal of Operational Research
Journal of the Operational Research Society
Mathematical Programming
Journal of Optimization Theory and Applications
Interfaces
OR - Spektrum
International Transactions in Operational Research
Annals of Operations Research
Central European Journal of Operations Research
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Build Your Knowledge
to increase your success in practice
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OR in Spreadsheets
Modeling Languages
Decision support systems
Genetic Algorithms, Neural Networks
Fuzzy Logic
Simulated Annealing
General AI
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Build Your Knowledge
to increase your success in practice
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Regression and Econometrics
Forecasting Models
Data Envelopment Analysis
General Measurement of Effectiveness
Cost Benefit Analysis (Reliability,Maintainability)
Data Mining Methods
Applied Stochastic Processes
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Production system
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Operations Research
Operations Research deals with
decision problems by formulating and
analyzing mathematical models –
mathematical representations of
pertinent problem features.
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Operations Research
The model-based OR approach to
problem solving works best on
problems important enough to
warrant the time and resources for a
careful study.
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OR Process
Assessment
Real world problem
Abstraction
Model
Real world solution
Interpretation
Analysis
Model solution
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Math Modeling is Only One Part of
Problem Solving
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Define an Opportunity or Problem
Formulate a Mathematical Model
Acquire Input Information and Data
Validate (Calibrate) Model and Data
Solve and Analyze Solution’s Sensitivity
Implement Solution
Monitor and Follow-Up
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OR models
The three fundamental concerns of forming
operations research models are
• decisions open to decision makers,
• the constraints limiting decision choices, and
• the objectives making some decisions
preferred to others.
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Mathematical Programs
Optimzation models (also called
mathematical programs) represent
choices as decision variables and seek
values that maximize or minimize
objective functions of the decisions
variables subject to constraints on
variable values expressing the limits on
possible decision choices.
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Feasible - Optimal
• A feasible solution is a choice of
values for the decision variables that
satisfies all constraints.
• Optimal solutions are feasible
solutions that achieve objective
functions value(s) as good as those of
any other feasible solutions.
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Parameters – Output Variables
• Parameters – quantities taken as given
– Weekly demand, fixed cost of
replenishment, cost for holding inventory,
cost per carat lost sales, lead time,
minimum order size.
• Parameters and decision variables
determine results measured as output
variables
– c(r,q ; d,f,h,s,l,m)
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Closed-form solution
Closed-form (analytic) solutions
represent the ultimate in analysis of
mathematical models because they
provide both immediate results and rich
sensitivity analysis.
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Sensitivity Analysis
Sensitivity Analysis is an exploration of
results from mathematical models to
evaluate how they depend on the
values chosen for parameters.
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Tractability-Validity
• Tractability in modeling means the degree
to which the model admits convenient
analysis.
• The validity of a model is the degree to
which inferences drawn from the model
hold for the underlying real world problem.
• Tradeoff between validity of models and
their tractability to analysis.
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Simulation
• A simulation model is a computer program
that simply steps through the behavior of a
system of interest and reports experience.
• Simulation models often possess high
validity because they track true system
behavior fairly accurately.
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Simulation
• Descriptive models (simulation)
• Prescriptive optimization models
(mathematical programming)
• Descriptive models yield fewer analytic
inferences (conclusions) than prescriptive
optimization models because they take
both input parameters and decision as
fixed.
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Numerical Search
Numerical search is a process of
systematically trying different choices for
the decision variables, keeping track of the
feasible one with the best objective
function value found so far.
Deals with specific values of the variables Not with symbolic quantities!
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MM
Numerical Part
Conclusions from numerical search are
limited to the specific points explored
unless mathematical structure in the
model support further deduction.
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Exact - Approximate
• An exact optimal solution is a feasible
solution to an optimization model that is
provably as good as any other in objective
function value.
• A approximate optimal solution is a
feasible solution derived from prescriptive
analysis that is not guaranteed to yield an
exact optimum.
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Exact - Approximate
• Losses from settling for approximate
instead of exact optimal solutions are often
dwarfed by variations associated with
questionable model assumption and
doubtful data.
• Exact optima add a satisfying degree of
certainty.
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Deterministic - Stochastic
• A mathematical model is termed
deterministic if all parameter values are
assumed to be known with certainty.
• A mathematical model is termed
probabilistic or stochastic if it involves
quantities known only in probability.
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Deterministic - Stochastic
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Deterministic - Stochastic
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MM
Stochastic Simulation
Besides providing only descriptive
analysis, stochastic simulation models
impose the extra analytic burden of
having to estimate results statistically
from a sample of system realizations.
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Deterministic - Stochastic
• The power and generality of available
mathematical tools for analysis of
stochastic models does not nearly match
that available for deterministic models.
• Most optimization models are deterministic
– not because all problem parameters are
known with certainty, but because useful
prescriptive results can often be obtained
only if stochastic variation is ignored.
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