Operations Research 1 f

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Operations Research 1für Wirtschaftsinformatiker

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• Josef Haunschmied

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Information

• Josef.Haunschmied_at_tuwien.ac.at
• Voice 43 1 58801 11925/11926
• Fax [phone]
• http//www.eos.tuwien.ac.at
• Argentinierstr. 8 / Inst. 105-4
• 1040 Vienna

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• INFORMS, a 12.000 member society representing
  professionals in the fields of Operations
  Research and the Management Sciences

http//www.informs.org
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(No Transcript)
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Build Your Knowledge
to increase your success in practice

• Goals
• Develop skill at the art of modeling of
  decision problems
• Learn to solve MP problems

Goals
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Model

• Definition A simplified rep. of reality
• Types of Models
• physical model (e.g., wind tunnel model)
• graphic model (e.g., a map or flow chart)
• symbolic model
• sheet music
• equations (mathematical model)
• Trade-off Plausibility vs. Tractability

Models
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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 todays 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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Operations Research

• Zweckmäßiges Vorbereiten, Durchführen,
  Kontrollieren und Ein-
• schätzen von Entscheidungen mit Hilfe von
  mathematische Methoden.
• Branstetters SciTech Dictionary ENG/GER

Operational Research (OR for short) looks at an
organisation's operations - the functions it
exists to perform. The objective of Operational
Researchers is to work with clients to find
practical and pragmatic solutions to operational
or strategic problems.
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Terminology

• OR Operations Research
• Operational Research
• MS Management Science
• OM Operations Management
• DS Decision Science

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Applications
grouped by type of organizational client

• Business
• Government and Non-Profit
• Health Care
• Military

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Applications
grouped by function

• 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

• Linear Programming
• Non-linear Programming
• Dynamic Programming
• Markov Decision Processes
• Multiple Criteria Decision Making
• Queuing Models
• General Simulation

Decisions
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OR Journals

• 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

• OR in Spreadsheets
• Modeling Languages
• Decision support systems
• Genetic Algorithms, Neural Networks
• Fuzzy Logic
• Simulated Annealing
• General AI

Computing
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Build Your Knowledge
to increase your success in practice

• Regression and Econometrics
• Forecasting Models
• Data Envelopment Analysis
• General Measurement of Effectiveness
• Cost Benefit Analysis (Reliability,Maintainability
  )
• Data Mining Methods
• Applied Stochastic Processes

Datas
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Operations Research

• Position in der
• Wirtschaftswelt

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Organisationen

• Produkte und Dienstleistungen
• Bspe von Organisationen
• Management von
• Menschen
• Kapital
• Information
• Material

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Organisationsbereiche

• Buchhaltung Finanzbuchhaltung und Kostenrechnung
• Finanzbereich Finanzmittelrechnung und
  Investition
• Personalwesen Anstellung und Ausbildung von
  Personal
• Marketing Nachfrageermittlung, Bedarf wecken,
  Ausrichtung auf Bedürfnisse der Kunden
• .......
• Operative Bereich Gestalten und steuern von
  Prozessen

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Prozess

• (Gruppe von) Aktivitäten
• Input
• Wertsteigerung (Transformation)
• Value added
• Output für Kunden
• Kunde !!!!!!!!!!!!!!!!!!!!!!!!!!!!

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Operations Management

• OM bezieht sich auf die Leitung und Kontrolle von
  Prozessen, die Input in Güter und
  Dienstleistungen umwandeln.

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Produktionssystem
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• OM als eine
• Funktion
• innerhalb eines Unternehmens

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OM als Funktion
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• OM als eine Ansammlung von
• Entscheidungen

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Entscheidungen

• Strategische
• Taktische

Decision Making
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Typen von Entscheidungen

• Operations-Strategie
• Prozess
• Kapazität, Standort, Layout
• Qualität
• Operations-Infrastruktur

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Prozessentscheidungen

• Prozessmanagement
• Technologiemanagement
• Belegschaftsmanagement

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Operations-Infrastruktur

• Supply Chain Management
• Lagerhaltung
• MRP (Material Requirements Planning)
• Terminplanung
• Projekt Management

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Mathematical Programming

• Problem Solving
• with Mathematical Models

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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
Real world solution
Abstraction
Interpretation
Analysis
Model solution
Model
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Math Modeling is Only One Part of Problem Solving

• Define an Opportunity or Problem
• Formulate a Mathematical Model
• Acquire Input Information and Data
• Validate (Calibrate) Model and Data
• Solve and Analyze Solutions Sensitivity
• Implement Solution
• Monitor and Follow-Up

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Example 1.1

• Mortimer Middleman

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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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Mortimer Middleman
The model consists of

• Decision variables (r,q)
• Constraints
• Objective function c(r,q)

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Mortimer Middleman

• Constant-Rate Demand Assumption
• 55
• Inventory periodic sawtooth form
• No lost sales Assumption r ? 55

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Mortimer Middleman
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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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Mortimer Middleman

• d ... weekly demand
• f ... fixed cost of replenishment
• h ... cost per carat per week holding
• s ... cost per carat lost sales
• l ... lead time
• m ... minimum order size

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Mortimer Middleman
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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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Mortimer Middleman

• Economic order quantity (EOQ)

Closed form solution!
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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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MM

• Simulation Table 1.1

Simulation for a fixed reorder point and reorder
quantity
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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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Numerical Search
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Numerical Search
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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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Break