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Operations Research 1 für Wirtschaftsinformatiker

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Operations Research 1 für Wirtschaftsinformatiker

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  1. To insert your company logo on this slide • From the Insert Menu • Select “Picture” • Locate your logo file • Click OK • To resize the logo • Click anywhere inside the logo. The boxes that appear outside the logo are known as “resize handles.” • Use these to resize the object. • If you hold down the shift key before using the resize handles, you will maintain the proportions of the object you wish to resize. Operations Research 1für Wirtschaftsinformatiker Josef Haunschmied

  2. Information Josef.Haunschmied@tuwien.ac.at Voice: +43 1 58801 11925/11926 Fax: +43 1 58801 11999 http://www.eos.tuwien.ac.at Argentinierstr. 8 / Inst. 105-4 1040 Vienna

  3. INFORMS, a 12.000 member society representing professionals in the fields of Operations Research and the Management Sciences http://www.informs.org

  4. 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

  5. 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

  6. 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.

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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

  12. 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

  13. 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

  14. 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

  15. Operations Research Zweckmäßiges Vorbereiten, Durchführen, Kontrollieren und Ein- schätzen von Entscheidungen mit Hilfe von mathematische Methoden. Branstetter’s 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.

  16. Terminology • OR Operations Research Operational Research • MS Management Science • OMOperations Management • DS Decision Science

  17. Applications grouped by type of organizational client • Business • Government and Non-Profit • Health Care • Military

  18. Applications grouped by function • Planning, Strategic Decision-Making • Production • Distribution, Logistics, Transportation • Supply Chain Management • Marketing Engineering • Financial Engineering

  19. 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

  20. 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

  21. 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

  22. 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

  23. Operations Research Position in der Wirtschaftswelt

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

  25. 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

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

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

  28. Produktionssystem

  29. OM als eine Funktion innerhalb eines Unternehmens

  30. OM als Funktion

  31. OM als eine Ansammlung von Entscheidungen

  32. Entscheidungen • Strategische • Taktische Decision Making

  33. Typen von Entscheidungen • Operations-Strategie • Prozess • Kapazität, Standort, Layout • Qualität • Operations-Infrastruktur

  34. Prozessentscheidungen • Prozessmanagement • Technologiemanagement • Belegschaftsmanagement

  35. Operations-Infrastruktur • Supply Chain Management • Lagerhaltung • MRP (Material Requirements Planning) • Terminplanung • Projekt Management

  36. Mathematical Programming Problem Solving with Mathematical Models

  37. Operations Research Operations Research deals with decision problems by formulating and analyzing mathematical models – mathematical representations of pertinent problem features.

  38. 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.

  39. OR Process Assessment Real world problem Real world solution Abstraction Interpretation Analysis Model Model solution

  40. 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 Solution’s Sensitivity • Implement Solution • Monitor and Follow-Up

  41. Example 1.1 Mortimer Middleman

  42. 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.

  43. 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.

  44. Mortimer Middleman • Decision variables (r,q) • Constraints • Objective function c(r,q) The model consists of:

  45. Mortimer Middleman Constant-Rate Demand Assumption: 55 Inventory: periodic sawtooth form No lost sales Assumption: r  55

  46. Mortimer Middleman

  47. 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.

  48. 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

  49. Mortimer Middleman

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