Introduction to Operations Research Lecture Notes PDF

Introduction to Operations Research 1  Terminology The British/Europeans refer to “Operational Research", the Americans/U.S. to “Operations Research" - but both are often shortened to just "OR". Another term used for this field is “...

Introduction to Operations Research 1  Terminology The British/Europeans refer to “Operational Research", the Americans/U.S. to “Operations Research" - but both are often shortened to just "OR". Another term used for this field is “Management Science" ("MS"). In U.S. OR and MS are combined together to form "OR/MS" or "ORMS". Yet other terms sometimes used are “Industrial Engineering" ("IE") and “Decision Science" ("DS"). 2  Introduction Operations Research is an Art and Science It had its early roots in World War II and is flourishing (‫ )ازدهار‬in business and industry with the aid of computer Primary applications areas of Operations Research include forecasting, production scheduling, inventory control, capital budgeting, and transportation. 3  What is Operations Research? Operations The activities carried out(‫ )تم تنفيذها‬in an organization. Research The process of observation and testing characterized (‫ )تتميز‬by the scientific method. Situation, problem statement, model construction, validation, experimentation, candidate solutions. Operations Research is a quantitative approach to decision making based on the scientific method of problem solving. (important) 4  What is Operations Research? Operations Research is the scientific approach to execute decision making, which consists of: – The art of mathematical modeling of complex situations – The science of the development of solution techniques used to solve these models – The ability to effectively communicate the results to the decision maker 5  What is Operations Research? Few other definitions of OR are as follows: OR is concerned with scientifically deciding how to best design and operate man- machine system usually requiring the allocation of scare resources. OR is essentially a collection of mathematical techniques and tools which in conjunction with system approach, are applied to solve practical decision problems of an economic or engineering nature". 6  What is Operations Research? Few other definitions of OR are as follows: "OR utilizes the planned approach (updated scientific method) and an interdisciplinary team in order to represent complex functional relationships as mathematical models for the purpose of providing a quantitative analysis". "OR is a scientific approach to problem solving for executive management"(important) 7  What Do We do 1. OR professionals aim to provide rational bases (‫ )أُسس منطقية‬for decision making by seeking )‫ (السعي‬to understand and structure )‫ (تنظيم‬complex situations and to use this understanding to predict )‫ (توقع‬system behavior and improve system performance. 2. Much of this work is done using analytical and numerical techniques to develop and manipulate mathematical and computer models of organizational systems composed of people, machines, and procedures. 8  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 9  Deterministic vs. Stochastic Models Deterministic models ❑ assume all data are known with certainty Stochastic models ❑ explicitly represent uncertain data via (by) random variables or stochastic processes. Deterministic models ❑ involve optimization Stochastic models ❑ characterize / estimate system performance. 10  History of OR OR is a relatively new discipline. 70 years ago it would have been possible to study mathematics, physics or engineering at university it would not have been possible to study OR. It was really only in the late 1930's that operations research began in a systematic way. 11 1890 1900 1910 1920 Frederick Taylor Henry Gannt F. W. Harris William Shewart Scientific [Project Scheduling] [Inventory Theory] [Control Charts] Management Andrey A. Markov E. K. Erlang H.Dodge – H.Roming [Industrial [Markov Processes] [Queuing Theory] [Quality Theory] Engineering] Assignment [Networks] 1960 1950 1940 1930 John D.C. Litle H.Kuhn - A.Tucker World War 2 Jon Von Neuman – [Queuing Theory] [Non-Linear Prog.] George Dantzig Oscar Morgenstern Simscript - GPSS Ralph Gomory [Linear [Game Theory] [Simulation] [Integer Prog.] Programming] PERT/CPM First Computer Richard Bellman [Dynamic Prog.] ORSA and TIMS 1970 1980 1990 2006 Microcomputer H. Karmarkar Spreadsheet You are here [Linear Prog.] Packages Personal computer INFORMS OR/MS Softwares 12  Scope of Operations Research National Planning and Budgeting OR is used for the preparation, Plans, annual budgets, forecasting of income Defence Services Basically, formulation of OR started from USA army, so it has wide application in the areas such as: development of new technology. ▪ Industrial Establishment and Private Sector units ▪ Research and development and Engineering ▪ Business Management and competition ▪ Agriculture and Irrigation ▪ Education and Training ▪ Transportation ▪ Home Management and Budgeting 13 Problem Solving and Decision Making 7 Steps of Problem Solving (First 5 steps are the process of decision making) – Identify and define the problem. – Determine the set of alternative solutions. – Determine the criteria for evaluating the alternatives. – Evaluate the alternatives. – Choose an alternative. --------------------------------------------------------------- – Implement the chosen alternative. – Evaluate the results. 14