Operations Research: An Introduction PDF

OPERATIONS RESEARCH “OR:THE SCIENCE OF BETTER” “Operations Research is the discipline of applying advanced analytical methods to help make better decisions.” Operations Research: An Introduction Dr. Waqar A...

OPERATIONS RESEARCH “OR:THE SCIENCE OF BETTER” “Operations Research is the discipline of applying advanced analytical methods to help make better decisions.” Operations Research: An Introduction Dr. Waqar Ahmed Khan 1 Recommended Books 3  Contents What is Operations Research (OR)? OR: Problem Solving (Step-by-Step) Approach Model & Its Types OR: Programming Languages & Software 3  Operations Research (OR): An Introduction ▪ The British / Europeans refer to “Operational Research", the Americans 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"). ▪ It is Often considered to be a sub-field of mathematics. 4  What is Operations Research (OR)? ▪ Optimal decision-making in, and modeling of, deterministic and probabilistic systems that originate from real life. These applications, which occur in government, business, engineering, economics, and the natural and social sciences, are largely characterized by the need to allocate limited resources. In these situations, considerable insight can be obtained from scientific analysis, such as that provided by Operations Research. (Hiller–Lieberman). ▪ OR: a new field which started in the late 1930's and has grown and expanded tremendously in the last 30 years TECHNIQUES Stochastic Meta-heuristics Deterministic OR Heuristics OR (OR/MS) o Linear Programming o Queuing Theory o Problem Based o Simulated Annealing o Integer Programming o Decision Theory o Neural Network o Network Analysis o Monte Carlo Markov Chain o Genetic Algorithms o Dynamic Programming o Markov Decision Process o Ant Colony Optimization o Non-linear Programming o Simulation o … o… o … 5  OR: Problem Solving Approach 1. Define problem & gather data Define the Problem ▪ OR teams work in advisory capacity Situation Problem Statement ▪ Determine appropriate objectives from management ▪ Concerned with the entire organization Data ▪ Data gathering 2. Formulate mathematical model Problem ▪ Problem identified with DECISION VARIABLES Statement o How many units to buy/sell... o How much time to spend on a task... ▪ Measure of performance is the OBJECTIVE FUNCTION o What is the goal?; → Usually: Max/Min: profit/cost/time/units o A function of the decision variables Model ▪ Restrictions of values of decision variables set in CONSTRAINTS o Min acceptable profit; Max available resources etc. ▪ PARAMETERS are the constants of the objective function and the constraints 3  OR: Problem Solving Approach… 3. Develop a computer-based procedure for deriving solutions from the model ▪ Mathematical representations are always approximations of the real world Model ▪ Type of model dictates the type of algorithm to use to obtain solution ▪ Models can be: o DETERMINISTIC o STOCHASTIC 4. Testing the Model ▪ Must ‘debug’ the model as with a computer program ▪ Process of testing/improving model is known as model validation 5. Preparing to Apply the Model Solution ▪ Install a system for applying the model ▪ Usually computer-based systems that are provided with up-to-date input 6. Implementation ▪ OR team explains system to management ▪ Develop procedures required to put system into operation Situation ▪ Management trains personnel 3  Operations Research Approach SYSTEM Vs Its MODEL REAL ▪ SIMPLIFICATION MODEL SYSTEM ▪ ABSTRACTION ▪ ASSUMPTIONS 8  Model & Its Types ▪ MODEL: A model is a representation of the structure of a real life system. – In general, models can be classified as fellows: Iconic models Analogue models Symbolic models ▪ SYMBOLIC MODELS: Symbolic (i.e., algebraic, numerical, logical) models represent the properties of the real life system through the means of symbols, mathematical equations, computer programs and simulation models are also symbolic models. – DETERMINISTIC MODELS: Deterministic models are models which do not contain the element of probability. Deterministic models involve optimization. – STOCHASTIC MODELS: stochastic models are models which contain the element of probability. Stochastic models characterize/estimate system performance. 9  Operations Research: Topics o Deterministic models: o Linear Programming (LP) o Integer Programming (IP) o Dynamic Programming (DP) o Network Programming (NP) o Non-Linear Programming (NLP) o Goal Programming (GP) o Programming: planning of activities o Stochastic models: o Stochastic Programming o Markov chain o Monte Carlo Markov Chain o Queuing theory o Markov decision processes, and simulation 10  OR: Programming Languages & Software ▪ Optimization Software o CPlex o Gurabi o AIMMS o Matlab o Lingo o R with Optimization packages (LpSolve, ROI etc.) o Excel Solver o Python with Optimization Libraries (PuLP, PyLPSolve etc.) ▪ Simulation Software o Arena o Simlu8 o Simio o Flexsim, etc. ▪ Computer Programming Languages o C++ o Java 11 o Python etc. QUESTIONS 12