Operations Research 4 EK 601 4 EK 601

Operations Research 4 EK 601

4 EK 601 - Operations Research Jan Fábry 434 NB fabry@vse. cz http: //nb. vse. cz/~fabry http: //isis. vse. cz ______________________________________ Operations Research Jan Fábry

4 EK 601 - Operations Research Literature Jan Fábry - Management Science. UEP, October 2003. Presentations: http: //nb. vse. cz/~fabry Content 1. 2. 3. 4. 5. 6. 7. Introduction Linear Programming Network Models Inventory Models Waiting Line Models Computer Simulation Multiple Criteria Decision Making ______________________________________ Operations Research Jan Fábry

Operations Research - Introduction Operations Research = Management Science Alternative Names Ø Ø Ø Ø operational research operations analysis quantitative methods systems analysis decision science History of OR/MS Ø World War II Ø End of the 20 th Century ______________________________________ Operations Research Jan Fábry

Operations Research - Introduction Software Ø Ø Ø Lingo (LINDO) MPL for Windows XPRESS (FICO) CPLEX (IBM ILOG) AIMMS AMPL Gurobi NEOS MS Excel (FRONTLINE SOLVERS) SIMPROCESS SIMUL 8 Matlab ______________________________________ Operations Research Jan Fábry

Operations Research - Introduction Definition 1. MS/OR is the application of scientific methods, techniques and tools to problems involving the operations of systems so as to provide those in control of the operations with optimum solutions to the problems. 2. MS/OR is the application of the scientific method to the study of the operations of large, complex organizations or activities. 3. MS/OR is the application of the scientific method to the analysis and solution of managerial decision problems. ______________________________________ Operations Research Jan Fábry

Operations Research - Introduction Definition - summary Ø Application of SCIENTIFIC METHOD Ø Study of LARGE & COMPLEX SYSTEMS Ø Analysis of MANAGERIAL PROBLEMS Ø Finding OPTIMAL SOLUTION Ø Use of MATHEMATICAL MODELS Ø Use of COMPUTERS & SPECIAL SW ______________________________________ Operations Research Jan Fábry

Operations Research - Introduction Modeling Process Real-World Problem Implementation Recognition and Definition of the Problem Interpretation Validation and Sensitivity Analysis of the Model Formulation and Construction of the Mathematical Model Solution of the Model ______________________________________ Operations Research Jan Fábry

Operations Research - Introduction Recognition & Definition of the Problem Ø Ø Ø Processes Restrictions Goal Mathematical Model Ø Variables Ø Constraints (equations, inequalities) Ø Objective function ______________________________________ Operations Research Jan Fábry

Operations Research - Introduction Mathematical Model Reality Model Finding a proper balance between the level of simplification of reality and good representation of reality. Model Ø Deterministic Ø Probabilistic ______________________________________ Operations Research Jan Fábry

Operations Research - Introduction Solution Ø Ø Ø Feasible Optimal Infeasible Model Interpretation Model Validation Sensitivity Analysis Implementation ______________________________________ Operations Research Jan Fábry

Operations Research - Introduction Management Science Techniques Ø Linear Programming linear objective function – min/max q linear constraints q Ø Integer LP, Binary LP, Mixed Integer LP Ø Nonlinear Programming nonlinear objective function and/or q nonlinear constraints q ______________________________________ Operations Research Jan Fábry

Operations Research - Introduction Management Science Techniques Ø Distribution Models special type of LP problems (special structure of model) q transportation problem q assignment problem q ______________________________________ Operations Research Jan Fábry

Operations Research - Introduction Management Science Techniques Ø Multiple Criteria Decision Making multiple criteria q compromise q limited/unlimited number of alternatives q goal programming q ______________________________________ Operations Research Jan Fábry

Operations Research - Introduction Management Science Techniques Ø Network Models network – nodes, arcs q evaluated network q minimal distance, maximal flow etc. q Ø Project Management planning, scheduling & controlling projects q CPM, PERT q ______________________________________ Operations Research Jan Fábry

Operations Research - Introduction Management Science Techniques Ø Inventory Models how much to order? q when to order? q deterministic/probabilistic models q Ø Waiting Line Models (Queuing Models) servers, customers q goal – optimal number of servers q analytical approach, computer simulation q ______________________________________ Operations Research Jan Fábry

Operations Research - Introduction Management Science Techniques Ø Computer Simulation computer experiments with models q complex systems q Ø Games Theory 2 or more decision makers q possible strategies q ______________________________________ Operations Research Jan Fábry