Quantitative Methods Quantitative Methods of of

ManagementManagement

Quantitative Methods of ManagementQuantitative Methods of Management

___________________________________________________________________________ Quantitative Methods of Management Jan Fábry

http://nb.vse.cz/http://nb.vse.cz/~~fabryfabry

fabry@vse.czfabry@vse.cz

Jan FábryJan Fábry

http://is.savs.czhttp://is.savs.cz

___________________________________________________________________________ Quantitative Methods of Management Jan Fábry

ContentContent1.1. IntroductionIntroduction2.2. Linear ProgrammingLinear Programming3.3. Network ModelsNetwork Models4.4. Inventory ModelsInventory Models5.5. Waiting Line ModelsWaiting Line Models6.6. Computer SimulationComputer Simulation7.7. Multiple Criteria Decision MakingMultiple Criteria Decision Making

LiteratureLiterature

Jan Fábry - Management Science. UEP, Jan Fábry - Management Science. UEP, October 2003.October 2003.

Presentations: http://Presentations: http://nb.vse.cz/~fabrynb.vse.cz/~fabry

Quantitative Methods of ManagementQuantitative Methods of Management

Operations Research - IntroductionOperations Research - Introduction

Operations Research = Management ScienceOperations Research = Management Science

Alternative Names Alternative Names operational researchoperational research operations analysisoperations analysis quantitative analysisquantitative analysis quantitative methodsquantitative methods systems analysissystems analysis decision analysisdecision analysis decision sciencedecision science

___________________________________________________________________________ Quantitative Methods of Management Jan Fábry

History of History of OROR//MSMS World War IIWorld War II End of the 20End of the 20thth Century Century

Operations Research - IntroductionOperations Research - Introduction

Lingo (LINDO)Lingo (LINDO) MPL for WindowsMPL for Windows XXPRESS (FICO)PRESS (FICO) CPLEX (IBM ILOGCPLEX (IBM ILOG)) AIMMS AIMMS AMAMPLPL GurobiGurobi NEOSNEOS MS EMS Excel (FRONTLINE xcel (FRONTLINE SOLVERS)SOLVERS) SIMPROCESS SIMPROCESS SIMUL 8SIMUL 8 MatlabMatlab

___________________________________________________________________________ Quantitative Methods of Management Jan Fábry

SoftwareSoftware

Operations Research - IntroductionOperations Research - Introduction

___________________________________________________________________________ Quantitative Methods of Management Jan Fábry

DefinitionDefinition

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 - IntroductionOperations Research - Introduction

___________________________________________________________________________ Quantitative Methods of Management Jan Fábry

DefinitionDefinition - summary Application ofApplication of SCIENTIFIC METHODSCIENTIFIC METHOD

Analysis ofAnalysis of MANAGERIAL PROBLEMSMANAGERIAL PROBLEMS

Study ofStudy of LARGE & COMPLEX SYSTEMSLARGE & COMPLEX SYSTEMS

Finding Finding OPTIMAL SOLUTIONOPTIMAL SOLUTION

UseUse of of MATHEMATICAL MODELSMATHEMATICAL MODELS UseUse of of COMPUTERS COMPUTERS & & SPECIAL SPECIAL SWSW

Operations Research - IntroductionOperations Research - Introduction

___________________________________________________________________________ Quantitative Methods of Management Jan Fábry

Modeling ProcessModeling Process

Real-WorldReal-WorldProblemProblem

Recognition and Recognition and Definition of the Definition of the

ProblemProblem

Formulation and Formulation and Construction of Construction of

the Mathematical the Mathematical ModelModel

SolutionSolutionof the Modelof the Model

InterpretationInterpretationValidation and Validation and

Sensitivity Sensitivity AnalysisAnalysis

of the Modelof the Model

ImplementationImplementation

Operations Research - IntroductionOperations Research - Introduction

___________________________________________________________________________ Quantitative Methods of Management Jan Fábry

Recognition & Definition of the ProblemRecognition & Definition of the Problem

PProcessesrocesses RRestrictions estrictions GoalGoal

Mathematical ModelMathematical Model

VariablesVariables CConstraints (equations, inequalities) onstraints (equations, inequalities) OObjective function bjective function

Operations Research - IntroductionOperations Research - Introduction

___________________________________________________________________________ Quantitative Methods of Management Jan Fábry

Mathematical ModelMathematical Model

Finding a proper balance between the Finding a proper balance between the level of simplification of level of simplification of realityreality and and

good representation of reality.good representation of reality.

RealityReality ModelModel

ModelModel DeterministicDeterministic ProbabilisticProbabilistic

Operations Research - IntroductionOperations Research - Introduction

___________________________________________________________________________ Quantitative Methods of Management Jan Fábry

SolutionSolution

InfeasibleInfeasible

FeasibleFeasible OptimalOptimal

Model InterpretationModel Interpretation

Sensitivity AnalysisSensitivity Analysis

ImplementationImplementation

Model ValidationModel Validation

Operations Research - IntroductionOperations Research - Introduction

___________________________________________________________________________ Quantitative Methods of Management Jan Fábry

Management Science TechniquesManagement Science Techniques

Linear ProgrammingLinear Programming linear objective function – min/maxlinear objective function – min/max linear constraintslinear constraints

Integer LP, BiInteger LP, Binarynary LP, Mixed Integer LP LP, Mixed Integer LP

Nonlinear Programming Nonlinear Programming nonlinear objective functionnonlinear objective function and/or and/or nonlinear constraintsnonlinear constraints

Operations Research - IntroductionOperations Research - Introduction

___________________________________________________________________________ Quantitative Methods of Management Jan Fábry

Management Science TechniquesManagement Science Techniques

special type of LP problems special type of LP problems (special structure of model) (special structure of model) transportation problemtransportation problem assignment problemassignment problem

Distribution Models Distribution Models

Operations Research - IntroductionOperations Research - Introduction

___________________________________________________________________________ Quantitative Methods of Management Jan Fábry

Management Science TechniquesManagement Science Techniques

multiple criteriamultiple criteria compromisecompromise limited/unlimited number of alternativeslimited/unlimited number of alternatives goal programminggoal programming

Multiple Criteria Decision Making Multiple Criteria Decision Making

Operations Research - IntroductionOperations Research - Introduction

___________________________________________________________________________ Quantitative Methods of Management Jan Fábry

Management Science TechniquesManagement Science Techniques

network – nodes, arcsnetwork – nodes, arcs evaluated networkevaluated network minimal distance, maximal flow etc.minimal distance, maximal flow etc.

planning, scheduling & controlling projectsplanning, scheduling & controlling projects CPM, PERTCPM, PERT

Network Models Network Models

Project Management Project Management

Operations Research - IntroductionOperations Research - Introduction

___________________________________________________________________________ Quantitative Methods of Management Jan Fábry

Management Science TechniquesManagement Science Techniques

how much to order?how much to order? when to order?when to order? deterministic/probabilistic modelsdeterministic/probabilistic models

servers, customersservers, customers goal – optimal number of serversgoal – optimal number of servers analytical approach, computer simulationanalytical approach, computer simulation

Inventory Models Inventory Models

Waiting Line Models (Queuing Models) Waiting Line Models (Queuing Models)

Operations Research - IntroductionOperations Research - Introduction

___________________________________________________________________________ Quantitative Methods of Management Jan Fábry

Management Science TechniquesManagement Science Techniques

computer experiments with modelscomputer experiments with models complex systemscomplex systems

Computer Computer Simulation Simulation

2 or more decision makers2 or more decision makers possible strategiespossible strategies

Games TheoryGames Theory