MATHEMATICAL TECHNIQUES – FUNCTIONS?
- Functions, equations and graphs: Linear, quadratic, cubic, exponential and logarithmic
- Application of mathematical functions in solving business problems
MATHEMATICAL TECHNIQUES – MATRIX ALGEBRA?
- Types and operations (addition, subtraction, multiplication, transposition and inversion)
- Application of matrices: statistical modelling, Markov analysis, inputoutput analysis and general applications
Application of matrices: statistical modelling, Markov analysis, inputoutput analysis and general applications
Application of mathematical functions in solving business problems
CALCULUS – DIFFERENTIATION?
- Rules of differentiation (general rule, chain, product, quotient)
- Differentiation of exponential and logarithmic functions
- Higher order derivatives: turning points (maxima and minima)
- Ordinary derivatives and their applications
- Partial derivatives and their applications
- Constrained optimisation; lagrangian multiplier
Rules of differentiation (general rule, chain, product, quotient)
Differentiation of exponential and logarithmic functions
Higher order derivatives: turning points (maxima and minima)
Ordinary derivatives and their applications
Partial derivatives and their applications
Constrained optimisation; lagrangian multiplier
CALCULUS INTEGRATION?
- Rules of integration
- Applications of integration to business problems
Rules of integration
Applications of integration to business problems
PROBABILITY-SET THEORY?
- Types of sets
- Set description: enumeration and descriptive properties of sets
- Operations of sets: union, intersection, complement and difference
- Venn diagrams
Types of sets
Set description: enumeration and descriptive properties of sets
Operations of sets: union, intersection, complement and difference
Venn diagrams
PROBABILITY THEORY?
- Definitions: event, outcome, experiment, sample space
- Types of events: elementary, compound, dependent, independent, mutually exclusive, exhaustive, mutually inclusive
- Laws of probability: additive and multiplicative rules
- Baye’s Theorem
- Probability trees
- Expected value, variance, standard deviation and coefficient of variation using frequency and probability
Definitions: event, outcome, experiment, sample space
Types of events: elementary, compound, dependent, independent, mutually exclusive, exhaustive, mutually inclusive
Laws of probability: additive and multiplicative rules
Baye’s Theorem
Probability trees
Expected value, variance, standard deviation and coefficient of variation using frequency and probability
PROBABILITY DISTRIBUTION?
- Discrete and continuous probability distributions (uniform, normal, binomial, poisson and exponential)
- Application of probability to business problems
Discrete and continuous probability distributions (uniform, normal, binomial, poisson and exponential)
Application of probability to business problems
HYPOTHESIS TESTING AND ESTIMATION?
- Hypothesis tests on the mean (when population standard deviation is unknown)
- Hypothesis tests on proportions
- Hypothesis tests on the difference between means (independent samples)
- Hypothesis tests on the difference between means (matched pairs)
- Hypothesis tests on the difference between two proportions
Hypothesis tests on the mean (when population standard deviation is unknown)
Hypothesis tests on proportions
Hypothesis tests on the difference between means (independent samples)
Hypothesis tests on the difference between means (matched pairs)
Hypothesis tests on the difference between two proportions
CORRELATION AND REGRESSION ANALYSIS?
- Scatter diagrams
- Measures of correlation –product moment and rank correlation coefficients (Pearson and Spearman)
- Regression analysis
- Simple and multiple linear regression analysis
- Assumptions of linear regression analysis
- Coefficient of determination, standard error of the estimate, standard error of the slope, t and F statistics
- Computer output of linear regression
- T-ratios and confidence interval of the coefficients
- Analysis of Variances (ANOVA)
Scatter diagrams
Measures of correlation –product moment and rank correlation coefficients (Pearson and Spearman)
Regression analysis
Simple and multiple linear regression analysis
Assumptions of linear regression analysis
Coefficient of determination, standard error of the estimate, standard error of the slope, t and F statistics
Computer output of linear regression
T-ratios and confidence interval of the coefficients
Analysis of Variances (ANOVA)
TIME SERIES?
- Definition of time series
- Components of time series (circular, seasonal, cyclical, irregular/ random, trend)
- Application of time series
- Methods of fitting trend: free hand, semi-averages, moving averages, least squares methods
- Models - additive and multiplicative models
- Measurement of seasonal variation using additive and multiplicative models
- Forecasting time series value using moving averages, ordinary least squares method and exponential smoothing
- Comparison and application of forecasts for different techniques
- Trend projection methods: linear, quadratic and exponential
Definition of time series
Components of time series (circular, seasonal, cyclical, irregular/ random, trend)
Application of time series
Methods of fitting trend: free hand, semi-averages, moving averages, least squares methods
Models – additive and multiplicative models
Measurement of seasonal variation using additive and multiplicative models
Forecasting time series value using moving averages, ordinary least squares method and exponential smoothing
Comparison and application of forecasts for different techniques
Trend projection methods: linear, quadratic and exponential
LINEAR PROGRAMMING?
- Definition of decision variables, objective function and constraints
- Assumptions of linear programming
- Solving linear programming using graphical method
- Solving linear programming using simplex method
- Sensitivity analysis and economic meaning of shadow prices in business situations
- Interpretation of computer assisted solutions
- Transportation and assignment problems
Definition of decision variables, objective function and constraints
Assumptions of linear programming
Solving linear programming using graphical method
Solving linear programming using simplex method
Sensitivity analysis and economic meaning of shadow prices in business situations
Interpretation of computer assisted solutions
Transportation and assignment problems
DECISION THEORY?
- Decision making process
- Decision making environment: deterministic situation (certainty)
- Decision making under risk - expected monetary value, expected opportunity loss, risk using coefficient of variation, expected value of perfect information
- Decision trees - sequential decision, expected value of sample information
- Decision making under uncertainty - maximin, maximax, minimax regret, Hurwicz decision rule, Laplace decision rule
Decision making process
Decision making environment: deterministic situation (certainty)
Decision making under risk – expected monetary value, expected opportunity loss, risk using coefficient of variation, expected value of perfect information
Decision trees – sequential decision, expected value of sample information
Decision making under uncertainty – maximin, maximax, minimax regret, Hurwicz decision rule, Laplace decision rule
GAME THEORY?
- Assumptions of game theory
- Zero sum games
- Pure strategy games (saddle point)
- Mixed strategy games (joint probability approach)
- Dominance, graphical reduction of a game
- Value of the game
- Non zero sum games
- Limitations of game theory
Assumptions of game theory
Zero sum games
Pure strategy games (saddle point)
Mixed strategy games (joint probability approach)
Dominance, graphical reduction of a game
Value of the game
Non-zero sum games
Limitations of game theory
NETWORK PLANNING AND ANALYSIS?
- Basic concepts – network, activity, event
- Activity sequencing and network diagram
- Critical path analysis (CPA)
- Float and its importance
- Crashing of activity/project completion time
- Project evaluation and review technique (PERT)
- Resource scheduling (leveling) and Gantt charts
- Advantages and limitations of CPA and PERT
Basic concepts – network, activity, event
Activity sequencing and network diagram
Critical path analysis (CPA)
Float and its importance
Crashing of activity/project completion time
Project evaluation and review technique (PERT)
Resource scheduling (leveling) and Gantt charts
Advantages and limitations of CPA and PERT
QUEUING THEORY?
- Components/elements of a queue: arrival rate, service rate, departure, customer behaviour, service discipline, finite and infinite queues, traffic intensity
- Elementary single server queuing systems
- Finite capacity queuing systems
- Multiple server queues
Components/elements of a queue: arrival rate, service rate, departure, customer behaviour, service discipline, finite and infinite queues, traffic intensity
Elementary single server queuing systems
Finite capacity queuing systems
Multiple server queues
SIMULATION?
- Types of simulation
- Variables in a simulation model
- Construction of a simulation model
- Monte Carlo simulation
- Random numbers selection
- Simple queuing simulation: single server, single channel “first come first served” (FCFS) model
- Application of simulation models
Types of simulation
Variables in a simulation model
Construction of a simulation model
Monte Carlo simulation
Random numbers selection
Simple queuing simulation: single server, single channel “first come first served” (FCFS) model
Application of simulation models
EMERGING ISSUES AND TRENDS