Introduction to Statistical and Operational Research Methods

Overview

Introduction to statistical software for applying the following topics in Operational Research and Statistical Methods:
Linear Programming: Characteristics of linear programming models, general form. Graphical solution. Simplex method: standard form of linear programming problem, conversion procedures, basic feasible solutions. Simplex algorithm: use of artificial variables.
Decision Theory: Characteristics of a decision problem. Decision making under uncertainty: maximax, maximin, generalised maximin (Hurwicz), minimax regret criteria. Decision making under risk: Bayes criterion, value of perfect information. Decision tree; Bayesian decision analysis.
Random Sampling and Simulation: Random sample from a finite population, from a probability distribution. Use of random number tables. General method for drawing a random sample from a discrete distribution. Drawing a random sample from a continuous distribution: inverse transformation method, exponential distribution. Dynamic simulation techniques: application to queueing problems. Computer aspects: random number generators, sampling from normal distributions.
Initial Data Analysis: Scales of measurement. Discrete and continuous variables. Sample mean, variance, standard deviation, percentile for ungrouped data; boxplot. Frequency table for grouped discrete data: relative frequency, cumulative frequency, bar diagram; sample mean, variance, percentile. Frequency table for grouped continuous data: stem-and-leaf plot, histogram, cumulative percentage frequency plot; sample mean, variance, percentile. Linear transformation. Bivariate data; scatter diagram, sample correlation coefficient.

Learning Objectives

Perform linear programming using computer software.
Utilise decision analysis methods, such as decision trees.
Simulate date and produce random samples.
Calculate descriptive statistics for a given data set identifying the key characteristics and any unusual features.
Summarise data using appropriate graphical and tabular techniques.

Skills

Apply a range of statistical and OR techniques to data using an appropriate method. Computational skills in statistical software to manage and analyse data. Ability to interpret results and add meaning to the analysis. Understanding sampling processes and the appropriate process to undertake.

Assessment

None.