QMT425

COURSE DESCRIPTION

This course covers several quantitative methods including Decision Analysis, Linear Programming, Transportation, Assignment, Project Scheduling: Critical Path Method (CPM), Program Evaluation Review Technique (PERT), Inventory Control and Simulation models. In addition, this course explains how the methods work and how they can be applied and interpreted by the decision-maker. The emphasis is on the application of the methods rather than pure mathematics per say.

COURSE OUTCOMES

Upon completing this course, the students should be able to:

1.  Describe and explain the concepts and the role of quantitative methods in the decision-making process. (C1)

2.  Apply the quantitative techniques in problem-solving. (C2)

3.  Ability to interpret the results and make a good decision. (C3)

SYLLABUS CONTENT

Chapter 1: Introduction to Quantitative Analysis

• Introduction

• What is Quantitative Analysis

• The Quantitative Analysis Approach

Chapter 2: Decision Theory

• The Structure of Decision

• Types of Decision-Making Environments

• Decision Making Under Uncertainty

→ Maximax

→ Maximin

→ Equally likely (Laplace)

→ Criterion of realism (Hurwicz)

→ Minimax

• Decision Making Under Risk

→ Expected Monetary Value (EMV)

→ Expected Opportunity Loss (EOL)

→ Expected Value of Perfect Information (EVPI)

• Decision Tree

→ Solving a multi-stage decision-making problem using a tree diagram

→ Revised probability

→ Expected value of sample information (EVSI)

Chapter 3: Linear Programming

• Requirement of a LP Problem

• Formulating LP Problem

• Graphical Solution to a LP Problem (Two-Variable)

→ Solving maximization problems (Corner point method, Iso-profit line)

→ Solving minimization problems (Corner point method, Iso-cost line)

→ Special cases in LP

• Simplex Method

→ How to set up an initial simplex tableau (maximization and minimization)

→ Simplex solution (solving maximization only)

→ Interpretation of optimal simplex tableau

→ Special Cases in LP

→ Sensitivity Analysis – Shadow Prices

• The Dual in LP

→ Dual-primal relationships

→ Formulating the dual from the primal and vice versa

→ Obtaining the dual’s optimal solution from the primal’s optimal tableau and vice versa

→ Interpretation of the dual

Chapter 4: Transportation and Assignment Model

TRANSPORTATION MODEL

• Minimization Problems

→ Setting up a transportation table

→ Developing an initial solution (North-West, Least Cost Method, VAM)

→ Finding an optimal solution (Stepping Stone Method, MODI Method)

→ Unbalanced transportation problems

→ Degeneracy

→ Alternative optional solutions

• Maximization Problems

ASSIGNMENT MODEL

→ Approach to the assignment model

→ Unbalanced assignment problems

→ Minimization and maximization problems

Chapter 5: Inventory Model

• Importance of Inventory Control

• The Inventory Decision

• The Economic Order Quantity (EOQ) Model, Reorder Point (ROP)

• Quantity Discounts Model

Chapter 6: Project Scheduling  - PERT/CPM

• The Framework of PERT/CPM Analysis

• Network Diagram and Critical Path Method (CPM)

• Total and Free Slacks

• PERT Analysis

• Project Crashing

Chapter 7: Simulation

• The Simulation Process

• Advantages and Disadvantages of Simulation

• Monte Carlo Simulation

→ Simulation model for an inventory policy

→ Simulation model for a queuing problem

→ Other applications