Decision 2

 

Chapter 1 - Critical Path Analysis

Representation of compound projects by activity networks, algorithm to find the critical path(s); cascade (or Gantt) diagrams; resource histograms and resource levelling.

 

Activity-on-node representation will be used for project networks.

Heuristic procedures only are required for resource levelling.

Candidates may be required to comment on the appropriateness of their solution in its context
 

Chapter 2 - Allocation
The Hungarian algorithm.

Including the use of a dummy row or column for unbalanced problems.

The use of an algorithm to establish a maximal matching may be required.

Chapter 3 - Dynamic Programming

The ability to cope with negative edge lengths.

Application to production planning.

Finding minimum or maximum path through a network.

Solving maximin and minimax problems.

A stage and state approach may be required in dynamic programming problems.

Chapter 4 - Network Flows

Maximum flow/minimum cut theorem.


Labelling procedure.

Problems may require super-sources and sinks, may have upper and lower capacities and may have vertex restrictions.

For flow augmentation.

 

Chapter 5 - Linear Programming

The Simplex method and the Simplex tableau.

Candidates will be expected to introduce slack variables, iterate using a tableau and interpret the outcome at each stage.

Chapter 6 - Game Theory for Zero Sum Games

Pay-off matrix, play-safe strategies and saddle points.

Optimal mixed strategies for the graphical method.

Reduction of pay-off matrix using dominance arguments.

Candidates may be required to comment on the appropriateness of their solution in its context

 

Chapter 7 - Mathematical Modelling

The application of mathematical modelling to situations that relate to the topics covered in this module.

 

Including the interpretation of results in context.