30 Decision 2

Candidates will be expected to be familiar with the knowledge, skills and understanding implicit in the linear programming section of Decision 1.

 

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

 

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.

 

The ability to cope with negative edge lengths. A stage and state approach may be required in dynamic programming problems.
Application to production planning.  
Finding minimum or maximum path through a network.  
Solving maximin and minimax problems.  
Maximum flow/minimum cut theorem. Problems may require super-sources and sinks, may have upper and lower capacities and may have vertex restrictions.
Labelling procedure. For flow augmentation.
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.
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.
The application of mathematical modelling to situations that relate to the topics covered in this module. Including the interpretation of results in context.