# SACE Stage 2 General Mathematics – Discrete Models

5.1 Critical Path Analysis

5.2 Assignment Problems

This topic focuses on finding optimal solutions for problems involving critical path analysis and assignment. In critical path analysis, students determine the shortest time in which a complex task can be completed and identify the critical components of that task. To demonstrate the diversity of discrete models, students also investigate assignment problems and learn the application of the Hungarian algorithm to their solution.

In both subtopics, before being presented with solution algorithms, students attempt to solve problems set in familiar contexts by trial and error so that they can appreciate the nature and complexity of those problems. Once the algorithms have been introduced, new problems are posed in broader contexts so that students understand that, although the calculations are relatively simple, the methods they are learning underpin some powerful techniques.

As part of their study, students investigate the effects of changing the initial conditions or parameters of problems to improve the solutions. For instance, which jobs could be shortened to improve the minimum completion time in a critical path analysis? They also consider the model’s assumptions and whether they preclude a better solution.

The arithmetic computations required for solving the problems presented in this topic can be conducted without electronic technology.

Source – Subject Outline, South Australian Certificate of Education 2023

SACE Stage 2 General Mathematics Courses

SACE Stage 2 General Mathematics Syllabus

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