Networks, scheduling and assignment.
Plan projects with precedence networks and critical paths, then allocate people and resources using assignment models.
Work through the topic
Learn the method, follow the examples, then try the worksheet.
- 01
Precedence tables
Translate task descriptions into immediate-predecessor tables without adding dependencies that the project does not need.
- 02
Directed project networks
Represent a project's dependencies with activity arrows and numbered events, then read the network without confusing arrows and vertices.
- 03
Dummy activities
Use zero-duration dummy arrows to show dependencies correctly in an activity-on-arrow network.
- 04
Forward and backward scans
Calculate earliest event times forwards and latest event times backwards, using max at a merge and min at a split.
- 05
Earliest/latest times
Turn event times into earliest and latest start/finish times for individual activities.
- 06
Critical paths
Find every controlling start-to-finish chain and explain why a critical path is a longest path, not a shortest one.
- 07
Minimum completion time
Interpret the network's earliest finish as a lower bound under stated assumptions, and test how time reductions change that finish.
- 08
Slack and changes to activities
Calculate total float and assess delays or reductions without assuming every allowance can be used independently.
- 09
Assignment cost tables
Read an assignment table, enforce the one-person/one-job constraints and evaluate complete assignments using the original entries.
- 10
Hungarian algorithm
Use row and column reductions, independent zeros and a justified adjustment to solve a minimum assignment.
- 11
Minimum-cost and maximum-profit assignments
Choose the correct optimisation direction and convert a profit problem into a minimum-cost assignment without changing the best pairing.
- 12
Rectangular tables and dummy rows/columns
Balance a rectangular assignment table with meaningful dummy entries and distinguish an idle worker from an uncompleted required job.
- 13
Checking assumptions and interpreting recommendations
Translate a numerical optimum into a defensible recommendation, including resource limits, unavailable pairings and model uncertainty.
Topic review
Revisit the key ideas, then choose a practice paper.