Precedence graph

As explained in Optimization Algorithms: AI techniques for design, planning, and control problems

A precedence graph is a directed representation of task dependencies that specifies which tasks must be completed before others can begin.

A precedence graph is a directed representation of task dependencies: each relationship identifies work that must finish before dependent work can begin. It keeps task sequences feasible when assigning work to assembly-line stations. section 6.6

Bike assembly

A frame must be assembled before installing the forks and handlebar. Attaching the wheels depends on completing both the frame and forks. Thus, task 2 precedes tasks 3 and 4, as shown in a precedence diagram. section 6.6

Figure 6.21 A precedence diagram

Inspect the precedence diagram to follow dependency edges between assembly tasks. section 6.6

How Optimization Algorithms: AI techniques for design, planning, and control problems covers it

How deep it goes

Explains dependencies through a bike example and diagram, then applies them within assembly-line balancing problems.

Examples

Uses bike assembly, precedence diagrams, task sequences, and workstation assignments as concrete examples.

What it assumes

Assumes familiarity with tasks and assembly stations while introducing dependency ordering through concrete examples.

What you can do after

Apply it to assign assembly tasks without violating dependency relationships.

How it connects

Connects task dependencies with assembly line balancing, workstations, cycle time, and tabu search.

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Related concepts

• assembly line balancing problemconfigures · An assembly line balancing problem assigns production tasks to workstations while satisfying constraints and optimizing measures such as station count, cycle time, or idle time.

This explainer was generated by Manning's knowledge graph from the text of Optimization Algorithms: AI techniques for design, planning, and control problems. The section links point to the parts of the book it draws on.