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Smoothing index

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

A smoothing index is a quantitative measure of how uniformly workload is distributed among workstations.

The smoothing index (SI) measures how uniformly workload is distributed among workstations in an assembly line. It helps evaluate whether task assignments create balanced or uneven station workloads. section 6.6

Use SI alongside the main assembly-line balancing decisions:

  • Compare workstation workloads after assigning tasks while respecting cycle time and precedence constraints. section 6.6
  • Use SI to assess solutions produced by tabu search, rather than treating the search procedure itself as the metric. section 6.6

Contrasting workload profiles

One six-task sequence produces five workstation workloads of [3, 3, 3, 3, 3] and SI 0.0. A larger instance produces [42, 44, 20, 45, 34] and SI 12.296340919151518, showing less uniform distribution.

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

How deep it goes
Defines the metric and demonstrates its outputs, but does not provide its mathematical formula.
Examples
Uses equal five-station workloads of three and uneven workloads of 42, 44, 20, 45, and 34.
What it assumes
Assumes familiarity with workstations, task assignment, and assembly-line balancing; does not require advanced optimization background in the examples.
What you can do after
Evaluate assembly-line solutions by comparing workstation workload uniformity and SI values.
How it connects
Connects workload uniformity with assembly line balancing, cycle time, precedence constraints, and tabu search.
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