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Planning with limiting factors

Shadow prices and slack

5.1 Slack

When discussing constraints, slack is the amount by which a resource
is under-utilised, i.e. slack occurs when the maximum availability of a
resource is not used. Graphically speaking, it will occur when the
optimum point does not fall on a given resource line.

 The optimal solution will typically occur where two ("critical") constraint lines
cross. There will be no slack for these constraints/resources as they will be fully
utilised.

 For other constraint lines, the fact that the optimal solution is not on these lines
means that the resources are not fully utilised, so there will be slack.

Slack is important for two reasons

 For critical constraints (zero slack), then gaining additional units of these scarce
resources will allow the optimal solution to be improved (e.g. higher contribution
earned). Similarly if another department wants these resources then it will result
in lower contribution.

 For non-critical constraints, gaining or losing a small number of units of the
scarce resource will have no impact on the optimal solution.

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