The following section describes the distance from success and search strength algorithm discussed in Chapter 5.

To calculate the quantitative distance between a cluster or geographic unit from the measurement criteria, the following formula is used:

• If the Resident Employed Labour Force is lower than the minimum population, then the distance is defined as:

• If the Resident Employed Labour Force is higher than the target population, then the distance is defined as:

$Distance=\mathrm{m}\mathrm{i}\mathrm{n}\left\{\left(MS-\frac{RW}{REFL}\right),0\right\}+\mathrm{min}\left\{\left(MS-\frac{RW}{WELF}\right),0\right\}$

In the R package, the distance from success is called validity and the following formula is used:

Where W is the number of workers that live in the cluster and SC is the minimum self-containment (between SSC and DSC) of the cluster.

The search strengths between two geographic units, A and B is calculated based on the commuting flows between A to B ${F}_{\left\{a,b\right\}}$ and from B to A the number of workers that live in area A and B ${W}_{\left\{b\right\}}$, and the number of workers that are resident in area A  and B ${R}_{\left\{B\right\}}$.

${Strength=\frac{{F}_{\left\{a,b\right\}}}{{R}_{\left\{a\right\}}}\mathrm{*}\frac{{F}_{\left\{a,b\right\}}}{{W}_{\left\{b\right\}}}+\frac{{F}_{\left\{b,a\right\}}}{{R}_{\left\{b\right\}}}\mathrm{*}\frac{{F}_{\left\{b,a\right\}}}{{W}_{\left\{a\right\}}}}_{}$