Annex B. Methodological algorithms

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

Distances from success

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:

$\mathrm{ }Distance={\sqrt{{(HS-RELF)}^2+{(LP-RELF)}^2}}^{}+{\sqrt{{(HS-WELF)}^2+{(LP-WELF)}^2}}^{}$

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

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

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

$V\left(SC,W\right)=\left[1-\left(1-\frac{{SC}_{min}}{{SC}_{target}}\right)\bullet \max \left(\frac{W_{target}\mathrm{ }-\mathrm{ }W}{W_{target}-\mathrm{ }{W}_{min}},0\right)\right]\bullet \left[\frac{\min (SC,\mathrm{ }{SC}_{target})}{{SC}_{target}}\right]$

$V(SC,W)\ge \mathrm{ }\frac{{SC}_{min}}{{SC}_{target}}$

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.

Search strength

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 $F_{\left\{b,a\right\}}$the number of workers that live in area A $R_{\left\{a\right\}}$and B $W_{\left\{b\right\}}$, and the number of workers that are resident in area A  $W_{\left\{A\right\}}$and B $R_{\left\{B\right\}}$.

${Strength=\frac{F_{\left\{a,b\right\}}}{R_{\left\{a\right\}}}\mathrm{*}\frac{F_{\left\{a,b\right\}}}{W_{\left\{b\right\}}}+\frac{F_{\left\{b,a\right\}}}{R_{\left\{b\right\}}}\mathrm{*}\frac{F_{\left\{b,a\right\}}}{W_{\left\{a\right\}}}}_{}$