## 3 Specialisation
### Determining the Specialisation of Tasks  
First of all, it is necessary to define a measure of specialisation to classify the organisations, the members into an organisation and the tasks that they perform. In [71] the specialisation of tasks is defined as the number of different tasks performed by a worker and the frequency with which they are repeated, taking into account the decision-making ability of that job for self-management. Tasks specialisation, in turn, is divided into vertical and horizontal tasks specialisation. Horizontal specialisation can be defined as the number of tasks to be performed by a particular job and its main objective is the increase in productivity. This specialisation is considered high when the tasks are repetitive and simple, and low when it is necessary to perform non repetitive tasks. This specialisation regulates the extent of the job. On the other hand, vertical specialisation refers to the differentiation between the planning of the tasks and its control and execution, that is to say, if there is a hierarchy that plans and controls these tasks. The vertical specialisation is high when the worker only performs tasks that have been planned by someone else, and it is low when the tasks to be executed have not been planned by someone else. Both types of specialisation are necessary and they are closely related, since a job in which there is a high degree of horizontal specialisation also requires a high degree of vertical specialisation, because the person which performs a task may lose sight of the global objectives. Therefore, another person with a global vision must plan, organise and control such work [71]. The degree of specialisation of tasks in a specific job, \(E_{T}\), is defined in [72] by Equation (9),  
Figure 4: The firefly \(i\) moves towards the neighbours brighter than it (fireflies 2, 3 and 7 in this example). where \(N_{T}\) is the number of tasks performed by each person in that job. Taking into account that in this case we are measuring the tasks that are performed in a single job position, we have \(P=1\). However, it is possible that in a work team (considered as a unit) several jobs are developed, in which case \(P\) would take values other than \(1\). \[E_{T}=\frac{P}{N_{T}} \tag{9}\]  
If \(E_{TH}\) is the degree of specialisation of horizontal tasks, the relationship between \(E_{TH}\) and \(E_{T}\) is given by Equation (10). \[E_{TH}(E_{T})=\left\{ \begin{array}{ll}\text{if }E_{T}\geq 0.2&E_{TH}\text{ is very high}\\ \text{if }0.2>E_{T}\geq 0.1&E_{TH}\text{ is high}\\ \text{if }0.1>E_{T}\geq 0.05&E_{TH}\text{ is low}\\ \text{if }E_{T}<0.05&E_{TH}\text{ is very low}\end{array} \right. \tag{10}\]  
The degree of vertical specialisation in a given job, \(E_{TV}\), is computed by Equation (11), where \(N_{TP}\) is the number of tasks that a person performs, which have been planned and controlled by another person. \(N_{TP}\) must be in \((0,N_{T}]\); if \(N_{TP}=0\), there is no specialisation. \[E_{TV}=\frac{P}{N_{TP}} \tag{11}\]  
The relationship between \(E_{TV}\) and \(E_{T}\) is given by Equation (12). Taking into account that the vertical task specialisation measures the proportion of tasks that are planned externally on a job, this implies that this type of specialisation increases as the number of tasks planned externally approaches the total number of tasks. Therefore, the maximum is obtained when all the tasks performed in a job are externally planned. \[E_{TV}(E_{T})=\left\{ \begin{array}{ll}\text{if }E_{TV}\simeq E_{T}&E_{TV} \text{ is very high}\\ \text{if }E_{TV}>E_{T}&E_{TV}\text{ is high}\\ \text{if }E_{TV}\gg E_{T}&E_{TV}\text{ is low}\end{array} \right. \tag{12}\]  
The thresholds established are part of an observation process in the industrial environment, as well as the results presented in [73; 74; 75]. These investigations measure the dispersion in a job and the variation of the different roles affected in work environments.