4. Model Formulation

4.2. Decision Variables

The used decision variables can be described as follows:

\(x_{i j k l}= \begin{cases}1, & \text { if employee } i \text { of category } j \\ & \text { is working in shift } k \text { on day } l \\ 0, & \text { otherwise. }\end{cases}\)

\(D_{i j w}\) : the number of overtime shifts of employee \(i\) of category \(j\) in week \(w\), \(R_{i j}\) : the number of days where the employee \(i\) of category \(j\) worked and normally he does not want to work,

\(y_{i w}= \begin{cases}1, & \text { if employee } i \text { is working external } \\ & \text { shift during the week } w \\ 0, & \text { otherwise. }\end{cases}\)