Algorithm 1.

Heuristic approach

1:  Set initial value X0             ⊳ (Initialization)

2:  for $i\in \mathcal{I}\backslash \left\{0\right\}$ do

3:     $X_i=X_{i-1}+\mathcal{F}(X_{i-1},f_{\text{PV}},{\Delta }_t)$             ⊳ (Integration)

4:     if Xi, 3>X3,up: then             ⊳ (Check for violation)

5:        if $i\in \mathcal{T}:$ then             ⊳ (Treatment if allowed)

6:           $X_{i,3}=X_{i,3}-\frac{V_{\text{max}}}{V_{\text{pat}}}·X_{i,3}$

7:        else             ⊳ (Shift treatment)

8:           Find largest $i^{*}\in \mathcal{T}$ with $i^{*}+i_{\text{dwell}}<i$ and

9:           Set i = i*

10:           $X_{i,3}=X_{i,3}-\frac{V_{\text{max}}}{V_{\text{pat}}}·X_{i,3}$