Step 1:

1) Let $t:=1$ ; $x_{g,c_{0g},0}:=\text{initialvalue}$ $\forall g\in \mathcal{G}$ .

2) Obtain the predicted drift trajectories and velocity of vessels and tugboats.

3) Run the BIP model to obtain the optimal positions of patrol tugs.

4) Implement only the first period of the BIP solution.

Step 2:

1) Let $t\mathrm{<mo>\; :\; </mo>}=t+1$ ; $x_{g\mathrm{,}{c}_{0g}\mathrm{,0}}\mathrm{<mo>\; :\; </mo>}=x_{gct-1}$ $\forall g\in \mathcal{C}$ .

2) Update the predicted drift trajectories and velocity of vessels and tugboats. Additionally, update the current number of oil tankers moving along the zone of interest as well as the available number of tugboats. Update the probability of successful hook-up matrix.

3) Run the BIP model to obtain the optimal tugboats policy.

4) Implement the first period of the new BIP solution.

Step 3: Go back to Step 2 or stop if $t=T+1$ .